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MICHAEL SHORT: And to try
something out a little real,

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I took a detector that you all
have, as well, my cell phone.

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And this morning I
went down with EHS

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to one of the very
radioactive cobalt-60 sources,

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a 10 millicurie source.

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If you note, the source that
we were playing around here

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was one microcurie, so this is
a 10,000 times stronger source.

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00:00:44,910 --> 00:00:48,780
It was actually able to show the
difference between a background

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00:00:48,780 --> 00:00:50,070
count of my phone.

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00:00:50,070 --> 00:00:53,010
You shouldn't see much going
on, except for that one

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00:00:53,010 --> 00:00:56,680
malfunctioning pixel,
because not much is going on.

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And when I put the phone
over the source itself,

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00:01:01,420 --> 00:01:03,250
things look a little different.

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You guys see all that digital
noise, or snow in the video?

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00:01:08,300 --> 00:01:10,880
Every one of those white
flashes that you see

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00:01:10,880 --> 00:01:14,660
is a gamma interaction with the
semiconductor in the cell phone

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00:01:14,660 --> 00:01:17,160
camera, with one or
more pixels in your CCD,

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00:01:17,160 --> 00:01:19,640
or charged couple device,
or your CMOS detector,

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00:01:19,640 --> 00:01:22,173
whichever one it happens to be.

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00:01:22,173 --> 00:01:23,590
So I thought this
was pretty cool.

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00:01:23,590 --> 00:01:26,605
You can actually use your cell
phone as a radiation detector.

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We're going to understand why,
and what sort of radiation

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00:01:28,980 --> 00:01:31,980
it could detect by virtue of its
size and its composition today.

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00:01:34,890 --> 00:01:37,000
Anyone ever try this before?

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00:01:37,000 --> 00:01:37,677
You have?

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00:01:37,677 --> 00:01:38,302
AUDIENCE: Yeah.

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00:01:38,302 --> 00:01:39,226
MICHAEL SHORT: Cool.

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00:01:39,226 --> 00:01:42,020
AUDIENCE: [INAUDIBLE]

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00:01:42,020 --> 00:01:43,520
MICHAEL SHORT:
Probably more intense

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00:01:43,520 --> 00:01:45,020
than this if you were
making neutrons, right?

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00:01:45,020 --> 00:01:45,860
AUDIENCE: Yeah.

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00:01:45,860 --> 00:01:46,980
MICHAEL SHORT: Awesome.

40
00:01:46,980 --> 00:01:49,990
OK, cool.

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00:01:49,990 --> 00:01:52,240
So let's just first
figure out, well,

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00:01:52,240 --> 00:01:53,770
where is this
radiation coming from?

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00:01:53,770 --> 00:01:55,810
This is the link between
the first part of the course

44
00:01:55,810 --> 00:01:58,030
and what we're going to be
doing over the next month.

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00:01:58,030 --> 00:01:59,780
As we've seen from
the decay diagrams--

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00:01:59,780 --> 00:02:02,290
and I think I've harped on
potassium-40 as an example

47
00:02:02,290 --> 00:02:03,590
for a reason--

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00:02:03,590 --> 00:02:07,450
it can undergo electron
capture or positron release.

49
00:02:07,450 --> 00:02:10,690
And if it undergoes electron
capture by this likely route

50
00:02:10,690 --> 00:02:14,440
it gives off a
1.461 MeV gamma ray

51
00:02:14,440 --> 00:02:16,870
as the only possible
transition here.

52
00:02:16,870 --> 00:02:18,663
It also undergoes
beta decay, which

53
00:02:18,663 --> 00:02:20,830
you don't want to forget
about if you're calculating

54
00:02:20,830 --> 00:02:22,390
the activity of potassium-40.

55
00:02:22,390 --> 00:02:23,890
But today we're
going to be focusing

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00:02:23,890 --> 00:02:26,410
on what does this
gamma ray actually

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00:02:26,410 --> 00:02:28,420
do when it encounters matter?

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00:02:28,420 --> 00:02:31,480
Or what are the possible
things that can happen?

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00:02:31,480 --> 00:02:33,990
I'm going to introduce
them conceptually today,

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00:02:33,990 --> 00:02:36,490
and we're going to go through
the math of the cross sections

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00:02:36,490 --> 00:02:38,470
and the energetics
more tomorrow.

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00:02:38,470 --> 00:02:43,010
So I'm doing a context first,
theory second kind of approach.

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There's three main things
that gamma rays will

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do in matter depending
on their energy

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00:02:48,100 --> 00:02:50,370
and the actual matter itself.

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There is one called the
photoelectric effect,

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where a gamma ray simply ejects
an electron from the nucleus.

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00:02:56,070 --> 00:03:00,810
So let's say we've got
our potassium-40 atom,

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have a bunch of
electron shells--

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I'm not going to draw
all the electrons,

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but I'll draw a few inner
and outer ones here.

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00:03:08,580 --> 00:03:12,090
One of the things that
the gamma ray can do

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is just eject that electron,
have it come firing out.

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00:03:17,250 --> 00:03:20,050
And the energy balance
for that isn't that hard,

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because this gamma has
some energy E-gamma.

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This electron had some
binding energy, E-binding.

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And the kinetic energy, let's
call it t, of the electron

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is simply the gamma ray in minus
the binding energy back out.

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It's just however
much energy it takes

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to remove that electron,
that's what it takes.

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And so you end up
with, if we go back

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to our banana
spectrum, what we call

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a photo peak, or a photoelectric
emission peak, right here.

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If you trace down
this line, it's

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awfully close to
1,469 KeV, Or 1.46--

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what was it?

87
00:04:01,390 --> 00:04:05,020
1.461 MeV.

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00:04:05,020 --> 00:04:07,210
It won't be exactly
at that energy,

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because it does take
a little bit of energy

90
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to remove that electron.

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Anyone have a guess on
what order of magnitude

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that might be?

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00:04:19,690 --> 00:04:20,190
Yeah.

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00:04:20,190 --> 00:04:23,260
KeV all the way down to eV.

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So this photo peak
will typically

96
00:04:24,940 --> 00:04:28,120
be extremely close,
but not exactly equal,

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00:04:28,120 --> 00:04:30,340
to the energy of the
gamma ray coming out.

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00:04:30,340 --> 00:04:32,853
For most detectors that don't
have that good resolution,

99
00:04:32,853 --> 00:04:34,270
you can pretty
much assume they'll

100
00:04:34,270 --> 00:04:37,943
be in the same channel,
or the same energy bin,

101
00:04:37,943 --> 00:04:40,360
because you're detector will
have some sort of resolution.

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00:04:40,360 --> 00:04:44,440
It may have 1,024 or
2,048 channels that

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00:04:44,440 --> 00:04:45,830
span the full energy range.

104
00:04:45,830 --> 00:04:47,830
And you might not be able
to tell the difference

105
00:04:47,830 --> 00:04:50,230
between 1,460 MeV--

106
00:04:50,230 --> 00:04:55,350
or 1.46 MeV-- and
that minus a few eV.

107
00:04:55,350 --> 00:04:57,870
Potassium, in particular, has
quite a small work function.

108
00:04:57,870 --> 00:05:00,482
And we'll get into why
that is in a second.

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00:05:00,482 --> 00:05:01,940
The next thing you
can do is what's

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00:05:01,940 --> 00:05:05,810
called Compton scattering, in
the general case, which means

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00:05:05,810 --> 00:05:07,580
that there is an electron here.

112
00:05:07,580 --> 00:05:11,630
A gamma ray comes
in with E-gamma.

113
00:05:11,630 --> 00:05:15,860
And then it bounces off with
some energy, E-prime-gamma.

114
00:05:15,860 --> 00:05:22,330
And then the electron goes off
with some other kinetic energy.

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00:05:22,330 --> 00:05:24,850
Then the last one is what's
called pair production.

116
00:05:24,850 --> 00:05:27,370
Just like in the
Q equation, if you

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00:05:27,370 --> 00:05:28,930
have anything
related to positrons

118
00:05:28,930 --> 00:05:30,820
you have to first create them.

119
00:05:30,820 --> 00:05:36,250
So pair production doesn't
happen below about 1.022 MeV.

120
00:05:36,250 --> 00:05:38,650
And it happens with
increasing probability

121
00:05:38,650 --> 00:05:40,420
as the energy of
the photon goes up,

122
00:05:40,420 --> 00:05:42,880
kind of like in
radioactive decay.

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00:05:42,880 --> 00:05:44,920
There's a lot of parallels here.

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00:05:44,920 --> 00:05:48,950
Is you can make an
electron-positron pair

125
00:05:48,950 --> 00:05:50,920
at 1.022 MeV.

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00:05:50,920 --> 00:05:53,020
It's just not very likely.

127
00:05:53,020 --> 00:05:55,510
And what we're going
to find out tomorrow

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00:05:55,510 --> 00:05:59,800
is why the most likely
photon effect is shown

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00:05:59,800 --> 00:06:01,810
in these different regions.

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00:06:01,810 --> 00:06:02,770
Anyone have any idea?

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00:06:02,770 --> 00:06:05,410
Why do you think the
photoelectric effect

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00:06:05,410 --> 00:06:10,882
would be most likely at
low energies and high Z?

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00:06:10,882 --> 00:06:12,590
You just have to give
an intuitive guess.

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Yeah, Luke?

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AUDIENCE: Because
the binding energy

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00:06:14,680 --> 00:06:18,010
isn't very large for the
outer electron shells.

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00:06:18,010 --> 00:06:19,940
MICHAEL SHORT: That's right.

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00:06:19,940 --> 00:06:22,970
So that explains
the low energy idea.

139
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So it doesn't take very much.

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In fact, does anyone know
what the minimum energy

141
00:06:27,378 --> 00:06:29,420
you need to make the
photoelectric effect happen?

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00:06:32,860 --> 00:06:35,380
Well, what's a typical
order of magnitude

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for binding energy of the
lowest, or the outermost,

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00:06:38,320 --> 00:06:41,689
electron shell, or the
lowest bound electron?

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00:06:41,689 --> 00:06:43,397
AUDIENCE: Work function?

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00:06:43,397 --> 00:06:44,230
MICHAEL SHORT: Yeah.

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00:06:44,230 --> 00:06:45,563
That's called the work function.

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00:06:45,563 --> 00:06:49,140
Anyone know an order of
magnitude, guess what it is?

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It's in the single eV range.

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In some cases, it can
even be slightly lower.

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And that, we're talking
about visible light.

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So green light,
even yellow light,

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can eject electrons via
the photoelectric effect.

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00:07:03,110 --> 00:07:05,575
And then the reason that
goes more likely with higher

155
00:07:05,575 --> 00:07:06,950
and higher Z,
we'll get into that

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when we look at the different
cross sections of interaction.

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00:07:09,920 --> 00:07:12,890
Pair production is much more
likely at higher energies,

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because at higher
energy you're more

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00:07:14,600 --> 00:07:17,510
likely to create a positron.

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00:07:17,510 --> 00:07:20,510
And in addition, pair
production happens

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when a photon interacts with
either the electron cloud,

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00:07:24,920 --> 00:07:26,102
or the nucleus there.

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00:07:26,102 --> 00:07:27,560
And that gets more
and more likely,

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00:07:27,560 --> 00:07:29,227
let's say, the denser
the electron cloud

165
00:07:29,227 --> 00:07:31,565
is or the higher charge
there is on the nucleus.

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So first, the simplest one,
the photoelectric effect, this

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00:07:37,200 --> 00:07:40,050
is actually what Einstein
won the Nobel Prize for.

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00:07:40,050 --> 00:07:41,580
Not E equals mc
squared, which has

169
00:07:41,580 --> 00:07:44,378
been the bane of our
existence for the last month.

