1
00:00:01,000 --> 00:00:04,000
The following content is
provided by MIT OpenCourseWare

2
00:00:04,000 --> 00:00:06,000
under a Creative Commons
license.

3
00:00:06,000 --> 00:00:10,000
Additional information about
our license and MIT

4
00:00:10,000 --> 00:00:15,000
OpenCourseWare in general is
available at ocw.mit.edu.

5
00:00:15,000 --> 00:00:17,000
Where were we,
last time?

6
00:00:17,000 --> 00:00:22,000
Last time, we said we were
setting aside the problem of the

7
00:00:22,000 --> 00:00:26,000
structure of the atom.
We were setting it aside

8
00:00:26,000 --> 00:00:30,000
because we were stuck,
and what we had to do was to

9
00:00:30,000 --> 00:00:34,000
look at another area of
discussion.

10
00:00:34,000 --> 00:00:38,000
And that is this wave-particle
duality of light and matter,

11
00:00:38,000 --> 00:00:43,000
because it is that discussion
that is going to give us the

12
00:00:43,000 --> 00:00:48,000
clues about how to proceed.
We are putting aside the

13
00:00:48,000 --> 00:00:53,000
discussion of the structure of
the atom all the way until next

14
00:00:53,000 --> 00:00:57,000
Wednesday, because next Monday,
I was reminded,

15
00:00:57,000 --> 00:01:10,000
is a student holiday.
[APPLAUSE]

16
00:01:10,000 --> 00:01:14,000
And so we started.
We talked about the wave-like

17
00:01:14,000 --> 00:01:19,000
properties of light.
We said that the property of

18
00:01:19,000 --> 00:01:23,000
superposition,
the fact that you can put waves

19
00:01:23,000 --> 00:01:29,000
at the same point in space and
their amplitudes add.

20
00:01:29,000 --> 00:01:33,000
Since waves have both positive
and negative amplitude,

21
00:01:33,000 --> 00:01:37,000
that means that you have
constructive and destructive

22
00:01:37,000 --> 00:01:40,000
interference.
And it is those interference

23
00:01:40,000 --> 00:01:43,000
phenomena, then,
that are evidence for wave-like

24
00:01:43,000 --> 00:01:46,000
property.
And we did the two-slit

25
00:01:46,000 --> 00:01:50,000
experiment to try to give you an
example of interference

26
00:01:50,000 --> 00:01:53,000
phenomena.
We were trying to understand

27
00:01:53,000 --> 00:01:57,000
those interference phenomena,
and did so in terms of this

28
00:01:57,000 --> 00:02:02,000
diagram here.
The interference phenomena that

29
00:02:02,000 --> 00:02:07,000
we saw was an array,
actually a row of bright spots,

30
00:02:07,000 --> 00:02:10,000
dark spots, bright spots,
dark spots.

31
00:02:10,000 --> 00:02:15,000
And we drew these semicircles
here around each one of the

32
00:02:15,000 --> 00:02:18,000
slits.
They represent a little bit of

33
00:02:18,000 --> 00:02:22,000
the wave that emanated through
those slits.

34
00:02:22,000 --> 00:02:27,000
Because those slits are small,
then, those waves emanated

35
00:02:27,000 --> 00:02:33,000
equally in all directions.
That is why these semicircles

36
00:02:33,000 --> 00:02:37,000
represent the wave maxima.
And what we discovered is that

37
00:02:37,000 --> 00:02:42,000
if we looked along this line
here, this line which led to

38
00:02:42,000 --> 00:02:45,000
this bright spot,
that all of the waves along

39
00:02:45,000 --> 00:02:48,000
this line were constructively
interfering.

40
00:02:48,000 --> 00:02:53,000
That is, we had the maximum of
the two waves at the same point

41
00:02:53,000 --> 00:02:58,000
in space, or the minimum of the
two waves at the same point in

42
00:02:58,000 --> 00:03:02,000
space.
And we noticed that everywhere

43
00:03:02,000 --> 00:03:05,000
along this line,
where we had that constructive

44
00:03:05,000 --> 00:03:08,000
interference,
the difference in the distance

45
00:03:08,000 --> 00:03:10,000
of the waves traveled was one
lambda.

