1
00:00:01,170 --> 00:00:03,780
PROFESSOR: So we're
building this story.

2
00:00:03,780 --> 00:00:07,620
We had the photoelectric effect.

3
00:00:07,620 --> 00:00:11,370
But at this moment,
Einstein, in the same year

4
00:00:11,370 --> 00:00:14,400
that he was talking
about general relativity,

5
00:00:14,400 --> 00:00:17,380
he came back to the photon.

6
00:00:17,380 --> 00:00:24,030
And there there's actually a
quote of Einstein's saying,

7
00:00:24,030 --> 00:00:27,840
his greatest
discoveries, for sure,

8
00:00:27,840 --> 00:00:31,790
were special relativity
and general relativity.

9
00:00:31,790 --> 00:00:34,590
The photo-- he got
the Nobel Prize

10
00:00:34,590 --> 00:00:38,100
for the photoelectric effect,
and he certainly helped

11
00:00:38,100 --> 00:00:43,110
invent the quantum theory
and many important things

12
00:00:43,110 --> 00:00:46,920
in this subject, but in
retrospect, his greatest

13
00:00:46,920 --> 00:00:48,480
successes were that.

14
00:00:48,480 --> 00:00:52,360
But he may have not quite
seen it exactly that way.

15
00:00:52,360 --> 00:00:57,420
He wrote, that some
stage of his whole life

16
00:00:57,420 --> 00:01:03,210
had been a difficult struggle
against the quantum, pulsed

17
00:01:03,210 --> 00:01:08,100
by some small happy interludes
of some other discoveries.

18
00:01:08,100 --> 00:01:13,350
But the quantum theory
certainly made him very--

19
00:01:16,430 --> 00:01:20,430
well, he was very suspicious
about the truth, the deep truth

20
00:01:20,430 --> 00:01:22,200
of the quantum theory.

21
00:01:22,200 --> 00:01:27,930
So 1916, he is busy
with general relativity,

22
00:01:27,930 --> 00:01:34,620
but then he's more ready
to admit that the photon is

23
00:01:34,620 --> 00:01:38,940
a particle, because he adds
that the photon now has momentum

24
00:01:38,940 --> 00:01:39,580
as well.

25
00:01:39,580 --> 00:01:46,200
So it's a-- these photons that
were not called photons yet

26
00:01:46,200 --> 00:01:50,550
are quanta for energy.

27
00:01:53,500 --> 00:01:56,320
But now he adds it's
also for momentum.

28
00:02:01,490 --> 00:02:06,250
So this already
characterizes particles.

29
00:02:06,250 --> 00:02:12,090
You see, there is the
relativistic relation, well

30
00:02:12,090 --> 00:02:17,165
known by then, that e squared
minus p squared c squared

31
00:02:17,165 --> 00:02:22,220
is equal to m squared
c to the fourth.

32
00:02:22,220 --> 00:02:25,120
You might say, well, this
is a little surprising.

33
00:02:25,120 --> 00:02:29,520
And If you don't remember
too much special relativity,

34
00:02:29,520 --> 00:02:32,960
this may not quite be
your favorite formula.

35
00:02:32,960 --> 00:02:37,700
Your favorite formulas might
be that the energy is mc

36
00:02:37,700 --> 00:02:43,310
squared divided by 1 minus
v squared over c squared.

37
00:02:43,310 --> 00:02:47,930
And that the momentum
is the ordinary momentum

38
00:02:47,930 --> 00:02:54,470
again multiplied by this
denominator like this.

39
00:02:54,470 --> 00:02:58,430
But these two equations,
with a little bit of algebra,

40
00:02:58,430 --> 00:03:04,790
yield this equation,
which summarizes something

41
00:03:04,790 --> 00:03:06,800
about a particle,
that basically if you

42
00:03:06,800 --> 00:03:09,590
know the energy and the
momentum of a particle,

43
00:03:09,590 --> 00:03:11,990
you know its mass.

44
00:03:11,990 --> 00:03:14,090
And it comes out from this.

45
00:03:14,090 --> 00:03:19,130
This is the relativistic
version of similar equations

46
00:03:19,130 --> 00:03:29,780
in which you have energy one
half mv squared, momentum, mv,

47
00:03:29,780 --> 00:03:36,490
and then energy equal p squared
over 2m, a very important

48
00:03:36,490 --> 00:03:39,000
relation that you can check.