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00:07:44,378 --> 00:07:46,170
That's not what he got
the Nobel Prize for.

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00:07:46,170 --> 00:07:49,240
It was demonstration of
the photoelectric effect,

172
00:07:49,240 --> 00:07:53,010
where if you start firing
photons of an energy times

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00:07:53,010 --> 00:07:54,900
Planck's constant
times its frequency--

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00:07:54,900 --> 00:07:57,900
and in the next page I'll give
you a quick photon math primer,

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00:07:57,900 --> 00:08:00,360
in case you don't know
what those quantities are--

176
00:08:00,360 --> 00:08:02,310
there will be no
photoelectric emission

177
00:08:02,310 --> 00:08:06,420
until you hit that
work function.

178
00:08:06,420 --> 00:08:09,270
Yeah, like Julio was
saying, that lowest

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00:08:09,270 --> 00:08:10,860
bound electron energy.

180
00:08:10,860 --> 00:08:13,310
And then, emission
will simply go up.

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00:08:13,310 --> 00:08:16,680
And so this was demonstrated
by applying a voltage

182
00:08:16,680 --> 00:08:19,470
to two different plates,
two different metal plates,

183
00:08:19,470 --> 00:08:21,870
and then sending in
light via this window

184
00:08:21,870 --> 00:08:25,290
and seeing when the current
actually became non-zero.

185
00:08:25,290 --> 00:08:27,690
So the way you detect
photoelectric emission

186
00:08:27,690 --> 00:08:29,970
is, if you've got electrons
boiling off of one surface

187
00:08:29,970 --> 00:08:32,459
to the other, that's
the movement of charge,

188
00:08:32,459 --> 00:08:34,250
and that's a current.

189
00:08:34,250 --> 00:08:36,980
And so you can measure a
current with an ammeter.

190
00:08:36,980 --> 00:08:38,780
That's-- it actually
is that simple.

191
00:08:38,780 --> 00:08:46,220
But very elegant experiment,
back for the 1910s or 1920s.

192
00:08:46,220 --> 00:08:48,320
And as a quick primer
on photon quantities,

193
00:08:48,320 --> 00:08:50,330
so you know what all of
these different symbols

194
00:08:50,330 --> 00:08:55,220
mean, the photon energy we
give as Planck's constant times

195
00:08:55,220 --> 00:08:56,410
its frequency.

196
00:08:56,410 --> 00:08:59,300
And I gave you Planck's constant
right here, for reference.

197
00:08:59,300 --> 00:09:01,220
I do recommend that you
guys try checking out

198
00:09:01,220 --> 00:09:03,400
all the units to make
sure that they work out.

199
00:09:03,400 --> 00:09:06,320
Because if you ever
forget, is it h times nu,

200
00:09:06,320 --> 00:09:08,150
or is hc over lambda,
you can always

201
00:09:08,150 --> 00:09:10,520
check the units of your
expression to make sure

202
00:09:10,520 --> 00:09:12,250
they come out to an energy.

203
00:09:12,250 --> 00:09:15,800
Which in SI units is what?

204
00:09:15,800 --> 00:09:16,703
AUDIENCE: Joules?

205
00:09:16,703 --> 00:09:17,620
MICHAEL SHORT: Joules.

206
00:09:17,620 --> 00:09:21,160
And then how about in these
sorts of things, the most

207
00:09:21,160 --> 00:09:22,690
reduced SI units?

208
00:09:22,690 --> 00:09:23,787
AUDIENCE: eV?

209
00:09:23,787 --> 00:09:24,745
MICHAEL SHORT: Is what?

210
00:09:24,745 --> 00:09:25,287
AUDIENCE: eV?

211
00:09:25,287 --> 00:09:28,090
MICHAEL SHORT: eV is
another unit of energy

212
00:09:28,090 --> 00:09:30,160
similar to the joule,
like 1.6 times 10

213
00:09:30,160 --> 00:09:31,900
to the minus 19 joules.

214
00:09:31,900 --> 00:09:36,390
But what about in meters,
kg, seconds, other SI units?

215
00:09:36,390 --> 00:09:37,558
[INTERPOSING VOICES]

216
00:09:37,558 --> 00:09:38,350
MICHAEL SHORT: Yep.

217
00:09:38,350 --> 00:09:41,740
Kilogram meters squared
per second squared.

218
00:09:41,740 --> 00:09:42,847
Indeed.

219
00:09:42,847 --> 00:09:44,430
Per meter squared,
per second squared.

220
00:09:44,430 --> 00:09:46,660
Yeah.

221
00:09:46,660 --> 00:09:49,277
So just make sure sure
you remember that,

222
00:09:49,277 --> 00:09:50,985
because if you're just
looking for joules

223
00:09:50,985 --> 00:09:52,730
and you don't remember
what a joule is,

224
00:09:52,730 --> 00:09:54,960
it's going to make unit
balance kind of hard.

225
00:09:54,960 --> 00:09:57,870
And also, we can describe the
momentum, or p, of the photon

226
00:09:57,870 --> 00:10:01,123
as Planck's constant over
lambda, its wavelength.

227
00:10:01,123 --> 00:10:02,790
This is going to get
real important when

228
00:10:02,790 --> 00:10:05,430
I ask you guys to
do a derivation,

229
00:10:05,430 --> 00:10:07,875
much like the q equation one
that we were doing before.

230
00:10:07,875 --> 00:10:10,500
But instead of me just doing it
at the board and you copying it

231
00:10:10,500 --> 00:10:13,620
down, I want you guys to
try working through it.

232
00:10:13,620 --> 00:10:15,870
And it's going to be
another energy and momentum

233
00:10:15,870 --> 00:10:18,780
conservation thing,
just like before.

234
00:10:18,780 --> 00:10:20,640
And this way you know
what the energy is

235
00:10:20,640 --> 00:10:22,182
and you'll know what
the momentum is.

236
00:10:25,450 --> 00:10:26,800
So now onto this work function.

237
00:10:26,800 --> 00:10:28,240
What is it, actually?

238
00:10:28,240 --> 00:10:31,570
There's a great
paper by Michaelson--

239
00:10:31,570 --> 00:10:34,960
I did not look up whether this
is the Michaelson of Michaelson

240
00:10:34,960 --> 00:10:37,900
Interferometry, but I
wouldn't be surprised.

241
00:10:37,900 --> 00:10:39,140
I'm going to check into that.

242
00:10:39,140 --> 00:10:41,290
But I did dig out this
paper that actually

243
00:10:41,290 --> 00:10:44,080
shows the different patterns
in the work functions

244
00:10:44,080 --> 00:10:45,740
of different elements.

245
00:10:45,740 --> 00:10:49,067
So what do you guys notice
in terms of patterns, here?

246
00:10:49,067 --> 00:10:51,400
First of all, which elements
are all the way to the left

247
00:10:51,400 --> 00:10:54,584
or have the lowest
work function?

248
00:10:54,584 --> 00:10:55,417
AUDIENCE: Group one.

249
00:10:55,417 --> 00:10:56,417
MICHAEL SHORT: The what?

250
00:10:56,417 --> 00:10:57,770
AUDIENCE: The group one metals?

251
00:10:57,770 --> 00:10:59,270
MICHAEL SHORT: The
group one metals,

252
00:10:59,270 --> 00:11:00,950
like sodium, lithium, potassium.

253
00:11:00,950 --> 00:11:02,412
Why do you think that is?

254
00:11:02,412 --> 00:11:03,620
AUDIENCE: I mean, they have--

255
00:11:06,620 --> 00:11:08,005
I don't know.

256
00:11:08,005 --> 00:11:09,630
MICHAEL SHORT: They've
got one electron

257
00:11:09,630 --> 00:11:10,672
in their outermost shell.

258
00:11:10,672 --> 00:11:14,330
So it looks like my potassium
picture is not quite accurate.

259
00:11:14,330 --> 00:11:17,420
I'm going to draw another
shell, and put one lone electron

260
00:11:17,420 --> 00:11:19,730
in that for accuracy.

261
00:11:19,730 --> 00:11:21,900
And so that electron
is extremely unbound.

262
00:11:21,900 --> 00:11:23,970
That's the same reason
that these elements are so

263
00:11:23,970 --> 00:11:25,380
chemically reactive.

264
00:11:25,380 --> 00:11:29,980
They want to ditch that electron
to have a filled outer shell.

265
00:11:29,980 --> 00:11:33,210
So you may also expect the
work function of noble gases

266
00:11:33,210 --> 00:11:35,430
to be extremely high.

267
00:11:35,430 --> 00:11:37,170
I don't know if any
are plotted here,

268
00:11:37,170 --> 00:11:40,140
but you do see the next row
over, like barium, strontium,

269
00:11:40,140 --> 00:11:43,650
calcium, magnesium, has a
slightly higher work function.

270
00:11:43,650 --> 00:11:46,050
And as you move this way
through the periodic table,

271
00:11:46,050 --> 00:11:49,710
to the left, until you hit the
transition metal craziness,

272
00:11:49,710 --> 00:11:51,973
it follows a pretty
regular pattern.

273
00:11:51,973 --> 00:11:53,640
And so you can have
a good guess of what

274
00:11:53,640 --> 00:11:57,210
the work function of something
will be depending on it's Z,

275
00:11:57,210 --> 00:11:59,440
and depending on which--

276
00:11:59,440 --> 00:11:59,940
what is it?

277
00:11:59,940 --> 00:12:02,426
Which column it's in
in the periodic table.

278
00:12:02,426 --> 00:12:03,970
Now, can anyone
tell me, why do you

279
00:12:03,970 --> 00:12:10,490
think that work functions tend
to increase with decreasing Z?

280
00:12:10,490 --> 00:12:11,340
Yeah.

281
00:12:11,340 --> 00:12:13,370
AUDIENCE: For smaller Z,
the outermost electron

282
00:12:13,370 --> 00:12:15,963
is closer to the nucleus,
so it's more tightly bound.

283
00:12:15,963 --> 00:12:16,880
MICHAEL SHORT: Indeed.

284
00:12:16,880 --> 00:12:17,930
Yep, exactly.

285
00:12:17,930 --> 00:12:22,250
For the smaller Z, that first or
second shell is a hell of a lot

286
00:12:22,250 --> 00:12:23,660
closer to the nucleus.

287
00:12:23,660 --> 00:12:27,380
Even though it has a lower
total charge in the nucleus,

288
00:12:27,380 --> 00:12:30,060
it's much more tightly
bound, being much closer.

289
00:12:30,060 --> 00:12:33,400
So, like the outermost electron
in caesium is quite far away,

290
00:12:33,400 --> 00:12:36,770
it does not feel as
much coulomb attraction.

291
00:12:36,770 --> 00:12:39,640
Yeah, good point.

292
00:12:39,640 --> 00:12:41,013
So now onto Compton scattering.

293
00:12:41,013 --> 00:12:42,430
I'd say though the
most difficult,

294
00:12:42,430 --> 00:12:45,430
conceptually, to
understand the energetics.

295
00:12:45,430 --> 00:12:49,430
But the kinematics, or what
actually physically happens,

296
00:12:49,430 --> 00:12:51,280
should look strikingly
similar to what

297
00:12:51,280 --> 00:12:53,390
we've spent the last month on.

298
00:12:53,390 --> 00:12:55,580
Instead of two
particles colliding,

299
00:12:55,580 --> 00:12:59,265
it's a photon colliding
with an electron.

300
00:12:59,265 --> 00:13:00,640
Does anyone remember
what we read

301
00:13:00,640 --> 00:13:03,970
in that first day of class,
with the Chadwick paper?

302
00:13:03,970 --> 00:13:06,460
When he said, hey, maybe
this quantum of energy

303
00:13:06,460 --> 00:13:10,720
is done in a process analogous
to Compton scattering.