46
00:03:10,000 --> 00:03:13,000
We noticed, here,
that everywhere along this line

47
00:03:13,000 --> 00:03:17,000
that led to a very bright spot,
we had constructive

48
00:03:17,000 --> 00:03:20,000
interference.
And the difference in distance

49
00:03:20,000 --> 00:03:23,000
traveled by those two waves was
two lambda.

50
00:03:23,000 --> 00:03:25,000
And, likewise,
up here, along this line,

51
00:03:25,000 --> 00:03:31,000
the difference in the distance
traveled was zero lambda.

52
00:03:31,000 --> 00:03:34,000
And from just that,
in a sense, qualitative

53
00:03:34,000 --> 00:03:37,000
observation, we drew a
conclusion.

54
00:03:37,000 --> 00:03:41,000
And that conclusion was in
order to get maximum

55
00:03:41,000 --> 00:03:46,000
constructive interference,
a condition that had obtain,

56
00:03:46,000 --> 00:03:50,000
is that the difference in the
distance traveled by the two

57
00:03:50,000 --> 00:03:55,000
waves has to be an integral
multiple of the wavelength.

58
00:03:55,000 --> 00:03:59,000
N could be 0,
1, 2, 3, etc.

59
00:03:59,000 --> 00:04:03,000
And so, the very bright spot
here that always bisects the two

60
00:04:03,000 --> 00:04:06,000
slits, since N is 0,
we call that the zero-order

61
00:04:06,000 --> 00:04:10,000
interference feature,
or the zero-order fraction

62
00:04:10,000 --> 00:04:13,000
feature.
The bright spot that is either

63
00:04:13,000 --> 00:04:17,000
to the left or to the right or
up or down of that center bright

64
00:04:17,000 --> 00:04:21,000
spot is the first-order
diffraction feature or the

65
00:04:21,000 --> 00:04:23,000
first-order interference
feature.

66
00:04:23,000 --> 00:04:28,000
And then the second bright spot
up or down from the center is a

67
00:04:28,000 --> 00:04:32,000
second-order diffraction
feature.

68
00:04:32,000 --> 00:04:35,000
And so on and so on.
And in recitation section,

69
00:04:35,000 --> 00:04:40,000
what you also should have done,
is you should have reasoned

70
00:04:40,000 --> 00:04:45,000
through what the condition was
for destructive interference.

71
00:04:45,000 --> 00:04:50,000
That is in between these bright
spots, you have dark spots as a

72
00:04:50,000 --> 00:04:53,000
result of destructive
interference.

73
00:04:53,000 --> 00:04:58,000
And that results because,
say, right here you get a dark

74
00:04:58,000 --> 00:05:02,000
spot --
Right here at that point you

75
00:05:02,000 --> 00:05:07,000
would see the maximum of one
wave at the same point in space

76
00:05:07,000 --> 00:05:12,000
as the minimum of the other,
and so they exactly cancel.

77
00:05:12,000 --> 00:05:17,000
And so by just analyzing what
waves were destructively

78
00:05:17,000 --> 00:05:21,000
interfering, you should have
come up with a general

79
00:05:21,000 --> 00:05:24,000
expression for destructive
interference,

80
00:05:24,000 --> 00:05:27,000
of N plus one-half,
that quanity,

81
00:05:27,000 --> 00:05:32,000
times lambda.
That is your general condition

82
00:05:32,000 --> 00:05:37,000
for destructive interference,
the difference in the distance

83
00:05:37,000 --> 00:05:41,000
traveled by the two waves.
This kind of diagram here we

84
00:05:41,000 --> 00:05:45,000
are also going to see on Friday,
because this interference

85
00:05:45,000 --> 00:05:49,000
phenomenon is the property
associated with waves.