49
00:03:39,000 --> 00:03:42,680
For out of these
two comes this one.

50
00:03:42,680 --> 00:03:44,650
And this is nonrelativistic.

51
00:03:53,770 --> 00:04:05,225
So for photons, we will
have particles of zero mass.

52
00:04:08,620 --> 00:04:15,420
Photons have zero mass, m
of the photon equals zero,

53
00:04:15,420 --> 00:04:22,485
and therefore e is equal
to pc for a photon.

54
00:04:25,120 --> 00:04:28,880
So we can look at what
the photon momentum is,

55
00:04:28,880 --> 00:04:32,190
for example photon momentum.

56
00:04:32,190 --> 00:04:41,980
We can treat it as some
particle and the photon momentum

57
00:04:41,980 --> 00:04:49,050
would be e of the photon
divided by c, or h

58
00:04:49,050 --> 00:04:52,570
Nu of the photon divided by c.

59
00:04:52,570 --> 00:05:00,310
And it's h over lambda
of the photon of gamma.

60
00:05:02,890 --> 00:05:05,470
So this is a very
interesting relation

61
00:05:05,470 --> 00:05:08,860
between the momentum
of the photon

62
00:05:08,860 --> 00:05:10,480
and the wavelength of photons.

63
00:05:13,130 --> 00:05:17,890
So the idea that the
photon is really a particle

64
00:05:17,890 --> 00:05:22,660
is starting to gather
evidence, but people were not

65
00:05:22,660 --> 00:05:27,480
convinced about it until
Compton did his work.

66
00:05:27,480 --> 00:05:35,200
So the same Compton that we
used this length over there,

67
00:05:35,200 --> 00:05:40,660
he works on this problem
and does the following.

68
00:05:43,240 --> 00:05:48,120
So is Compton scattering,
the name of the work.

69
00:05:48,120 --> 00:05:53,000
Compton Scattering.

70
00:05:58,900 --> 00:06:03,600
So what is Compton scattering?

71
00:06:03,600 --> 00:06:11,350
It is x-rays shining
on atoms again,

72
00:06:11,350 --> 00:06:16,130
but this time, these are
very energetic photons,

73
00:06:16,130 --> 00:06:18,070
energetic x-rays.

74
00:06:18,070 --> 00:06:21,940
X-rays can have anything
from a hundred EV

75
00:06:21,940 --> 00:06:27,280
to 100kEV, 100,000
electron volts.

76
00:06:27,280 --> 00:06:31,000
And what are the energies,
of binding energies

77
00:06:31,000 --> 00:06:33,280
of electrons in atoms?

78
00:06:33,280 --> 00:06:37,720
10 EV, 13 EV for
hydrogen. So you're

79
00:06:37,720 --> 00:06:41,330
talking about
100,000 EV coming in,

80
00:06:41,330 --> 00:06:47,200
so it's easily going to shake
electrons and release them

81
00:06:47,200 --> 00:06:48,830
very easily.

82
00:06:48,830 --> 00:06:51,100
So you're going to have almost--

83
00:06:51,100 --> 00:06:53,170
even though you're
shining on electrons

84
00:06:53,170 --> 00:06:55,690
that are bound to
atoms, it's almost

85
00:06:55,690 --> 00:07:00,640
like shining light on free
electrons if it's x-rays.

86
00:07:00,640 --> 00:07:04,090
So a few things happening.

87
00:07:04,090 --> 00:07:09,010
So this is photons
scattering on electrons.

88
00:07:09,010 --> 00:07:27,660
Scattering on electrons
that are virtually free.

89
00:07:27,660 --> 00:07:29,790
And the first thing
that happens is

90
00:07:29,790 --> 00:07:36,450
that there is a
violation of what

91
00:07:36,450 --> 00:07:46,380
was called the classical
Thomson scattering, that you

92
00:07:46,380 --> 00:07:52,380
may have started in 802.