304
00:13:10,720 --> 00:13:12,820
Well, this is
Compton scattering.

305
00:13:12,820 --> 00:13:15,220
His analogous process
was maybe an electron

306
00:13:15,220 --> 00:13:17,740
hits a proton and
something happens,

307
00:13:17,740 --> 00:13:20,040
which is not actually
what happens.

308
00:13:20,040 --> 00:13:24,400
And in this case, you have
a photon with energy h nu,

309
00:13:24,400 --> 00:13:26,920
and momentum h nu
over c, striking

310
00:13:26,920 --> 00:13:30,700
an electron with rest
mass m of electron

311
00:13:30,700 --> 00:13:34,120
c squared, or 0.511 MeV.

312
00:13:34,120 --> 00:13:37,410
And afterwards, the photon
leaves at sum angle theta,

313
00:13:37,410 --> 00:13:40,270
and the electron leaves
at sum angle phi.

314
00:13:40,270 --> 00:13:43,630
So I'm going to show you guys
some of the Compton scattering

315
00:13:43,630 --> 00:13:47,960
energetics relations, like
what is the wavelength shift.

316
00:13:47,960 --> 00:13:49,840
Which means that if
this photon comes

317
00:13:49,840 --> 00:13:52,300
in with a certain
wavelength, lambda,

318
00:13:52,300 --> 00:13:54,340
and it gives some of its
energy to the electron,

319
00:13:54,340 --> 00:13:56,875
it comes out at a
different wavelength.

320
00:13:56,875 --> 00:13:58,750
Is it going to be lower
or higher wavelength,

321
00:13:58,750 --> 00:14:00,082
do you think?

322
00:14:00,082 --> 00:14:03,638
[INTERPOSING VOICES]

323
00:14:03,638 --> 00:14:05,180
MICHAEL SHORT: I
heard a bit of both.

324
00:14:05,180 --> 00:14:07,114
So who says lower?

325
00:14:07,114 --> 00:14:08,575
AUDIENCE: Me.

326
00:14:08,575 --> 00:14:10,530
It can be wavelength.

327
00:14:10,530 --> 00:14:12,500
MICHAEL SHORT: So
lower wavelength.

328
00:14:12,500 --> 00:14:15,780
Let's go back to
the photon formula.

329
00:14:15,780 --> 00:14:18,300
Would a lower wavelength
result in a lower or a higher

330
00:14:18,300 --> 00:14:20,004
photon energy?

331
00:14:20,004 --> 00:14:20,870
AUDIENCE: Higher.

332
00:14:20,870 --> 00:14:21,930
MICHAEL SHORT: OK.

333
00:14:21,930 --> 00:14:24,060
So in a Compton
scatter, you start off

334
00:14:24,060 --> 00:14:26,160
with an electron
kind of at rest.

335
00:14:26,160 --> 00:14:28,530
They're definitely
not actually at rest.

336
00:14:28,530 --> 00:14:30,600
But compared to the
energy of the photon,

337
00:14:30,600 --> 00:14:32,100
they're at rest enough.

338
00:14:32,100 --> 00:14:35,100
And then you give some of
that energy to the electron.

339
00:14:35,100 --> 00:14:37,200
That energy has got to go down.

340
00:14:37,200 --> 00:14:40,110
And because these two
quantities here are constants,

341
00:14:40,110 --> 00:14:42,450
the wavelength has
got to increase.

342
00:14:42,450 --> 00:14:44,370
And hopefully this
makes intuitive sense.

343
00:14:44,370 --> 00:14:46,590
The photon does what
we call a redshift.

344
00:14:46,590 --> 00:14:50,170
It shifts closer to the red
end of the visible spectrum

345
00:14:50,170 --> 00:14:51,505
than the blue end.

346
00:14:51,505 --> 00:14:53,400
And as you guys know,
the high energy light

347
00:14:53,400 --> 00:14:56,070
in the visible spectrum hits
towards the ultraviolet.

348
00:14:56,070 --> 00:14:58,650
That's what tans you, or
gives you skin cancer.

349
00:14:58,650 --> 00:15:01,170
Red light, or infrared light,
doesn't do much of anything

350
00:15:01,170 --> 00:15:03,020
at all.

351
00:15:03,020 --> 00:15:05,750
And so this is that on
the extreme scale, where

352
00:15:05,750 --> 00:15:07,670
when we say redshift,
we don't necessarily

353
00:15:07,670 --> 00:15:09,590
mean the photon is visible.

354
00:15:09,590 --> 00:15:12,830
But we do mean that
it's shifting to a lower

355
00:15:12,830 --> 00:15:17,300
energy, or a higher wavelength.

356
00:15:17,300 --> 00:15:21,580
And so this wavelength shift
is always going to be, well,

357
00:15:21,580 --> 00:15:24,665
is it going to be
positive or negative?

358
00:15:37,760 --> 00:15:39,535
AUDIENCE: Positive, right?

359
00:15:39,535 --> 00:15:40,493
MICHAEL SHORT: Is what?

360
00:15:40,493 --> 00:15:40,926
AUDIENCE: Positive?

361
00:15:40,926 --> 00:15:42,843
MICHAEL SHORT: So you
say the wavelength shift

362
00:15:42,843 --> 00:15:45,170
is going to be
positive, which would

363
00:15:45,170 --> 00:15:48,920
mean an increase in wavelength?

364
00:15:48,920 --> 00:15:49,750
There you go.

365
00:15:49,750 --> 00:15:50,260
Yep.

366
00:15:50,260 --> 00:15:53,638
Because it's got to be--
it's got to lose energy.

367
00:15:53,638 --> 00:15:55,930
So I'm not going to go through
the derivation of these,

368
00:15:55,930 --> 00:15:58,138
because I want you guys to
go through the derivation.

369
00:15:58,138 --> 00:16:00,340
But we're going to do it
in the exact same way,

370
00:16:00,340 --> 00:16:02,620
and I'll help kind
of kick you off.

371
00:16:02,620 --> 00:16:06,560
Where, in this case, what
are the three quantities

372
00:16:06,560 --> 00:16:09,216
we can conserve in every
physics, everywhere?

373
00:16:09,216 --> 00:16:11,070
AUDIENCE: Mass,
energy, and momentum?

374
00:16:11,070 --> 00:16:12,820
MICHAEL SHORT: Mass,
energy, and momentum.

375
00:16:12,820 --> 00:16:14,903
The trick here is, what
is the mass of the photon?

376
00:16:18,030 --> 00:16:19,480
Massless.

377
00:16:19,480 --> 00:16:22,260
So we've got energy
and momentum.

378
00:16:22,260 --> 00:16:25,380
And we've got, let's say, some
wavelength shift to determine,

379
00:16:25,380 --> 00:16:27,290
which is some change in energy.

380
00:16:27,290 --> 00:16:29,370
And we've got two
angles to deal with.

381
00:16:29,370 --> 00:16:30,940
That's three unknowns.

382
00:16:30,940 --> 00:16:32,640
We need three equations.

383
00:16:32,640 --> 00:16:34,980
So we know that our
initial energy coming

384
00:16:34,980 --> 00:16:40,650
in is going to be h nu
plus approximately 0

385
00:16:40,650 --> 00:16:46,860
becomes h nu bar, and the
kinetic energy of the electron.

386
00:16:46,860 --> 00:16:49,280
So that's our energy
conservation relation.

387
00:16:49,280 --> 00:16:51,030
And then what do we
do about the momentum?

388
00:16:57,050 --> 00:16:59,836
What do we do last time?

389
00:16:59,836 --> 00:17:01,260
AUDIENCE: Split it into x and y.

390
00:17:01,260 --> 00:17:02,218
MICHAEL SHORT: Exactly.

391
00:17:02,218 --> 00:17:04,200
Split it up into
x and y momentum.

392
00:17:04,200 --> 00:17:06,150
So the x momentum
of the photon--

393
00:17:06,150 --> 00:17:07,710
so I'll just label
this as energy--

394
00:17:10,910 --> 00:17:18,290
put the x momentum of the
photon is h nu over c.

395
00:17:18,290 --> 00:17:22,250
And there was no x momentum
of the electron to begin with.

396
00:17:22,250 --> 00:17:26,240
So then we're going to say
this has outgoing momentum h

397
00:17:26,240 --> 00:17:33,090
nu prime over c times
cosine theta plus whatever

398
00:17:33,090 --> 00:17:42,190
the electron momentum is, let's
say m electron v, or root 2 m

399
00:17:42,190 --> 00:17:48,818
electron, T
electron, cosine phi.

400
00:17:48,818 --> 00:17:50,235
And then how about
the y momentum?

401
00:17:55,230 --> 00:17:58,375
What's the y momentum of
the system at the beginning?

402
00:17:58,375 --> 00:17:59,000
AUDIENCE: Zero?

403
00:17:59,000 --> 00:18:00,060
MICHAEL SHORT: Yep.

404
00:18:00,060 --> 00:18:03,330
Nothing for the photon,
nothing for the electron.

405
00:18:03,330 --> 00:18:10,520
And at the end we've got h
nu over c sine theta minus,

406
00:18:10,520 --> 00:18:16,450
because it's in the negative
y direction, momentum

407
00:18:16,450 --> 00:18:20,918
of the electron sine phi.

408
00:18:20,918 --> 00:18:22,710
I'm going to stop my
part of the derivation

409
00:18:22,710 --> 00:18:24,660
there, because I don't want to
steal away your whole homework

410
00:18:24,660 --> 00:18:25,470
problem.

411
00:18:25,470 --> 00:18:28,170
But you're going to start it
out exactly in the same way

412
00:18:28,170 --> 00:18:32,250
as we were doing kinematics
of two particle collisions.

413
00:18:32,250 --> 00:18:34,200
Because what is a
particle, but a wave?

414
00:18:34,200 --> 00:18:35,587
They're all the same thing.

415
00:18:35,587 --> 00:18:36,420
It's modern physics.

416
00:18:39,470 --> 00:18:41,700
And then-- here's an
interesting bit, here--

417
00:18:41,700 --> 00:18:44,340
this maximum wavelength
shift, if you want

418
00:18:44,340 --> 00:18:46,090
to figure out what is the--

419
00:18:46,090 --> 00:18:46,590
well, look.

420
00:18:46,590 --> 00:18:49,230
Let's say, we call it
the Compton wavelength.

421
00:18:49,230 --> 00:18:55,580
So if you were to decide what
is the maximum wavelength shift,

422
00:18:55,580 --> 00:18:58,300
where would that be?

423
00:18:58,300 --> 00:18:59,030
At what angle?

424
00:19:07,607 --> 00:19:10,190
Did you have a question, or did
you say what was the question?

425
00:19:10,190 --> 00:19:11,150
AUDIENCE: Yeah.

426
00:19:11,150 --> 00:19:12,340
MICHAEL SHORT: Oh, OK.

427
00:19:12,340 --> 00:19:13,587
Is what?

428
00:19:13,587 --> 00:19:14,420
AUDIENCE: Pi over 2.

429
00:19:14,420 --> 00:19:16,045
MICHAEL SHORT: Is
that angle pi over 2?

430
00:19:16,045 --> 00:19:20,010
Because at that point cosine
of pi over 2 equals zero.

431
00:19:20,010 --> 00:19:20,510
Yep.

432
00:19:20,510 --> 00:19:22,730
And so then you get
this interesting result.

433
00:19:22,730 --> 00:19:25,010
No matter what the incoming
energy of the photon

434
00:19:25,010 --> 00:19:30,518
is, you get this
0.238 MeV shift.