86
00:05:49,000 --> 00:05:54,000
And what we are going to do is
see this diagram again when we

87
00:05:54,000 --> 00:06:00,000
scatter electrons for particles.
We are going to see that

88
00:06:00,000 --> 00:06:04,000
particles, also,
will destructively and

89
00:06:04,000 --> 00:06:09,000
constructively interfere.
They also have wave-like

90
00:06:09,000 --> 00:06:13,000
properties.
That is what we will do on

91
00:06:13,000 --> 00:06:15,000
Friday.
We have established,

92
00:06:15,000 --> 00:06:20,000
now, the wave-like properties
of radiation,

93
00:06:20,000 --> 00:06:26,000
so I would like to move on and
talk about the evidence for the

94
00:06:26,000 --> 00:06:31,000
particle-like nature of
radiation.

95
00:06:36,000 --> 00:06:41,000
The evidence for the
particle-like nature of

96
00:06:41,000 --> 00:06:48,000
radiation comes from an effect
called the photoelectric effect.

97
00:06:48,000 --> 00:06:53,000
Shortly after Thompson
discovered the electron,

98
00:06:53,000 --> 00:07:00,000
scientists were noticing that
if you took a metal and shined

99
00:07:00,000 --> 00:07:06,000
radiation on that metal,
that indeed electrons were

100
00:07:06,000 --> 00:07:10,000
emitted.
Electrons came off.

101
00:07:10,000 --> 00:07:14,000
These were called
photoelectrons.

102
00:07:14,000 --> 00:07:20,000
However, the radiation that you
shined on the metal had to have

103
00:07:20,000 --> 00:07:26,000
a frequency nu that was greater
than or equal to some threshold

104
00:07:26,000 --> 00:07:32,000
frequency, nu nought.
That is, if you took radiation

105
00:07:32,000 --> 00:07:38,000
of some frequency here,
nu, that was less than this

106
00:07:38,000 --> 00:07:43,000
threshold frequency,
well, you did not get any

107
00:07:43,000 --> 00:07:48,000
electrons off.
Well, another way to kind of

108
00:07:48,000 --> 00:07:54,000
understand that data or that
effect is to just plot the

109
00:07:54,000 --> 00:08:01,000
number of the electrons that
come off as a function of the

110
00:08:01,000 --> 00:08:08,000
frequency of the radiation.
And so at low frequency,

111
00:08:08,000 --> 00:08:12,000
there are no electrons,
but all of a sudden you get to

112
00:08:12,000 --> 00:08:16,000
nu nought, and then electrons
start coming off.

113
00:08:16,000 --> 00:08:21,000
And no matter how high you
increase the frequency here,

114
00:08:21,000 --> 00:08:25,000
the number of electrons that
come off remains the same,

115
00:08:25,000 --> 00:08:30,000
remains constant.
And it turned out that for the

116
00:08:30,000 --> 00:08:34,000
metals that were looked at,
at that time,

117
00:08:34,000 --> 00:08:38,000
the threshold frequency,
here, was in the UV range of

118
00:08:38,000 --> 00:08:43,000
the electromagnetic spectrum.
Well, in addition to just

119
00:08:43,000 --> 00:08:47,000
measuring the number of
electrons and generally

120
00:08:47,000 --> 00:08:52,000
observing this effect,
scientists did not understand

121
00:08:52,000 --> 00:08:56,000
what was going on.
So they just started measuring

122
00:08:56,000 --> 00:09:02,000
everything they could think
about measuring.

123
00:09:02,000 --> 00:09:06,000
And one quantity that they
measured was the kinetic energy

124
00:09:06,000 --> 00:09:10,000
of these electrons that were
being emitted.

125
00:09:10,000 --> 00:09:15,000
And so you take kinetic energy
here, KE, as a function of the

126
00:09:15,000 --> 00:09:18,000
frequency.
They found that at low

127
00:09:18,000 --> 00:09:22,000
frequency, again,
there is no kinetic energy,

128
00:09:22,000 --> 00:09:27,000
because there are no electrons.
And then at some frequency,

129
00:09:27,000 --> 00:09:32,000
all of a sudden electrons
started coming off.

130
00:09:32,000 --> 00:09:38,000
And the kinetic energy of those
electrons seemed to increase

131
00:09:38,000 --> 00:09:43,000
with the frequency once past
that threshold frequency,

132
00:09:43,000 --> 00:09:47,000
nu nought.
Well, this was really another

133
00:09:47,000 --> 00:09:51,000
one of these conundrums,
here, at that time,

134
00:09:51,000 --> 00:09:57,000
because classical physics,
classical electromagnetism,

135
00:09:57,000 --> 00:10:04,000
classical physics had no way of
explaining these data.