93
00:07:52,380 --> 00:07:57,600
So the reason Compton
scattering did

94
00:07:57,600 --> 00:08:00,720
the job and physicists
finally admitted

95
00:08:00,720 --> 00:08:03,480
the photon was a
particle is that it made

96
00:08:03,480 --> 00:08:08,190
it look like particle collision
of a photon with an electron,

97
00:08:08,190 --> 00:08:11,370
it could calculate
and measure and treat

98
00:08:11,370 --> 00:08:14,460
the photon as a particle, just
like another particle like

99
00:08:14,460 --> 00:08:18,130
the electron, and out
came the right result.

100
00:08:18,130 --> 00:08:22,620
So the classical
Thomson scattering

101
00:08:22,620 --> 00:08:25,230
was a photon as a wave.

102
00:08:25,230 --> 00:08:27,070
And what does that do?

103
00:08:27,070 --> 00:08:30,900
Well, you have a free
electron, and here comes

104
00:08:30,900 --> 00:08:35,340
an electromagnetic
wave, E and B.

105
00:08:35,340 --> 00:08:39,770
And if it's low frequency
wave, low energy electron,

106
00:08:39,770 --> 00:08:41,730
this electric--
the magnetic field

107
00:08:41,730 --> 00:08:45,720
does very little, because this
election doesn't move too fast

108
00:08:45,720 --> 00:08:48,810
and the velocity is being
small, the Lorentz force

109
00:08:48,810 --> 00:08:51,180
is very small.

110
00:08:51,180 --> 00:08:54,740
But the electric field
shakes the electron.

111
00:08:54,740 --> 00:08:59,070
And as the electron is being
shaken, it's accelerating,

112
00:08:59,070 --> 00:09:02,070
and therefore it
radiates itself.

113
00:09:02,070 --> 00:09:10,020
And it radiates in a pattern,
so you get photons out.

114
00:09:10,020 --> 00:09:12,840
And the pattern
is the following.

115
00:09:12,840 --> 00:09:16,430
I'll write the formula
with this cross-section.

116
00:09:20,460 --> 00:09:23,670
We'll maybe not explain
too much about what

117
00:09:23,670 --> 00:09:27,330
this cross-section
means, it could

118
00:09:27,330 --> 00:09:29,340
be a nice thing for recitation.

119
00:09:32,310 --> 00:09:35,610
This is the formula for
the Thomson cross-section

120
00:09:35,610 --> 00:09:41,460
as a function of the
angle between the incident

121
00:09:41,460 --> 00:09:46,360
direction of the photon and
the photon that emerges.

122
00:09:46,360 --> 00:09:53,920
So you detect photons out and
this is the cross-section.

123
00:09:53,920 --> 00:09:55,940
What does it mean,
cross-section?

124
00:09:55,940 --> 00:09:59,500
Well this has units.

125
00:09:59,500 --> 00:10:02,120
I will say, very
briefly, units of area.

126
00:10:08,400 --> 00:10:12,040
Area per solid angle, but
solid angle has no units.

127
00:10:12,040 --> 00:10:16,560
So if you imagine a
little solid angle here

128
00:10:16,560 --> 00:10:19,300
and you multiply by
this cross-section,

129
00:10:19,300 --> 00:10:22,290
it gives you some
area that represents

130
00:10:22,290 --> 00:10:25,230
the solid angle you're
looking at to see

131
00:10:25,230 --> 00:10:28,380
how many photons you get.

132
00:10:28,380 --> 00:10:33,330
And the solid angle that
you have multiplied here

133
00:10:33,330 --> 00:10:35,880
to give you an area,
the area should

134
00:10:35,880 --> 00:10:42,090
be thought of as the area that
captures from the incoming beam

135
00:10:42,090 --> 00:10:46,290
the energy that is being
sent into this solid angle.

136
00:10:46,290 --> 00:10:51,030
So it represents an area, and
an area represents an energy,

137
00:10:51,030 --> 00:10:54,210
because if you have a beam
coming in from a magnetic wave

138
00:10:54,210 --> 00:10:56,960
through a little area,
some energy goes in.

139
00:10:56,960 --> 00:10:59,910
So that area that
you get is that area

140
00:10:59,910 --> 00:11:02,910
that extracts from
the incident beam

141
00:11:02,910 --> 00:11:06,240
the energy that you need to go
in this solid angle direction.

142
00:11:06,240 --> 00:11:11,820
So basically, this is a plot
of intensity of the radiation

143
00:11:11,820 --> 00:11:13,500
as a function of angle.