435
00:19:30,518 --> 00:19:32,810
And that's actually going to
help explain, to jump back

436
00:19:32,810 --> 00:19:38,630
to our banana spectrum, what the
distance is between our photo

437
00:19:38,630 --> 00:19:39,590
peak--

438
00:19:39,590 --> 00:19:41,540
which is our
photoelectric peak, which

439
00:19:41,540 --> 00:19:44,900
is pretty close to the
energy of the photon--

440
00:19:44,900 --> 00:19:49,160
and this part right here,
which we call the Compton edge.

441
00:19:49,160 --> 00:19:53,870
Which would mean the
maximum scattered energy

442
00:19:53,870 --> 00:19:56,170
of that photon, in this case.

443
00:19:56,170 --> 00:19:57,410
Or no, I'm sorry.

444
00:19:57,410 --> 00:20:01,290
That would be the maximum
energy imparted to the electron.

445
00:20:01,290 --> 00:20:03,360
Almost misspoke there.

446
00:20:03,360 --> 00:20:05,640
And no matter what this
energy of the photon

447
00:20:05,640 --> 00:20:11,610
is, that distance right there,
that's the Compton wavelength.

448
00:20:11,610 --> 00:20:14,130
Interesting quirk
of physics, huh?

449
00:20:14,130 --> 00:20:15,630
Because in the end,
all that matters

450
00:20:15,630 --> 00:20:18,088
is if the angle's all the same,
everything else cancels out

451
00:20:18,088 --> 00:20:20,146
and you just get a
bunch of constants.

452
00:20:20,146 --> 00:20:21,330
Let me jump back to there.

453
00:20:24,218 --> 00:20:26,510
So now we'll take another
look at our detector spectrum

454
00:20:26,510 --> 00:20:28,880
and start identifying
some of these peaks.

455
00:20:28,880 --> 00:20:33,410
If you notice, this
0.238 MeV looks just

456
00:20:33,410 --> 00:20:35,245
like what it does on the graph.

457
00:20:35,245 --> 00:20:37,120
This is the kind of cool
thing, like you guys

458
00:20:37,120 --> 00:20:38,912
threw some bananas in
a detector last week.

459
00:20:38,912 --> 00:20:41,710
We got a spectrum
yesterday morning,

460
00:20:41,710 --> 00:20:43,270
and how well-timed it was.

461
00:20:43,270 --> 00:20:46,180
We're actually going to
start explaining it today.

462
00:20:46,180 --> 00:20:49,670
There's a whole lot more going
on in this banana spectrum.

463
00:20:49,670 --> 00:20:51,410
Part of what we'll be
explaining tomorrow

464
00:20:51,410 --> 00:20:56,930
is, why do you get this kind of
bowl shape, this Compton bowl?

465
00:20:56,930 --> 00:20:59,810
And it turns out that there's
a different probability

466
00:20:59,810 --> 00:21:02,150
of scattering at
every different angle,

467
00:21:02,150 --> 00:21:05,900
or what we call a
differential cross-section.

468
00:21:05,900 --> 00:21:12,410
A d theta over d omega.

469
00:21:12,410 --> 00:21:14,000
Because the probability
of that photon

470
00:21:14,000 --> 00:21:17,480
scattering off in any
direction is not equal.

471
00:21:17,480 --> 00:21:20,890
But if you know what direction
the photon scatters off in,

472
00:21:20,890 --> 00:21:23,903
you know what energy it has,
or you know what sort of energy

473
00:21:23,903 --> 00:21:25,570
it gives to the
electron, because that's

474
00:21:25,570 --> 00:21:27,410
a one to one relation.

475
00:21:27,410 --> 00:21:30,530
And that's why you end
up with this very smooth,

476
00:21:30,530 --> 00:21:34,390
almost cosine-ish
looking kind of curve.

477
00:21:34,390 --> 00:21:36,830
You guys will actually get
to derive that yourselves.

478
00:21:41,240 --> 00:21:43,590
So then onto the wavelength
and energy shift.

479
00:21:43,590 --> 00:21:46,740
By looking at the
electron recoil energy

480
00:21:46,740 --> 00:21:48,690
and this wavelength
shift, from that

481
00:21:48,690 --> 00:21:51,210
you can actually get some
sort of an energy shift.

482
00:21:51,210 --> 00:21:56,528
You can arrive at what is the
recoil energy of that electron.

483
00:21:56,528 --> 00:21:59,070
And so here's one of the topics
that's usually hard for folks

484
00:21:59,070 --> 00:22:02,120
to understand, but I want
to stress it right now.

485
00:22:02,120 --> 00:22:06,490
When you send gamma
rays into a detector--

486
00:22:06,490 --> 00:22:09,200
let's draw an
imaginary detector.

487
00:22:09,200 --> 00:22:13,220
In fact, let's draw the real
one that we used in our banana

488
00:22:13,220 --> 00:22:15,110
counting experiment.

489
00:22:15,110 --> 00:22:24,710
So we had these copper walls,
we had our bag of bananas,

490
00:22:24,710 --> 00:22:30,150
and we had our high
purity germanium detector.

491
00:22:30,150 --> 00:22:31,890
Let's say we had a
good shield on top,

492
00:22:31,890 --> 00:22:33,432
and then a good
shield on the bottom.

493
00:22:35,930 --> 00:22:38,240
That right there is
our active detector,

494
00:22:38,240 --> 00:22:43,820
and this banana is sending off
gamma rays into that detector.

495
00:22:43,820 --> 00:22:48,370
The way a detector works is
not by counting the energy

496
00:22:48,370 --> 00:22:49,930
of the gamma ray directly.

497
00:22:49,930 --> 00:22:51,910
It can't actually do that.

498
00:22:51,910 --> 00:22:55,870
In this germanium
detector you've

499
00:22:55,870 --> 00:22:57,740
got a huge voltage
applied across it.

500
00:23:00,700 --> 00:23:02,200
I think what Mike
Ames actually said

501
00:23:02,200 --> 00:23:05,300
was the one we used
was about 2000 volts.

502
00:23:05,300 --> 00:23:08,770
What happens here
is, let's say--

503
00:23:08,770 --> 00:23:11,490
I'll actually need
three colors for this--

504
00:23:11,490 --> 00:23:13,260
let's say a gamma ray comes in--

505
00:23:16,110 --> 00:23:17,450
that's our gamma ray--

506
00:23:17,450 --> 00:23:20,120
and interacts in the detector.

507
00:23:20,120 --> 00:23:23,265
That gamma ray will redshift--
let me get a redder color,

508
00:23:23,265 --> 00:23:25,790
because that'll be like
physically accurate--

509
00:23:25,790 --> 00:23:28,280
that gamma ray is going
to hit an electron,

510
00:23:28,280 --> 00:23:33,920
go off at a different angle,
and redshift, or get lower

511
00:23:33,920 --> 00:23:35,300
in wavelength.

512
00:23:35,300 --> 00:23:42,530
Meanwhile, that electron that
it hit actually goes flying off

513
00:23:42,530 --> 00:23:47,870
and in the other direction,
we're going to call it a hole.

514
00:23:47,870 --> 00:23:51,140
A defect missing one
electron of some sort

515
00:23:51,140 --> 00:23:52,670
in this semiconductor.

516
00:23:52,670 --> 00:23:55,153
Normally if there was
no voltage applied here

517
00:23:55,153 --> 00:23:57,320
these two would just find
each other and annihilate,

518
00:23:57,320 --> 00:23:58,730
and you would have nothing.

519
00:23:58,730 --> 00:24:00,320
So what's to count?

520
00:24:00,320 --> 00:24:02,700
But by applying a
gigantic voltage,

521
00:24:02,700 --> 00:24:05,270
let's say this voltage
was really plus

522
00:24:05,270 --> 00:24:07,430
and this voltage
was really minus,

523
00:24:07,430 --> 00:24:10,400
this electron keeps on
moving and this hole

524
00:24:10,400 --> 00:24:12,770
keeps on moving
to the electrode.

525
00:24:12,770 --> 00:24:15,240
Instead of recombining
in the detector,

526
00:24:15,240 --> 00:24:21,620
they're actually then
sent through where they're

527
00:24:21,620 --> 00:24:27,710
counted in some sort of ammeter
or some sort of energy pulse

528
00:24:27,710 --> 00:24:28,730
counter.

529
00:24:28,730 --> 00:24:30,590
And what we're
actually measuring

530
00:24:30,590 --> 00:24:33,920
is the recoil spectrum
of the electrons

531
00:24:33,920 --> 00:24:35,330
that the photons make.

532
00:24:35,330 --> 00:24:38,090
You're not directly
measuring photon energy,

533
00:24:38,090 --> 00:24:41,060
you're measuring the
electron effects.

534
00:24:41,060 --> 00:24:44,270
Part of that is because
chances are photons

535
00:24:44,270 --> 00:24:46,067
just go through everything.

536
00:24:46,067 --> 00:24:47,900
This is why I wasn't
so worried this morning

537
00:24:47,900 --> 00:24:51,650
standing with my face over a
10 millicurie cobalt source.

538
00:24:51,650 --> 00:24:53,150
Because while I was
getting billions

539
00:24:53,150 --> 00:24:55,423
of gammas per second
flying through my brain,

540
00:24:55,423 --> 00:24:57,590
most of those billions just
flew out the other side.

541
00:24:57,590 --> 00:25:00,660
It's literally in one
ear, out the other.

542
00:25:00,660 --> 00:25:03,120
And so most of these gammas,
if they interact at all,

543
00:25:03,120 --> 00:25:04,710
will escape again.

544
00:25:04,710 --> 00:25:06,390
The electrons, however,
because they're

545
00:25:06,390 --> 00:25:09,960
charged and very low mass,
have a very low range

546
00:25:09,960 --> 00:25:11,200
in the detector.

547
00:25:11,200 --> 00:25:12,630
So chances are
the electrons that

548
00:25:12,630 --> 00:25:14,850
are made are going
to stay there,

549
00:25:14,850 --> 00:25:17,760
unless you happen to make
one, like, right here

550
00:25:17,760 --> 00:25:21,300
at that surface few
atoms, and it escapes.

551
00:25:21,300 --> 00:25:23,160
That almost never happens.

552
00:25:23,160 --> 00:25:24,030
So forget that.

553
00:25:28,920 --> 00:25:31,530
This was, last year, a
huge source of confusion

554
00:25:31,530 --> 00:25:33,630
to say, why are we seeing
some of the other peaks

555
00:25:33,630 --> 00:25:35,700
that I'll be explaining
in five or 10 minutes?

556
00:25:35,700 --> 00:25:41,280
Or, why aren't we
seeing a 0.238 MeV peak?

557
00:25:41,280 --> 00:25:47,110
Because what you're seeing
here is a photon losing

558
00:25:47,110 --> 00:25:50,800
it's energy minus 0.238
MeV in its maximum energy

559
00:25:50,800 --> 00:25:54,550
transfer, which is
given to that electron.

560
00:25:54,550 --> 00:25:56,860
Then what actually happens
next is this electron slams

561
00:25:56,860 --> 00:25:58,360
into a bunch of
other ones, and that

562
00:25:58,360 --> 00:26:02,470
slams into a bunch of other
ones until all the energy

563
00:26:02,470 --> 00:26:04,780
is lost in the detector.

564
00:26:04,780 --> 00:26:11,080
And all of those electrons
get sucked into the electrode

565
00:26:11,080 --> 00:26:13,000
by this very high voltage.

566
00:26:13,000 --> 00:26:16,870
And then, the way you count
the energy of an interaction

567
00:26:16,870 --> 00:26:19,390
is by how many electrons you
get in a certain little amount

568
00:26:19,390 --> 00:26:20,720
of time.

569
00:26:20,720 --> 00:26:23,590
And so that's why, for
example, for the photo peak,

570
00:26:23,590 --> 00:26:25,560
that's the kind of
simplest reaction.