136
00:10:04,000 --> 00:10:06,000
And, in fact,
what classical physics

137
00:10:06,000 --> 00:10:10,000
predicted is that the kinetic
energy of these electrons,

138
00:10:10,000 --> 00:10:14,000
that that kinetic energy should
have nothing to do with the

139
00:10:14,000 --> 00:10:18,000
frequency of the light.
That is, the kinetic energy was

140
00:10:18,000 --> 00:10:21,000
constant.
As you increased the frequency

141
00:10:21,000 --> 00:10:24,000
of the light,
classical physics would tell

142
00:10:24,000 --> 00:10:28,000
you that the kinetic energy
should not be affected by the

143
00:10:28,000 --> 00:10:33,000
frequency of the light.
There was nothing in the

144
00:10:33,000 --> 00:10:38,000
classical way of thinking,
classical electromagnetism that

145
00:10:38,000 --> 00:10:43,000
connected the frequency of the
light to the kind of energy,

146
00:10:43,000 --> 00:10:48,000
to the kinetic energy.
There was no way for blue light

147
00:10:48,000 --> 00:10:52,000
to make the electrons have a
larger kinetic energy,

148
00:10:52,000 --> 00:10:57,000
and for blue light to have an
effect on the kinetic energy,

149
00:10:57,000 --> 00:11:04,000
and red light to not have an
effect on the kinetic energy.

150
00:11:04,000 --> 00:11:07,000
In addition,
what classical physics

151
00:11:07,000 --> 00:11:13,000
predicted is that the kinetic
energy of the electrons should

152
00:11:13,000 --> 00:11:17,000
be dependent on the intensity of
the light.

153
00:11:17,000 --> 00:11:22,000
That is, the more and more
intense the radiation on the

154
00:11:22,000 --> 00:11:28,000
metal, the more and more kinetic
energy those electrons should

155
00:11:28,000 --> 00:11:31,000
have.
Because, after all,

156
00:11:31,000 --> 00:11:36,000
if you increase the intensity
of the light going into the

157
00:11:36,000 --> 00:11:41,000
metal, you are putting more and
more energy into it.

158
00:11:41,000 --> 00:11:45,000
That should be reflected in
just how energetic those

159
00:11:45,000 --> 00:11:49,000
electrons were picked out.
The more energy in,

160
00:11:49,000 --> 00:11:54,000
the electrons ought to come out
with larger and larger kinetic

161
00:11:54,000 --> 00:11:58,000
energy.
Of course, the observation was

162
00:11:58,000 --> 00:12:03,000
that the kinetic energy of the
electrons had nothing to do with

163
00:12:03,000 --> 00:12:09,000
the intensity of light.
The kinetic energy of the

164
00:12:09,000 --> 00:12:14,000
electrons did not increase as
you made the light brighter and

165
00:12:14,000 --> 00:12:18,000
brighter.
As you put more and more energy

166
00:12:18,000 --> 00:12:21,000
in, the kinetic energy remained
the same.

167
00:12:21,000 --> 00:12:26,000
It didn't have an effect.
This was a real conundrum here.

168
00:12:26,000 --> 00:12:31,000
The known classical physics was
making predictions really just

169
00:12:31,000 --> 00:12:36,000
contrary to what was being
observed.

170
00:12:36,000 --> 00:12:41,000
These data, here,
of the kinetic energy versus

171
00:12:41,000 --> 00:12:45,000
the frequency,
were around for a few years

172
00:12:45,000 --> 00:12:50,000
before Einstein took a look at
them in 1905,

173
00:12:50,000 --> 00:12:56,000
a hundred years ago.
And he looked at these data for

174
00:12:56,000 --> 00:13:03,000
many different metals.
Here is some data for metal A,

175
00:13:03,000 --> 00:13:07,000
for example,
and here is some data for metal

176
00:13:07,000 --> 00:13:09,000
B.
And, in both cases,

177
00:13:09,000 --> 00:13:15,000
it certainly looked like the
kinetic energy was linearly

178
00:13:15,000 --> 00:13:19,000
dependent on the frequency of
the radiation.