144
00:11:13,500 --> 00:11:16,080
But the most important
thing, not only-- this

145
00:11:16,080 --> 00:11:20,430
is not quite accurate when
the photon is of high energy.

146
00:11:20,430 --> 00:11:22,680
The thing that is
pretty wrong about this

147
00:11:22,680 --> 00:11:36,990
is that the outgoing photon
or wave has the same frequency

148
00:11:36,990 --> 00:11:39,120
as the original wave.

149
00:11:45,940 --> 00:11:50,290
So that's a property
of this scattering.

150
00:11:50,290 --> 00:11:53,440
The electron is being
moved at the frequency

151
00:11:53,440 --> 00:11:55,990
of the electric
field, and therefore

152
00:11:55,990 --> 00:11:58,960
the frequency of the
radiation is the same.

153
00:11:58,960 --> 00:12:01,520
And this is all classical.

154
00:12:01,520 --> 00:12:05,980
But out comes, when
you have a high energy,

155
00:12:05,980 --> 00:12:12,050
this thing is not accurate, and
you have a different result.

156
00:12:12,050 --> 00:12:16,025
So what did Compton find?

157
00:12:19,770 --> 00:12:24,587
Well, the first thing is
a couple of observations.

158
00:12:24,587 --> 00:12:25,087
.

159
00:12:29,560 --> 00:12:31,560
Treat the photon as a particle.

160
00:12:40,500 --> 00:12:43,560
OK, so it has some
energy and some momentum.

161
00:12:43,560 --> 00:12:46,460
The electron has some
energy and momentum.

162
00:12:46,460 --> 00:12:51,050
You should analyze the collision
using energy and momentum

163
00:12:51,050 --> 00:12:52,200
conservation.

164
00:12:52,200 --> 00:13:00,260
So before the collision,
you have an incoming photon

165
00:13:00,260 --> 00:13:03,050
that has some energy
and some momentum,

166
00:13:03,050 --> 00:13:06,870
and you have an
electron, maybe here.

167
00:13:06,870 --> 00:13:09,330
And then after a
while, the electron

168
00:13:09,330 --> 00:13:14,220
flies away in some
direction, E minus.

169
00:13:14,220 --> 00:13:21,250
And the photon also, a photon
prime of different frequency

170
00:13:21,250 --> 00:13:21,930
flies away.

171
00:13:21,930 --> 00:13:23,270
It's like a collision.

172
00:13:26,760 --> 00:13:31,740
You can do this calculation
and maybe it could even

173
00:13:31,740 --> 00:13:33,090
be done in recitation.

174
00:13:33,090 --> 00:13:35,730
It's a relativistic calculation.

175
00:13:35,730 --> 00:13:43,230
You were asked in first homework
to show that the photon can not

176
00:13:43,230 --> 00:13:46,330
be absorbed by the
electron, and that

177
00:13:46,330 --> 00:13:48,720
uses the relativistic
relations if you

178
00:13:48,720 --> 00:13:51,870
want to show you
just can't absorb it.

179
00:13:51,870 --> 00:13:56,050
It's not consistent with energy
and momentum conservation.

180
00:13:56,050 --> 00:13:58,930
So it's something you
can try to figure out.

181
00:13:58,930 --> 00:14:01,470
The other thing that
should become obvious

182
00:14:01,470 --> 00:14:06,210
is that the photon is
going to lose some energy,

183
00:14:06,210 --> 00:14:10,020
because as it hits the electron,
it gives the electron a kick.

184
00:14:10,020 --> 00:14:12,430
The electron now
has kinetic energy.

185
00:14:12,430 --> 00:14:14,130
Think of this in the lab.

186
00:14:14,130 --> 00:14:17,290
The electron was static,
the photon was coming.

187
00:14:17,290 --> 00:14:19,290
After a while, the
electron has moved,

188
00:14:19,290 --> 00:14:21,250
it's moving now
with some velocity.

189
00:14:21,250 --> 00:14:24,180
The photon must have
lost some energy.

190
00:14:24,180 --> 00:14:28,300
So photon loses energy.

191
00:14:31,870 --> 00:14:37,770
And therefore, the final
lambda must be bigger

192
00:14:37,770 --> 00:14:39,300
than the initial lambda.