571
00:26:25,560 --> 00:26:28,810
A gamma goes in, a really
high electron comes out,

572
00:26:28,810 --> 00:26:32,260
it smashes into tons of
other electrons imparting

573
00:26:32,260 --> 00:26:34,840
all of its kinetic energy
in the detector, which

574
00:26:34,840 --> 00:26:37,000
is all summed up
in a nanosecond,

575
00:26:37,000 --> 00:26:39,190
or however long we collect for.

576
00:26:39,190 --> 00:26:43,630
And then we say that we saw
an energy blip containing

577
00:26:43,630 --> 00:26:47,350
about 1,460 KeV of energy.

578
00:26:47,350 --> 00:26:49,467
It all came from
that first gamma.

579
00:26:49,467 --> 00:26:51,550
And then it was all given
to that first photo peak

580
00:26:51,550 --> 00:26:54,353
electron, which then slammed
into a whole bunch of others.

581
00:26:54,353 --> 00:26:56,020
And they slammed into
a bunch of others.

582
00:26:56,020 --> 00:26:59,410
And there's this what's called
this ionization cascade, where

583
00:26:59,410 --> 00:27:02,080
a whole bunch of electrons
make a whole bunch more

584
00:27:02,080 --> 00:27:05,200
until all of them
have too little energy

585
00:27:05,200 --> 00:27:06,720
to ionize anything else.

586
00:27:06,720 --> 00:27:08,810
And then they're just collected.

587
00:27:08,810 --> 00:27:12,590
So that's what we mean
by a pulse in a detector.

588
00:27:12,590 --> 00:27:14,840
It's not exactly an
intuitive concept,

589
00:27:14,840 --> 00:27:16,782
because it's not like
the gamma goes in

590
00:27:16,782 --> 00:27:17,990
and we just count its energy.

591
00:27:17,990 --> 00:27:20,790
There's more things that
physically happen in here.

592
00:27:20,790 --> 00:27:24,480
But it's important
for you guys to know,

593
00:27:24,480 --> 00:27:27,030
especially when we start
to look at pair production.

594
00:27:27,030 --> 00:27:29,280
You guys remember some of
this stuff from the positron

595
00:27:29,280 --> 00:27:31,570
annihilation spectroscopy?

596
00:27:31,570 --> 00:27:35,380
Well, the way we actually know
that positron annihilation

597
00:27:35,380 --> 00:27:39,370
spectroscopy, or PAS,
works is by measuring

598
00:27:39,370 --> 00:27:42,630
photons, or their
eventual electron recoil,

599
00:27:42,630 --> 00:27:45,710
that can only be possible
from this process.

600
00:27:45,710 --> 00:27:48,730
So as a quick review, let's
say you had a positron source,

601
00:27:48,730 --> 00:27:53,440
like sodium-22, which naturally
undergoes radioactive decay,

602
00:27:53,440 --> 00:27:57,160
and forms a positron
along with a gamma

603
00:27:57,160 --> 00:28:00,790
ray from a very short
isometric transition, or IT.

604
00:28:00,790 --> 00:28:04,150
Then that positron bounces
around in the material

605
00:28:04,150 --> 00:28:07,060
until it reaches an electron.

606
00:28:07,060 --> 00:28:10,570
And once it hits that electron,
because the positron--

607
00:28:10,570 --> 00:28:14,980
let's see, the rest mass
of the positron is the same

608
00:28:14,980 --> 00:28:22,730
as the rest mass of the
electron, which is 0.511 MeV--

609
00:28:22,730 --> 00:28:24,350
once the two of
these combine, they

610
00:28:24,350 --> 00:28:32,480
annihilate, producing two
511 KeV or 0.511 MeV photons.

611
00:28:32,480 --> 00:28:36,470
And it's those photons at
this exact energy all the time

612
00:28:36,470 --> 00:28:38,850
that really give it away.

613
00:28:38,850 --> 00:28:40,680
Because there's not
many other processes

614
00:28:40,680 --> 00:28:46,360
that produce a huge amount
of exactly that photon.

615
00:28:46,360 --> 00:28:49,180
Now that we've talked a little
bit about momentum and energy

616
00:28:49,180 --> 00:28:51,640
conservation, does
anybody know why

617
00:28:51,640 --> 00:28:53,920
you get what's called a
blueshift or a redshift

618
00:28:53,920 --> 00:28:56,291
in positron annihilation
spectroscopy?

619
00:28:59,365 --> 00:29:00,240
I'll give you a hint.

620
00:29:00,240 --> 00:29:01,920
It goes down to
conserving the same thing

621
00:29:01,920 --> 00:29:03,170
that we're doing all the time.

622
00:29:03,170 --> 00:29:04,586
Yeah, Kristen?

623
00:29:04,586 --> 00:29:06,558
AUDIENCE: I was going to
say, is that something

624
00:29:06,558 --> 00:29:08,833
to do with wavelengths?

625
00:29:08,833 --> 00:29:10,000
MICHAEL SHORT: You're close.

626
00:29:10,000 --> 00:29:11,650
I mean, technically
you're close,

627
00:29:11,650 --> 00:29:14,920
if you treat electrons as
waves, which you totally can.

628
00:29:14,920 --> 00:29:18,670
The electrons themselves
do have a non-zero momentum

629
00:29:18,670 --> 00:29:23,390
as they're flying about in the
atom or around the nucleus.

630
00:29:23,390 --> 00:29:26,920
And when a electron
collides with a positron,

631
00:29:26,920 --> 00:29:29,710
if that electron already
has some momentum associated

632
00:29:29,710 --> 00:29:33,040
with it, then the cell system
of mass is not at rest.

633
00:29:33,040 --> 00:29:35,740
It's moving at some small speed.

634
00:29:35,740 --> 00:29:39,520
So this little minus delta
energy and plus delta energy

635
00:29:39,520 --> 00:29:42,580
accounts for the initial
momentum of the electron, which

636
00:29:42,580 --> 00:29:44,920
means not only can you
tell from the lifetime

637
00:29:44,920 --> 00:29:48,910
how many electron looking
defects there are, but you can

638
00:29:48,910 --> 00:29:52,570
probe electron momentum by
looking at the slight energy

639
00:29:52,570 --> 00:29:56,440
changes as positrons
collide with electrons.

640
00:29:56,440 --> 00:29:58,600
It's a really cool
and powerful technique

641
00:29:58,600 --> 00:30:02,080
that uses only 22.01
concepts to probe matter

642
00:30:02,080 --> 00:30:04,250
at its deepest level.

643
00:30:04,250 --> 00:30:06,640
So what's happening on
the atomic scale is,

644
00:30:06,640 --> 00:30:10,630
let's say a photon
made a positron,

645
00:30:10,630 --> 00:30:14,260
and the positron bounces about
what's called thermalizes,

646
00:30:14,260 --> 00:30:16,510
or just slows down
via collisions,

647
00:30:16,510 --> 00:30:19,570
via other types of collisions
that we'll go into soon,

648
00:30:19,570 --> 00:30:22,540
and then gets trapped in a
defect, which is a relatively

649
00:30:22,540 --> 00:30:23,800
electron-poor place.

650
00:30:23,800 --> 00:30:28,360
But it doesn't mean there's
no electrons, In every space

651
00:30:28,360 --> 00:30:30,130
everywhere, there's
a probability

652
00:30:30,130 --> 00:30:31,590
that there's an electron there.

653
00:30:31,590 --> 00:30:33,310
In a defect not
containing an atom

654
00:30:33,310 --> 00:30:36,290
that probability is
lower, but not zero.

655
00:30:36,290 --> 00:30:39,170
And so by figuring out
how long they last,

656
00:30:39,170 --> 00:30:41,690
and when those 511 KeV
gammas are emitted,

657
00:30:41,690 --> 00:30:45,890
you can tell, let's say,
what size defect that was.

658
00:30:45,890 --> 00:30:49,170
But now let's talk about
what happens to these 511 KeV

659
00:30:49,170 --> 00:30:51,800
gammas.

660
00:30:51,800 --> 00:30:54,860
What evidence do we have
that positron pair production

661
00:30:54,860 --> 00:30:56,152
actually exists?

662
00:30:56,152 --> 00:30:57,860
So before I reveal
the labels, can anyone

663
00:30:57,860 --> 00:31:00,980
tell me what on
this graph suggests

664
00:31:00,980 --> 00:31:03,150
that positrons are happening?

665
00:31:03,150 --> 00:31:05,280
And there's actually two things.

666
00:31:05,280 --> 00:31:06,030
What do you think?

667
00:31:12,710 --> 00:31:13,366
Yeah.

668
00:31:13,366 --> 00:31:14,793
AUDIENCE: There's
a peak 511 KeV.

669
00:31:14,793 --> 00:31:15,960
MICHAEL SHORT: That's right.

670
00:31:15,960 --> 00:31:16,835
That's exactly right.

671
00:31:16,835 --> 00:31:24,980
There's a peak at 511 KeV
that if I trace that up,

672
00:31:24,980 --> 00:31:25,680
I went one over.

673
00:31:25,680 --> 00:31:26,740
Yeah, right there.

674
00:31:26,740 --> 00:31:28,370
511 KeV.

675
00:31:28,370 --> 00:31:30,210
Is it exactly 511 KeV?

676
00:31:33,862 --> 00:31:34,820
What do you guys think?

677
00:31:38,640 --> 00:31:41,210
So forget the fact that
it came from a positron,

678
00:31:41,210 --> 00:31:47,570
let's say a 511 KeV
gamma came in somewhere.

679
00:31:47,570 --> 00:31:52,300
How would it then release
electrons to be counted?

680
00:31:52,300 --> 00:31:55,180
It then undergoes
photoelectric emission.

681
00:31:55,180 --> 00:31:56,730
So the actual
energy of this would

682
00:31:56,730 --> 00:32:01,518
be 511 KeV minus the work
function of the material.

683
00:32:01,518 --> 00:32:03,060
This is one of those
tricky questions

684
00:32:03,060 --> 00:32:05,950
that you might not even
see it on the spectrum,

685
00:32:05,950 --> 00:32:08,920
but I want you to physically
understand what happens here.

686
00:32:08,920 --> 00:32:12,600
It's not like 511 KeV
positron photons magically

687
00:32:12,600 --> 00:32:14,550
get counted at 511 KeV.

688
00:32:14,550 --> 00:32:18,720
They then have to eject
an electron, somehow.

689
00:32:18,720 --> 00:32:21,870
And for those electrons
to be counted,

690
00:32:21,870 --> 00:32:24,570
they have to interact in
exactly the same way as all

691
00:32:24,570 --> 00:32:25,510
the other electrons.

692
00:32:25,510 --> 00:32:27,910
There's no difference.

693
00:32:27,910 --> 00:32:28,530
What else?

694
00:32:28,530 --> 00:32:29,030
Oh, yeah.

695
00:32:29,030 --> 00:32:30,130
Luke, you have a question?

696
00:32:30,130 --> 00:32:32,550
LUKE: So, from the banana.

697
00:32:32,550 --> 00:32:37,690
Is a gamma ray coming from a
banana, and then that gamma

698
00:32:37,690 --> 00:32:40,120
undergoes pair production?

699
00:32:40,120 --> 00:32:44,700
And then the gamma from
the pair production--

700
00:32:44,700 --> 00:32:47,930
I guess, where are the
gammas coming from?

701
00:32:47,930 --> 00:32:49,930
MICHAEL SHORT: That was
my next question to you.

702
00:32:49,930 --> 00:32:52,300
So let's think about
this a little bit.

703
00:32:52,300 --> 00:32:56,800
We'll start off with gammas
being emitted in all directions

704
00:32:56,800 --> 00:32:58,810
from our bag of banana ashes.