179
00:13:19,000 --> 00:13:25,000
But what was different for the
two different metals was the

180
00:13:25,000 --> 00:13:30,000
threshold frequency here,
nu nought.

181
00:13:30,000 --> 00:13:36,000
What Einstein did was,
he went and fitted a straight

182
00:13:36,000 --> 00:13:43,000
line to these data,
y equals mx plus b.

183
00:13:43,000 --> 00:13:46,000
And when he did that,

184
00:13:46,000 --> 00:13:51,000
and he went to calculate the
slope here, m,

185
00:13:51,000 --> 00:13:59,000
of these lines,
he thought "very interesting."

186
00:13:59,000 --> 00:14:05,000
Because the slope of those
lines was 6.626x10^-34 joule

187
00:14:05,000 --> 00:14:09,000
seconds.
The slope of those lines was

188
00:14:09,000 --> 00:14:14,000
something called Planck's
constant, h.

189
00:14:14,000 --> 00:14:19,000
You say so what?
Well, the reason he was so

190
00:14:19,000 --> 00:14:25,000
interested in this is because
just a few years earlier,

191
00:14:25,000 --> 00:14:31,000
there was a scientist by the
name of Max Planck who was

192
00:14:31,000 --> 00:14:38,000
interested in understanding what
was called the black-body

193
00:14:38,000 --> 00:14:44,000
radiation data.
What is a black-body?

194
00:14:44,000 --> 00:14:47,000
Well, let's just,
for simplicity purposes,

195
00:14:47,000 --> 00:14:53,000
think of the black-body as the
burner on an electric stove.

196
00:14:53,000 --> 00:14:58,000
What you know is that if you
turn up the voltage on that

197
00:14:58,000 --> 00:15:04,000
burner, the burner gets hot.
It increased in temperature.

198
00:15:04,000 --> 00:15:07,000
And you increase the
temperature, and sooner or

199
00:15:07,000 --> 00:15:10,000
later, that burner is glowing
bright red.

200
00:15:10,000 --> 00:15:13,000
And you increase the
temperature some more,

201
00:15:13,000 --> 00:15:16,000
and the burner is glowing a
brighter red.

202
00:15:16,000 --> 00:15:19,000
And you increase it some more,
and it is glowing orange.

203
00:15:19,000 --> 00:15:23,000
And you increase it some more,
which you shouldn't do,

204
00:15:23,000 --> 00:15:27,000
and it's glowing yellow.
And then if you could increase

205
00:15:27,000 --> 00:15:31,000
it some more,
it's glowing white.

206
00:15:31,000 --> 00:15:34,000
What is happening,
as you increase the

207
00:15:34,000 --> 00:15:39,000
temperature, is that the
radiation from that black-body,

208
00:15:39,000 --> 00:15:44,000
this is the black-body
radiation, is increasing in

209
00:15:44,000 --> 00:15:47,000
intensity.
But, more importantly,

210
00:15:47,000 --> 00:15:51,000
the frequency is getting larger
and larger.

211
00:15:51,000 --> 00:15:54,000
Dark red, bright red,
orange, yellow,

212
00:15:54,000 --> 00:15:57,000
white, those are all
frequencies.

213
00:15:57,000 --> 00:16:04,000
The frequency is shifting to
higher and higher values.

214
00:16:04,000 --> 00:16:10,000
And what was actually done at
that time is that the intensity

215
00:16:10,000 --> 00:16:16,000
of that black-body radiation,
oh, and this material is not in

216
00:16:16,000 --> 00:16:21,000
your notes, because you are not
responsible for it.

217
00:16:21,000 --> 00:16:27,000
I am just trying to make this
surprise that Einstein noticed

218
00:16:27,000 --> 00:16:32,000
about the slope.
I am just trying to put it in

219
00:16:32,000 --> 00:16:35,000
some context,
why he was so surprised and

220
00:16:35,000 --> 00:16:39,000
amazed at it.
This black-body intensity here,

221
00:16:39,000 --> 00:16:43,000
people had dispersed that
radiation and looked at the

222
00:16:43,000 --> 00:16:46,000
frequencies that were coming
off.