193
00:14:39,300 --> 00:14:44,010
Remember the shorter the
wavelength, the more energetic

194
00:14:44,010 --> 00:14:46,710
the photon is.

195
00:14:46,710 --> 00:14:49,510
So what is the difference?

196
00:14:49,510 --> 00:14:51,840
That's the result
of a calculation.

197
00:14:51,840 --> 00:14:55,860
It's a nice calculation,
all of you should do it.

198
00:14:55,860 --> 00:14:58,900
It's probably in some
book, in many books.

199
00:14:58,900 --> 00:15:03,570
And it's a nice exercise
also for recitation.

200
00:15:03,570 --> 00:15:06,375
Lambda final minus
lambda initial.

201
00:15:09,160 --> 00:15:10,910
Or I'll write it differently.

202
00:15:10,910 --> 00:15:17,270
Lambda final is equal to
lambda initial plus something

203
00:15:17,270 --> 00:15:20,480
that depends on the angle
theta, in fact, has a one

204
00:15:20,480 --> 00:15:23,270
minus cosine theta dependence.

205
00:15:23,270 --> 00:15:31,870
But here has to be something
with units of length

206
00:15:31,870 --> 00:15:35,875
And the only party you
have here is the electron.

207
00:15:39,170 --> 00:15:43,170
And this electron
has some length,

208
00:15:43,170 --> 00:15:45,840
which is the quantum
wavelength, which

209
00:15:45,840 --> 00:15:51,060
is very natural for a Compton
scattering problem, of course.

210
00:15:51,060 --> 00:15:55,340
And it's here, h over mec.

211
00:15:55,340 --> 00:16:00,720
So the l Compton
of the electron.

212
00:16:00,720 --> 00:16:05,940
And that's the correct formula
for the loss of energy,

213
00:16:05,940 --> 00:16:08,610
or change in frequency.

214
00:16:08,610 --> 00:16:19,080
So the most you can get is if
you don't interact when theta

215
00:16:19,080 --> 00:16:22,910
is equal to zero, the
photon keeps going,

216
00:16:22,910 --> 00:16:25,620
doesn't even kick the electron.

217
00:16:25,620 --> 00:16:28,050
And then you get zero,
the initial lambda

218
00:16:28,050 --> 00:16:30,180
is equal to the final lambda.

219
00:16:30,180 --> 00:16:37,140
But this can be as large as two,
for totally backwords photon

220
00:16:37,140 --> 00:16:38,440
emitted.

221
00:16:38,440 --> 00:16:43,110
So theta equals pi, cosine
pi is minus 1, you get 2.

222
00:16:43,110 --> 00:16:47,590
At 90 degrees, you
get the Compton shift.

223
00:16:47,590 --> 00:16:49,710
So it's a very nice
thing, you even

224
00:16:49,710 --> 00:16:53,730
know already what's
happening here.

225
00:16:53,730 --> 00:17:02,800
So let's describe the experiment
itself, of how it was done.

226
00:17:14,700 --> 00:17:26,579
So he used, Compton,
the experiment

227
00:17:26,579 --> 00:17:39,550
have a source of
molybdenum x-rays

228
00:17:39,550 --> 00:17:48,880
that have lambda equals
0.0709 nanometers.

229
00:17:48,880 --> 00:17:55,450
So smaller than nanometers,
it's 70 picometers.

230
00:17:55,450 --> 00:17:59,170
And that corresponds
to e photon--

231
00:17:59,170 --> 00:18:01,265
that's pretty small, so
it must be high energy--

232
00:18:01,265 --> 00:18:06,700
and it's 17.49 kEV.

233
00:18:06,700 --> 00:18:10,510
That's very big energy.

234
00:18:10,510 --> 00:18:13,555
And there was a
carbon foil here.

235
00:18:20,270 --> 00:18:25,660
And you send the photons
in this direction.

236
00:18:25,660 --> 00:18:28,790
And they were observed
at several degrees,

237
00:18:28,790 --> 00:18:31,520
but in particular,
I'll show you a plot

238
00:18:31,520 --> 00:18:36,245
of how it looked for theta
equal 90 degrees, so detector.