705
00:32:58,810 --> 00:33:01,930
Now the question is,
where do these 511 KeV

706
00:33:01,930 --> 00:33:03,790
photons come from?

707
00:33:03,790 --> 00:33:07,480
If the gamma ray interacts
with the detector

708
00:33:07,480 --> 00:33:10,322
by any mechanism
including pair production,

709
00:33:10,322 --> 00:33:12,280
what are the possible
things that could happen?

710
00:33:14,873 --> 00:33:16,290
There's three
different scenarios.

711
00:33:20,510 --> 00:33:24,810
Let's pick a 511 KeV color.

712
00:33:24,810 --> 00:33:28,950
Well first of all, it might
just undergo pair production.

713
00:33:28,950 --> 00:33:31,690
And it'll release
two 511 KeV gammas.

714
00:33:34,820 --> 00:33:37,735
Let's see, those are
our 511 KeV gammas.

715
00:33:37,735 --> 00:33:40,110
And because they're gammas,
and they interact with almost

716
00:33:40,110 --> 00:33:42,890
nothing, they can get out.

717
00:33:42,890 --> 00:33:45,400
So you might end up--

718
00:33:45,400 --> 00:33:48,250
your energy that you
detect in the detector

719
00:33:48,250 --> 00:33:53,710
might be the energy of your
gamma ray minus 2 times

720
00:33:53,710 --> 00:33:55,930
511 MeV.

721
00:33:55,930 --> 00:33:57,880
This is what we refer
to as double escape.

722
00:34:03,340 --> 00:34:06,010
Close the quotes like that.

723
00:34:06,010 --> 00:34:13,350
So if this gamma ray right
here came in at 1,460 KeV,

724
00:34:13,350 --> 00:34:16,320
and the double escape peak--
if it undergoes pair production

725
00:34:16,320 --> 00:34:19,469
in the detector and both of
those 511s elevens escape,

726
00:34:19,469 --> 00:34:21,030
because a lot of them do--

727
00:34:21,030 --> 00:34:23,850
where would you expect
there to be a double escape

728
00:34:23,850 --> 00:34:26,710
peak on this spectrum?

729
00:34:29,698 --> 00:34:34,247
AUDIENCE: Add that minus 11.022.

730
00:34:34,247 --> 00:34:35,080
MICHAEL SHORT: Yeah.

731
00:34:35,080 --> 00:34:36,880
Let's say, add that minus--

732
00:34:36,880 --> 00:34:39,730
so we're at 1,460 minus 1.022.

733
00:34:39,730 --> 00:34:43,420
That comes out to about 450 KeV.

734
00:34:43,420 --> 00:34:49,659
450 KeV right here, not
much going on, is there?

735
00:34:49,659 --> 00:34:52,620
You're not going to see
it in every detector.

736
00:34:52,620 --> 00:34:55,389
Especially the larger
the detector is,

737
00:34:55,389 --> 00:34:59,490
the less likely both of those
photons are going to escape.

738
00:34:59,490 --> 00:35:02,190
So this is where the
concept of detector size

739
00:35:02,190 --> 00:35:04,020
can tell you whether
or not you're

740
00:35:04,020 --> 00:35:07,030
going to see every peak
that's physically happening.

741
00:35:07,030 --> 00:35:09,300
So in this case, the germanium
detector is pretty big,

742
00:35:09,300 --> 00:35:10,830
it's pretty expensive.

743
00:35:10,830 --> 00:35:14,550
So chances are a lot
of those 511 KeVs,

744
00:35:14,550 --> 00:35:18,520
even though they're produced
in pairs, one of them

745
00:35:18,520 --> 00:35:20,080
didn't quite get out.

746
00:35:20,080 --> 00:35:20,870
Yeah, Luke?

747
00:35:20,870 --> 00:35:25,300
LUKE: So, the gamma from the
banana goes into the detector.

748
00:35:25,300 --> 00:35:27,500
And then it produces
pairs, and then

749
00:35:27,500 --> 00:35:30,633
those pairs are annihilated,
and that produces the vibration.

750
00:35:30,633 --> 00:35:31,800
MICHAEL SHORT: That's right.

751
00:35:31,800 --> 00:35:34,330
That's right, why don't we
write that down in steps

752
00:35:34,330 --> 00:35:37,315
for, let's call this pair
production in the detector.

753
00:35:46,340 --> 00:35:52,280
So step one would
be gamma emission.

754
00:35:52,280 --> 00:35:57,185
Step two would be
electron-positron creation.

755
00:36:00,860 --> 00:36:04,810
Step three would
be annihilation.

756
00:36:04,810 --> 00:36:11,330
Annihilation in the detector.

757
00:36:15,250 --> 00:36:18,590
And then step four would
be somewhere between zero

758
00:36:18,590 --> 00:36:24,990
to two photons escape.

759
00:36:31,330 --> 00:36:33,010
So we have, actually,
three scenarios

760
00:36:33,010 --> 00:36:36,880
that could happen here for pair
production inside the detector.

761
00:36:36,880 --> 00:36:38,590
One of them we just described.

762
00:36:38,590 --> 00:36:40,390
Where pair production
happens, you

763
00:36:40,390 --> 00:36:42,550
get annihilation in a
very short time frame,

764
00:36:42,550 --> 00:36:45,850
like tens of picoseconds
or hundreds of picoseconds.

765
00:36:45,850 --> 00:36:47,830
Both the gammas get out.

766
00:36:47,830 --> 00:36:50,620
That would have
produced a 460 KeV

767
00:36:50,620 --> 00:36:53,320
peak, which it might be there.

768
00:36:53,320 --> 00:36:55,540
But I can't tell if that's
a peak or if that's noise.

769
00:36:55,540 --> 00:36:56,773
So we don't really know.

770
00:36:56,773 --> 00:36:58,690
And chances are, the
reason that didn't happen

771
00:36:58,690 --> 00:37:01,080
is because the detector was big.

772
00:37:01,080 --> 00:37:03,130
So our next possibility.

773
00:37:03,130 --> 00:37:06,600
What if one of those photons
gets out and one of them

774
00:37:06,600 --> 00:37:07,560
doesn't?

775
00:37:07,560 --> 00:37:10,290
It then interacts via
Compton scattering,

776
00:37:10,290 --> 00:37:14,970
or photoelectric effect, or
any of the possible mechanisms.

777
00:37:14,970 --> 00:37:18,300
Then you'll end up
with an energy counted

778
00:37:18,300 --> 00:37:24,263
equal to energy of the
gamma minus only one

779
00:37:24,263 --> 00:37:25,430
of those things getting out.

780
00:37:25,430 --> 00:37:26,750
And we call that single escape.

781
00:37:31,200 --> 00:37:33,930
At what energy would that
single escape peak be?

782
00:37:38,580 --> 00:37:39,846
Oh.

783
00:37:39,846 --> 00:37:41,100
AUDIENCE: 511?

784
00:37:41,100 --> 00:37:42,270
MICHAEL SHORT: It would be--

785
00:37:42,270 --> 00:37:48,330
that peak would be at the energy
the gamma 1,460, minus 511 KeV.

786
00:37:48,330 --> 00:37:52,240
So roughly 900 KeV or so.

787
00:37:52,240 --> 00:37:55,820
There we go, there it is.

788
00:37:55,820 --> 00:37:57,320
That's the second
bit of evidence

789
00:37:57,320 --> 00:37:59,480
that there is pair
production going on.

790
00:37:59,480 --> 00:38:02,990
Not only do you have a peak
at 511 KeV, which we have not

791
00:38:02,990 --> 00:38:06,930
explained yet, but you also
have the single escape peak,

792
00:38:06,930 --> 00:38:10,010
which is the energy of
your gamma minus one

793
00:38:10,010 --> 00:38:14,900
escape from a 511 KeV photon.

794
00:38:14,900 --> 00:38:15,400
Yeah?

795
00:38:15,400 --> 00:38:16,940
LUKE: When you mean
escape, do you mean escapes

796
00:38:16,940 --> 00:38:18,770
through the detector,
or what is that?

797
00:38:18,770 --> 00:38:19,562
MICHAEL SHORT: Yes.

798
00:38:19,562 --> 00:38:22,040
I mean-- when I escape, I
mean it escapes the detector

799
00:38:22,040 --> 00:38:23,660
and is no longer counted.

800
00:38:23,660 --> 00:38:25,400
So it might go and
drop somewhere else,

801
00:38:25,400 --> 00:38:28,340
but your detector
doesn't know it.

802
00:38:28,340 --> 00:38:30,860
So what's the third
scenario that could happen?

803
00:38:30,860 --> 00:38:34,370
What if zero of
these photons escape?

804
00:38:34,370 --> 00:38:36,773
What energy will you count?

805
00:38:36,773 --> 00:38:37,690
AUDIENCE: [INAUDIBLE].

806
00:38:37,690 --> 00:38:38,678
MICHAEL SHORT: Exactly.

807
00:38:38,678 --> 00:38:40,220
So all that's going
to happen is it's

808
00:38:40,220 --> 00:38:43,390
going to look like the
photoelectric effect.

809
00:38:43,390 --> 00:38:45,982
In reality, you'll have
slightly, slightly lower

810
00:38:45,982 --> 00:38:47,440
energy, because
you have three work

811
00:38:47,440 --> 00:38:50,380
functions to subtract off from
the three photons doing stuff.

812
00:38:50,380 --> 00:38:52,270
But I would count
that as correct.

813
00:38:52,270 --> 00:38:54,700
It's going to look just like
the photoelectric effect.

814
00:38:54,700 --> 00:38:59,710
First, you get that
energy minus 1.022 MeV.

815
00:38:59,710 --> 00:39:02,500
And then both of
those 511 KeV photons

816
00:39:02,500 --> 00:39:05,710
interact in the
detector by, probably,

817
00:39:05,710 --> 00:39:07,330
photoelectric emission.

818
00:39:07,330 --> 00:39:12,930
And you just get another count
at this channel, right here.

819
00:39:12,930 --> 00:39:15,660
Now the last question
I want to ask you guys,

820
00:39:15,660 --> 00:39:18,060
where did this peak come from?

821
00:39:18,060 --> 00:39:20,490
Under what circumstance
would the detector just

822
00:39:20,490 --> 00:39:21,795
count 511 KeV?

823
00:39:30,885 --> 00:39:31,760
I'll give you a hint.

824
00:39:31,760 --> 00:39:36,818
There's a reason I drew gammas
going off in every direction.

825
00:39:36,818 --> 00:39:39,177
AUDIENCE: So they
don't hit the detector.

826
00:39:39,177 --> 00:39:40,010
MICHAEL SHORT: Yeah.

827
00:39:40,010 --> 00:39:42,170
So most of the gammas
don't hit the detector.

828
00:39:42,170 --> 00:39:47,380
But let's say you had a gamma
that went into anything else,

829
00:39:47,380 --> 00:39:51,606
like the copper shielding, and
it underwent pair production.

830
00:39:54,730 --> 00:39:57,040
And one of those gammas made
it through the detector.

831
00:40:00,340 --> 00:40:03,070
I'm sorry, one of those photons
made it through the detector.

832
00:40:03,070 --> 00:40:05,800
That's actually where these
things are coming from.

833
00:40:05,800 --> 00:40:07,600
Because most of
those gammas are not

834
00:40:07,600 --> 00:40:09,400
heading towards the detector.

835
00:40:09,400 --> 00:40:12,000
This is a very
small, solid angle.

836
00:40:12,000 --> 00:40:13,720
But surrounding the
rest of the detector

837
00:40:13,720 --> 00:40:17,690
is this really dense copper,
and these high energy gammas

838
00:40:17,690 --> 00:40:19,960
in this relatively
high Z material

839
00:40:19,960 --> 00:40:21,910
undergoes a lot of
pair production,

840
00:40:21,910 --> 00:40:26,860
so it's firing out 511 KeV
photons in all directions.