223
00:16:46,000 --> 00:16:49,000
This is intensity versus
frequency.

224
00:16:49,000 --> 00:16:54,000
Here is a general shape of that
intensity versus frequency.

225
00:16:54,000 --> 00:17:00,000
That was observed for some
temperature T one.

226
00:17:00,000 --> 00:17:05,000
That was a low temperature.
And then, when the temperature

227
00:17:05,000 --> 00:17:10,000
was increased and the intensity
versus frequency was observed,

228
00:17:10,000 --> 00:17:14,000
well, the frequencies generally
got higher.

229
00:17:14,000 --> 00:17:18,000
This is higher temperature.
Intensity goes up.

230
00:17:18,000 --> 00:17:22,000
And you increase the
temperature some more,

231
00:17:22,000 --> 00:17:25,000
and you get even higher
frequency.

232
00:17:25,000 --> 00:17:30,000
T three is the highest
temperature.

233
00:17:30,000 --> 00:17:36,000
And that is what the data were.
What Planck was trying to do

234
00:17:36,000 --> 00:17:43,000
was to understand the origin of
that black-body radiation.

235
00:17:43,000 --> 00:17:48,000
What he said was that in these
black-bodies,

236
00:17:48,000 --> 00:17:52,000
in these materials,
what there must be are

237
00:17:52,000 --> 00:17:59,000
oscillators that are giving off
this radiation.

238
00:17:59,000 --> 00:18:04,000
But he had another little kick
to these oscillators.

239
00:18:04,000 --> 00:18:10,000
These oscillators were giving
off radiation or energy in

240
00:18:10,000 --> 00:18:13,000
chunks, in quanta,
in particles.

241
00:18:13,000 --> 00:18:18,000
And using that idea,
plus some statistical

242
00:18:18,000 --> 00:18:23,000
mechanics, he was able to
calculate the shapes of these

243
00:18:23,000 --> 00:18:26,000
curves.
That is, he indeed got,

244
00:18:26,000 --> 00:18:32,000
for the lowest temperature
here, a curve that looked like

245
00:18:32,000 --> 00:18:36,000
this.
And for T two,

246
00:18:36,000 --> 00:18:39,000
he got a curve that looked like
this.

247
00:18:39,000 --> 00:18:44,000
And for T three,
he got a curve that looked like

248
00:18:44,000 --> 00:18:47,000
this.
He got the shape right,

249
00:18:47,000 --> 00:18:50,000
but he wanted to get the
intensity right,

250
00:18:50,000 --> 00:18:53,000
too.
What he realized he had to do

251
00:18:53,000 --> 00:18:57,000
was he essentially needed to
have a scaling factor,

252
00:18:57,000 --> 00:19:04,000
actually, in front of his
frequencies of his oscillators.

253
00:19:04,000 --> 00:19:07,000
He wanted a constant.
And so he said,

254
00:19:07,000 --> 00:19:13,000
what constant do I have to have
in order to make all of these

255
00:19:13,000 --> 00:19:18,000
data fit the observation?
That constant is Planck's

256
00:19:18,000 --> 00:19:22,000
constant, his own 6.626x10^-34
joule seconds.

257
00:19:22,000 --> 00:19:26,000
There it is.
That is Planck's constant.

258
00:19:26,000 --> 00:19:31,000
That is it.
There is nothing deeper here.

259
00:19:31,000 --> 00:19:36,000
It is a natural constant.
It comes from our observations

260
00:19:36,000 --> 00:19:39,000
of the world,
of nature.

261
00:19:39,000 --> 00:19:42,000
That is it.
It is a fitting constant.

262
00:19:42,000 --> 00:19:47,000
And so that is why Einstein was
so amazed, here,

263
00:19:47,000 --> 00:19:54,000
when he realized this number is
the same as what comes out of

264
00:19:54,000 --> 00:19:57,000
here.
There must be something very

265
00:19:57,000 --> 00:20:04,000
fundamental about this h,
this Planck's constant.