239
00:18:42,790 --> 00:18:48,440
So source comes in, carbon is
there, and what do you get?

240
00:18:48,440 --> 00:18:49,765
You get the following plot.

241
00:18:52,540 --> 00:18:57,220
Intensity-- so you plot the
intensity of the photons

242
00:18:57,220 --> 00:19:04,090
that you detect, as a
function of the wavelength

243
00:19:04,090 --> 00:19:07,240
of the photons that you
get, because there's

244
00:19:07,240 --> 00:19:11,960
supposed to be a wavelength,
a shift of wavelength.

245
00:19:11,960 --> 00:19:14,950
So it's actually
quite revealing,

246
00:19:14,950 --> 00:19:17,710
because you get
something like this.

247
00:19:17,710 --> 00:19:20,500
A bump and a bigger bump here.

248
00:19:20,500 --> 00:19:22,710
Something like that.

249
00:19:22,710 --> 00:19:28,330
Pretty surprising, I think,
to first approximation.

250
00:19:28,330 --> 00:19:33,000
And here is about--

251
00:19:33,000 --> 00:19:39,890
the first bump happens to
have about the same wavelength

252
00:19:39,890 --> 00:19:46,580
as the incoming
radiation, 0.0709.

253
00:19:46,580 --> 00:19:49,280
I should write it a
little more to the left.

254
00:19:49,280 --> 00:19:59,390
0.0709 nanometers over here.

255
00:19:59,390 --> 00:20:05,650
And then there is
another peak at lambda f,

256
00:20:05,650 --> 00:20:18,650
about 0.0731 nanometers.

257
00:20:18,650 --> 00:20:22,300
And the question is, what
is the interpretation?

258
00:20:22,300 --> 00:20:28,240
Why are there two peaks
and what's going on?

259
00:20:28,240 --> 00:20:31,800
Anybody has any idea?

260
00:20:31,800 --> 00:20:35,130
Let me ask a simpler question.

261
00:20:35,130 --> 00:20:38,100
Which is the lambda
that corresponds

262
00:20:38,100 --> 00:20:44,490
to the prediction of the
fact that the wavelength must

263
00:20:44,490 --> 00:20:46,930
change, the smaller
one or the bigger one?

264
00:20:49,770 --> 00:20:51,000
The bigger one.

265
00:20:51,000 --> 00:20:54,510
You certainly should loose
energy, so the lambda

266
00:20:54,510 --> 00:20:59,640
f, the thing we were expecting
to see, presumably that thing,

267
00:20:59,640 --> 00:21:03,600
because we were expecting
to see that at 90 degrees,

268
00:21:03,600 --> 00:21:05,670
the photons have this thing.

269
00:21:05,670 --> 00:21:09,090
So we seem to observe this one.

270
00:21:09,090 --> 00:21:12,690
And let's look at it in
a little more detail.

271
00:21:12,690 --> 00:21:21,540
You have this 0.0731 nanometers
and you have the original light

272
00:21:21,540 --> 00:21:29,700
was at 0.0709 nanometers.

273
00:21:29,700 --> 00:21:43,000
So the difference is
0.0022 nanometers,

274
00:21:43,000 --> 00:21:48,870
which is 10 to the minus 9, but
it's exactly, or pretty close,

275
00:21:48,870 --> 00:21:54,200
to this thing,
because a picometer is

276
00:21:54,200 --> 00:21:56,810
10 to the minus 3 nanometers.

277
00:21:56,810 --> 00:22:02,280
So this is 0.0024 nanometers.

278
00:22:02,280 --> 00:22:04,310
So this is pretty nice.

279
00:22:04,310 --> 00:22:09,050
Look, at 90 degrees,
cosine theta is zero.

280
00:22:09,050 --> 00:22:13,640
So the difference between
initial and final wavelengths

281
00:22:13,640 --> 00:22:16,280
should be equal to
the Compton wavelength

282
00:22:16,280 --> 00:22:20,210
with about 0.0024 nanometers.

283
00:22:20,210 --> 00:22:24,550
And that's about
it pretty close.

284
00:22:24,550 --> 00:22:28,040
So this peak is all right.

285
00:22:28,040 --> 00:22:30,920
Should've been there.

286
00:22:30,920 --> 00:22:35,590
The other peak, why is it there?