841
00:40:26,860 --> 00:40:28,780
And some of those
enter the detector

842
00:40:28,780 --> 00:40:31,370
when nothing else
enters the detector.

843
00:40:31,370 --> 00:40:36,190
And that's why you get this
511 KeV peak right here.

844
00:40:39,100 --> 00:40:41,530
So we haven't explained
every peak on this graph.

845
00:40:41,530 --> 00:40:44,700
Does anybody have
any ideas where--

846
00:40:44,700 --> 00:40:45,510
what's that about?

847
00:40:45,510 --> 00:40:47,170
Or that?

848
00:40:47,170 --> 00:40:47,785
Or those?

849
00:40:52,930 --> 00:40:54,380
AUDIENCE: Cosmic radiation?

850
00:40:54,380 --> 00:40:55,220
MICHAEL SHORT: Yeah.

851
00:40:55,220 --> 00:40:56,852
Could be cosmic rays.

852
00:40:56,852 --> 00:40:58,310
That's probably
what's contributing

853
00:40:58,310 --> 00:41:00,620
to a lot of the noise,
here, as well as

854
00:41:00,620 --> 00:41:02,720
thermal noise in the detector.

855
00:41:02,720 --> 00:41:04,350
But what else haven't
we accounted for?

856
00:41:04,350 --> 00:41:06,770
Now, to bring this a
little more into reality,

857
00:41:06,770 --> 00:41:08,690
we ran an experiment
where we burned bananas.

858
00:41:08,690 --> 00:41:11,540
We didn't put a potassium-40
certified source in.

859
00:41:11,540 --> 00:41:13,400
We put bananas in.

860
00:41:13,400 --> 00:41:16,198
What else could be going on?

861
00:41:16,198 --> 00:41:17,840
AUDIENCE: Other isotopes?

862
00:41:17,840 --> 00:41:19,090
MICHAEL SHORT: Other isotopes.

863
00:41:19,090 --> 00:41:20,290
That's right.

864
00:41:20,290 --> 00:41:23,110
But you can identify
them quite easily, one,

865
00:41:23,110 --> 00:41:26,140
by checking to see where
you expect the photo peak.

866
00:41:26,140 --> 00:41:29,350
So just from the
decay diagram, you'll

867
00:41:29,350 --> 00:41:32,800
expect to see some interactions
or photoelectric effect

868
00:41:32,800 --> 00:41:35,650
interactions, at these
transition levels.

869
00:41:35,650 --> 00:41:38,020
Luckily, you know they're
not due to potassium,

870
00:41:38,020 --> 00:41:42,060
because potassium has
only got one of them.

871
00:41:42,060 --> 00:41:45,630
In addition, you should see
some very similar features.

872
00:41:45,630 --> 00:41:48,230
So if you have a
photo peak here,

873
00:41:48,230 --> 00:41:52,932
you would expect to see another
Compton edge 0.238 MeV away--

874
00:41:52,932 --> 00:41:54,890
and it's kind of hard to
tell if it's going on,

875
00:41:54,890 --> 00:41:58,060
because that's a rather
weak photo peak--

876
00:41:58,060 --> 00:42:00,850
and you would expect, then,
for the high energy gamma rays

877
00:42:00,850 --> 00:42:04,300
to see another single escape
peak-- maybe right there--

878
00:42:04,300 --> 00:42:09,840
and add to the 511 KeV peak,
because those are all the same.

879
00:42:09,840 --> 00:42:12,710
So when you take the
spectrum of a real thing,

880
00:42:12,710 --> 00:42:15,650
and you have to deconvolute
it, or take it apart

881
00:42:15,650 --> 00:42:18,200
in terms of its
constituent interactions,

882
00:42:18,200 --> 00:42:22,527
it's important to know what all
these possible interactions are

883
00:42:22,527 --> 00:42:24,610
so that you can take them
apart and say, start off

884
00:42:24,610 --> 00:42:26,560
with a photo peak,
which should tell you

885
00:42:26,560 --> 00:42:28,150
what elements are there.

886
00:42:28,150 --> 00:42:30,430
And then you can subtract
off the expected amount

887
00:42:30,430 --> 00:42:32,680
of Compton scattering,
the expected

888
00:42:32,680 --> 00:42:35,050
amount of single
escape peak, and then

889
00:42:35,050 --> 00:42:38,321
see what's left over, what other
isotopes may there be that you

890
00:42:38,321 --> 00:42:39,404
haven't accounted for yet.

891
00:42:42,120 --> 00:42:47,040
The last thing I want us to
try, as a mental exercise,

892
00:42:47,040 --> 00:42:49,910
is to draw two spectra.

893
00:42:49,910 --> 00:42:52,200
Let's say, this will be
energy versus intensity.

894
00:42:58,010 --> 00:43:00,110
And for this I want you
to imagine that, at first,

895
00:43:00,110 --> 00:43:02,383
your detector is very small.

896
00:43:02,383 --> 00:43:04,550
And then I want you to
imagine that your detector is

897
00:43:04,550 --> 00:43:06,860
very large.

898
00:43:06,860 --> 00:43:10,100
And I'm going to keep
this visible so you can

899
00:43:10,100 --> 00:43:11,840
have this as a mental model.

900
00:43:11,840 --> 00:43:16,670
If we had just one
isotope, potassium-40,

901
00:43:16,670 --> 00:43:18,380
what do you think
the spectra would

902
00:43:18,380 --> 00:43:21,140
look like for an
extremely small detector

903
00:43:21,140 --> 00:43:22,910
and for an extremely
large detector?

904
00:43:26,535 --> 00:43:27,410
So where do we start?

905
00:43:31,775 --> 00:43:33,003
AUDIENCE: [INAUDIBLE]

906
00:43:33,003 --> 00:43:34,170
MICHAEL SHORT: That's right.

907
00:43:34,170 --> 00:43:36,270
And will there be any
difference between the two?

908
00:43:38,880 --> 00:43:41,040
Probably not.

909
00:43:41,040 --> 00:43:44,040
So small detector,
maybe a large detector

910
00:43:44,040 --> 00:43:47,330
is going to have a
larger intensity.

911
00:43:47,330 --> 00:43:48,830
But for the same
type of detector,

912
00:43:48,830 --> 00:43:51,930
you're going to have
pretty much the same thing.

913
00:43:51,930 --> 00:43:52,590
What's next?

914
00:43:56,430 --> 00:43:57,870
AUDIENCE: Compton edge?

915
00:43:57,870 --> 00:43:59,200
MICHAEL SHORT: Compton edge.

916
00:43:59,200 --> 00:44:01,480
So there's going
to be some energy

917
00:44:01,480 --> 00:44:03,430
that Compton scattering
is going to start out,

918
00:44:03,430 --> 00:44:07,290
and then it's going
to proceed up, thusly.

919
00:44:07,290 --> 00:44:10,235
Is there going to be any real
effect of the detector size?

920
00:44:14,790 --> 00:44:18,190
Probably not, because as soon
as you release that Compton

921
00:44:18,190 --> 00:44:21,380
electron, that electron slams
into all the other ones,

922
00:44:21,380 --> 00:44:24,100
and nanometers or
microns of material,

923
00:44:24,100 --> 00:44:26,200
and all the energy is collected.

924
00:44:26,200 --> 00:44:29,728
What's the real
difference going to be?

925
00:44:29,728 --> 00:44:31,073
AUDIENCE: The 511 peak?

926
00:44:31,073 --> 00:44:32,240
MICHAEL SHORT: That's right.

927
00:44:32,240 --> 00:44:35,660
So the 511 peak, and the
other associated ones.

928
00:44:35,660 --> 00:44:38,690
So for a really,
really small detector

929
00:44:38,690 --> 00:44:40,550
we have the possibility
for a double escape

930
00:44:40,550 --> 00:44:44,780
peak, a single escape peak,
and just more photo peak.

931
00:44:44,780 --> 00:44:48,180
What's the most likely scenario?

932
00:44:48,180 --> 00:44:49,180
AUDIENCE: Double escape?

933
00:44:49,180 --> 00:44:50,670
MICHAEL SHORT: Double escape.

934
00:44:50,670 --> 00:44:55,570
So if we go down here, let's
say if this difference is

935
00:44:55,570 --> 00:45:02,470
1.022 to MeV, you would expect
a larger double escape peak.

936
00:45:02,470 --> 00:45:07,050
And what would you expect
your single escape peak to be?

937
00:45:07,050 --> 00:45:08,020
AUDIENCE: Smaller?

938
00:45:08,020 --> 00:45:09,562
MICHAEL SHORT:
Significantly smaller.

939
00:45:11,660 --> 00:45:17,300
So let's say this difference
right here is 511 KeV.

940
00:45:17,300 --> 00:45:20,075
How about for a large detector?

941
00:45:20,075 --> 00:45:21,500
AUDIENCE: Opposite.

942
00:45:21,500 --> 00:45:22,950
MICHAEL SHORT:
Quite the opposite.

943
00:45:22,950 --> 00:45:25,490
You might expect a tiny
or even nonexistent

944
00:45:25,490 --> 00:45:29,320
double escape peak, maybe a
larger single escape peak.

945
00:45:29,320 --> 00:45:31,510
But most of the time
you're just going

946
00:45:31,510 --> 00:45:34,810
to add on to your photo peak,
depending on the resolution

947
00:45:34,810 --> 00:45:36,370
of the detector.

948
00:45:36,370 --> 00:45:39,070
Because in this case,
for a small detector,

949
00:45:39,070 --> 00:45:42,160
if you have an interaction
inside that volume chances are

950
00:45:42,160 --> 00:45:44,510
most of those 511s get out.

951
00:45:44,510 --> 00:45:46,010
For a large
detector, chances are

952
00:45:46,010 --> 00:45:49,760
most of them stay in and undergo
their own Compton scattering,

953
00:45:49,760 --> 00:45:51,810
or photo peak reactions.

954
00:45:51,810 --> 00:45:55,340
So let's say that all
these detectors will also

955
00:45:55,340 --> 00:45:58,910
have a 511 KeV.

956
00:45:58,910 --> 00:46:00,140
We'll just mark that off.

957
00:46:05,108 --> 00:46:06,650
Let's just give them
the same height.

958
00:46:10,070 --> 00:46:14,320
What else are we missing,
if this is an ideal scenario

959
00:46:14,320 --> 00:46:15,040
with no noise?

960
00:46:25,010 --> 00:46:29,060
Well what are those five-- what
can those 511 KeV photons do?

961
00:46:35,360 --> 00:46:39,680
Can they make pair
production of their own?

962
00:46:39,680 --> 00:46:40,180
No.

963
00:46:40,180 --> 00:46:41,770
They're not high enough energy.

964
00:46:41,770 --> 00:46:43,840
In fact, they're half
the required energy.

965
00:46:43,840 --> 00:46:46,160
Can they undergo
photoelectric effect?

966
00:46:46,160 --> 00:46:46,690
Sure.

967
00:46:46,690 --> 00:46:49,180
That's probably where
we're getting those 511s.

968
00:46:49,180 --> 00:46:53,210
Can they undergo
Compton scattering?

969
00:46:53,210 --> 00:46:54,320
Why not?

970
00:46:54,320 --> 00:46:56,980
There's no minimum
energy to scatter.

971
00:46:56,980 --> 00:47:04,670
So what you're going to end up
with, then, is 238 KeV away.

972
00:47:04,670 --> 00:47:07,100
You should have
another little Compton

973
00:47:07,100 --> 00:47:15,410
edge at a distance of 238
KeV away from the 511 KeV.

974
00:47:15,410 --> 00:47:18,330
Now in reality, you
probably won't see it

975
00:47:18,330 --> 00:47:20,080
because you're going
to have other X-rays,

976
00:47:20,080 --> 00:47:21,455
you'll have
bremsstrahlung, which

977
00:47:21,455 --> 00:47:23,990
we'll talk about tomorrow, which
is that breaking radiation.

978
00:47:23,990 --> 00:47:25,870
You'll have
background radiation.

979
00:47:25,870 --> 00:47:28,100
And it might be hard to
see, but technically it

980
00:47:28,100 --> 00:47:31,880
should be there, because
any photon of any energy

981
00:47:31,880 --> 00:47:35,830
is going to have that same
sort of Compton edge shape.

982
00:47:35,830 --> 00:47:37,450
The shape changes
just a little bit,

983
00:47:37,450 --> 00:47:39,190
depending on the
energy of the photon,

984
00:47:39,190 --> 00:47:40,940
but you're always
going to have an edge.

985
00:47:40,940 --> 00:47:42,940
You're always going to
have some sort of a bowl.

986
00:47:42,940 --> 00:47:45,190
Just how big the edge
is compared to the bowl,

987
00:47:45,190 --> 00:47:48,350
well, we'll get
to that tomorrow.

988
00:47:48,350 --> 00:47:50,318
So it's a little
after 5 of 5 of.

989
00:47:50,318 --> 00:47:51,860
I think this is a
good place to stop,

990
00:47:51,860 --> 00:47:55,670
because it's the full conceptual
explanation of the ways

991
00:47:55,670 --> 00:47:57,770
that photons can
interact with matter.

992
00:47:57,770 --> 00:48:00,530
So I want to ask you guys if
you have any questions based

993
00:48:00,530 --> 00:48:03,070
on what we've done today?

994
00:48:03,070 --> 00:48:03,660
Yep?

995
00:48:03,660 --> 00:48:06,168
AUDIENCE: So 511 KeV's
the rest mass of electron?

996
00:48:06,168 --> 00:48:06,960
MICHAEL SHORT: Yep.

997
00:48:06,960 --> 00:48:08,418
AUDIENCE: So that's
just the energy

998
00:48:08,418 --> 00:48:10,983
you assume it has when
you have pair production?

999
00:48:10,983 --> 00:48:12,150
MICHAEL SHORT: That's right.

1000
00:48:12,150 --> 00:48:14,580
So the electron and the
positron annihilate,

1001
00:48:14,580 --> 00:48:16,620
turning their mass into energy.

1002
00:48:16,620 --> 00:48:19,530
Since the rest mass of
each of those is 511 KeV,

1003
00:48:19,530 --> 00:48:21,512
the photons come off at 511 KeV.

1004
00:48:21,512 --> 00:48:22,054
AUDIENCE: OK.

1005
00:48:22,054 --> 00:48:22,685
Got it.

1006
00:48:22,685 --> 00:48:23,477
MICHAEL SHORT: Yep?

1007
00:48:23,477 --> 00:48:24,938
AUDIENCE: So when you say
the electron and the positron

1008
00:48:24,938 --> 00:48:27,373
annihilate, is the
positron just a hole?

1009
00:48:27,373 --> 00:48:28,890
MICHAEL SHORT:
Ah, good question.

1010
00:48:28,890 --> 00:48:30,810
The positron is not a hole.

1011
00:48:30,810 --> 00:48:33,690
So like here, we were talking
about an electron hole pair.

1012
00:48:33,690 --> 00:48:36,550
A hole would be, let's say, an
atom with a missing electron.

1013
00:48:36,550 --> 00:48:39,570
A positron is a particle
itself of antimatter

1014
00:48:39,570 --> 00:48:42,360
that has the same mass,
but the opposite charge,

1015
00:48:42,360 --> 00:48:44,300
as the electron.

1016
00:48:44,300 --> 00:48:46,610
And so every particle's got
its antimatter component,

1017
00:48:46,610 --> 00:48:49,820
like there are antiprotons
and antineutrons, that if they

1018
00:48:49,820 --> 00:48:55,610
find their regular matter
selves, do annihilate.

1019
00:48:55,610 --> 00:48:56,290
Yeah?

1020
00:48:56,290 --> 00:48:59,810
AUDIENCE: If the detector
doesn't pick up gamma rays

1021
00:48:59,810 --> 00:49:01,500
directly, how do you measure--

1022
00:49:01,500 --> 00:49:05,143
like, why would a small
detector see double escape?

1023
00:49:05,143 --> 00:49:06,560
MICHAEL SHORT: So
a small detector

1024
00:49:06,560 --> 00:49:08,870
would see double escape,
because at first--

1025
00:49:08,870 --> 00:49:12,980
let's say a gamma ray interacts
and undergoes pair production.

1026
00:49:12,980 --> 00:49:16,190
And so it's going
to, let's say, create

1027
00:49:16,190 --> 00:49:18,067
an electron-positron pair.

1028
00:49:18,067 --> 00:49:20,400
And it's going to give them
a whole lot of extra energy.

1029
00:49:20,400 --> 00:49:23,560
So they're going to knock
around and ionize things.

1030
00:49:23,560 --> 00:49:26,780
And that's going to
count up to the energy

1031
00:49:26,780 --> 00:49:29,000
of the gamma minus MeV.

1032
00:49:29,000 --> 00:49:30,830
Then, when they
annihilate, if it's

1033
00:49:30,830 --> 00:49:34,067
a small detector chances are
those gammas just get out.

1034
00:49:34,067 --> 00:49:35,650
We're going to be
going over why soon,

1035
00:49:35,650 --> 00:49:38,290
when we get into mass
attenuation coefficients,

1036
00:49:38,290 --> 00:49:41,278
or cross sections or
interaction probabilities.

1037
00:49:41,278 --> 00:49:42,820
But as the energy
of a gamma goes up,

1038
00:49:42,820 --> 00:49:46,100
it's interaction
probability goes way down.

1039
00:49:46,100 --> 00:49:48,970
And this is a fairly
high energy photon,

1040
00:49:48,970 --> 00:49:51,310
compared to, like,
the easier KeV X-rays

1041
00:49:51,310 --> 00:49:52,870
that you tend to see.

1042
00:49:52,870 --> 00:49:57,040
So chances are, these photons
get made from annihilation,

1043
00:49:57,040 --> 00:49:58,803
but they don't stay
in the detector.

1044
00:49:58,803 --> 00:50:00,970
Then the bigger the detector
is, the more mass there

1045
00:50:00,970 --> 00:50:04,360
is in the way, and more
likely they get counted.

1046
00:50:04,360 --> 00:50:07,370
But all of this happens,
well, at the speed of light.

1047
00:50:07,370 --> 00:50:09,740
At least the photon part.

1048
00:50:09,740 --> 00:50:12,130
And so it's so fast that
the detector picks it up

1049
00:50:12,130 --> 00:50:16,250
as that sum of all the different
processes of energy in one time

1050
00:50:16,250 --> 00:50:16,750
interval.

1051
00:50:21,330 --> 00:50:24,320
Like I said, this is the harder
stuff, because it's not direct.

1052
00:50:24,320 --> 00:50:27,868
It's a multi-step process
with different possibilities.

1053
00:50:27,868 --> 00:50:30,410
But it's important to know where
the single and double escape

1054
00:50:30,410 --> 00:50:32,810
come from, where
the 511s come from,

1055
00:50:32,810 --> 00:50:34,902
which is outside the detector.

1056
00:50:34,902 --> 00:50:36,100
Yes, have a question?

1057
00:50:36,100 --> 00:50:36,683
AUDIENCE: Yes.

1058
00:50:36,683 --> 00:50:39,070
Would you say the detector
can-- the detector

1059
00:50:39,070 --> 00:50:41,590
itself can measure the
energy of a photon?

1060
00:50:41,590 --> 00:50:44,430
Is the measurement of 511
KeV, is that due to the fact

1061
00:50:44,430 --> 00:50:48,320
that it will hit an electron and
cause the-- what is it called?

1062
00:50:48,320 --> 00:50:50,060
MICHAEL SHORT: Like
ionization cascade?

1063
00:50:50,060 --> 00:50:51,220
Exactly.

1064
00:50:51,220 --> 00:50:55,030
Yeah so if a 511 KeV
photon enters the detector,

1065
00:50:55,030 --> 00:50:58,600
the detector does not know
until an electron interaction

1066
00:50:58,600 --> 00:50:59,830
happens.

1067
00:50:59,830 --> 00:51:02,530
So most of the photons
that enter this detector

1068
00:51:02,530 --> 00:51:04,150
leave the detector.

1069
00:51:04,150 --> 00:51:07,870
That's why if you actually look
at the banana stuff, which I'll

1070
00:51:07,870 --> 00:51:18,200
pull up right now,
at the efficiency,

1071
00:51:18,200 --> 00:51:21,170
check out those values, there.

1072
00:51:21,170 --> 00:51:24,070
Efficiency is in the realm
of 10 to the minus 4 or 10

1073
00:51:24,070 --> 00:51:28,000
to the minus 3, which is to
say that out of every 1,000

1074
00:51:28,000 --> 00:51:32,140
or 10,000 photons that enter
the detector, one of them

1075
00:51:32,140 --> 00:51:34,150
undergoes an
electron interaction

1076
00:51:34,150 --> 00:51:37,990
and the other 9,999 just
goes screaming on through,

1077
00:51:37,990 --> 00:51:41,310
and the detector does not
know that they're there.

1078
00:51:41,310 --> 00:51:44,340
The way that Mike Ames
got these efficiencies is

1079
00:51:44,340 --> 00:51:46,320
by putting a source
of known activity

1080
00:51:46,320 --> 00:51:48,990
in, calculating how
many gammas the detector

1081
00:51:48,990 --> 00:51:52,140
should have picked
up, and taking that

1082
00:51:52,140 --> 00:51:55,520
divided by the number that
it actually picked up.

1083
00:51:55,520 --> 00:51:58,230
And so that way, you know how
many gammas really went in,

1084
00:51:58,230 --> 00:52:00,180
and how many gammas it saw.

1085
00:52:00,180 --> 00:52:02,580
And that's how you get
the detector efficiency.

1086
00:52:02,580 --> 00:52:05,070
And you will have to
account for this when you do

1087
00:52:05,070 --> 00:52:06,280
this on the homework problem.

1088
00:52:06,280 --> 00:52:08,072
So the only quantities
you're going to need

1089
00:52:08,072 --> 00:52:11,280
is how many gammas that you
get, what's the efficiency,

1090
00:52:11,280 --> 00:52:12,520
and then back that out.

1091
00:52:12,520 --> 00:52:16,340
So you'll have to calculate
the activity of the bananas,

1092
00:52:16,340 --> 00:52:19,070
and then figure out how much
a banana weighs, and then you

1093
00:52:19,070 --> 00:52:21,440
should be able to calculate
the radioactivity of one

1094
00:52:21,440 --> 00:52:24,800
banana in curies, or
becquerels, or microcuries.

1095
00:52:24,800 --> 00:52:27,840
It's all good.

1096
00:52:27,840 --> 00:52:30,850
So good question.

1097
00:52:30,850 --> 00:52:33,330
So it's three of, so I'm
going to let you guys go.

1098
00:52:33,330 --> 00:52:34,890
But I'll see you again
tomorrow, and we'll review

1099
00:52:34,890 --> 00:52:36,015
a little bit of this stuff.

1100
00:52:36,015 --> 00:52:38,430
And we'll get into more of
the math of the cross sections

1101
00:52:38,430 --> 00:52:41,580
and why Compton scattering
and pair production take up

1102
00:52:41,580 --> 00:52:43,820
the energies that they do.