266
00:20:04,000 --> 00:20:09,000
That is the story.
Isn't that amazing?

267
00:20:09,000 --> 00:20:16,000
What Einstein then proceeded to
do, of course,

268
00:20:16,000 --> 00:20:24,000
is to write down the equation
of the straight line that he

269
00:20:24,000 --> 00:20:33,000
just put through these data.
And so that equation is the

270
00:20:33,000 --> 00:20:38,000
kinetic energy equal to nu,
which is our x,

271
00:20:38,000 --> 00:20:44,000
h, which is the slope.
And then what he found was that

272
00:20:44,000 --> 00:20:50,000
the intercept here,
of course, is minus h times nu

273
00:20:50,000 --> 00:20:56,000
nought.
This is plus minus h times nu

274
00:20:56,000 --> 00:21:02,000
nought.
And that is the equation of a

275
00:21:02,000 --> 00:21:05,000
straight line.
Of course, he realized,

276
00:21:05,000 --> 00:21:11,000
if this is energy on this side,
boy, there better be energy on

277
00:21:11,000 --> 00:21:14,000
this side.
And so this h times nu

278
00:21:14,000 --> 00:21:18,000
better be an energy.
And since this nu was the

279
00:21:18,000 --> 00:21:22,000
frequency of the incident
radiation, therefore,

280
00:21:22,000 --> 00:21:27,000
h times nu better be the energy
of the incident radiation,

281
00:21:27,000 --> 00:21:32,000
E sub i.
That is where this expression,

282
00:21:32,000 --> 00:21:36,000
energy equals h times nu
comes from.

283
00:21:36,000 --> 00:21:40,000
Nothing more.
That is where it comes from,

284
00:21:40,000 --> 00:21:45,000
the photoelectric effect.
This was the first time that

285
00:21:45,000 --> 00:21:50,000
there was any relationship
between the frequency of the

286
00:21:50,000 --> 00:21:53,000
radiation and the energy of the
radiation.

287
00:21:53,000 --> 00:21:58,000
In classical electromagnetism,
there is no relationship

288
00:21:58,000 --> 00:22:03,000
between the frequency and the
energy.

289
00:22:03,000 --> 00:22:08,000
This was the first time in
which that relationship was

290
00:22:08,000 --> 00:22:12,000
observed.
And what this is saying is the

291
00:22:12,000 --> 00:22:16,000
following.
This is saying that you can

292
00:22:16,000 --> 00:22:23,000
have any frequency of radiation
you want, but the corresponding

293
00:22:23,000 --> 00:22:30,000
energy comes in these chunks of
h times nu.

294
00:22:30,000 --> 00:22:35,000
h is a quantization constant.
Radiation, nu,

295
00:22:35,000 --> 00:22:41,000
is continuous,
but the energy that corresponds

296
00:22:41,000 --> 00:22:48,000
to any given frequency of
radiation is h times nu.

297
00:22:48,000 --> 00:22:56,000
This E equals h times nu,
here, is thought of as a

298
00:22:56,000 --> 00:23:02,000
quantum of energy.
A particle of energy.

299
00:23:02,000 --> 00:23:08,000
A chunk of energy.
Later on, it became the photon,

300
00:23:08,000 --> 00:23:15,000
the energy of a photon.
If this h times nu here

301
00:23:15,000 --> 00:23:20,000
was an energy,
well, this h times nu nought

302
00:23:20,000 --> 00:23:25,000
also better be an  energy.

303
00:23:25,000 --> 00:23:32,000
It is the threshold energy.
Let's draw an energy level

304
00:23:32,000 --> 00:23:36,000
diagram to try to understand
that.

305
00:23:36,000 --> 00:23:40,000
I am going to plot an energy
here.

306
00:23:40,000 --> 00:23:44,000
Let's draw an energy level for
an electron.

307
00:23:44,000 --> 00:23:49,000
This is an electron,
here, bound to the metal.

308
00:23:49,000 --> 00:23:56,000
And we know that it takes some
energy to rip this electron off

309
00:23:56,000 --> 00:24:01,000
of the metal.
Up here, at higher energy,

310
00:24:01,000 --> 00:24:03,000
is going to be our free
electron.

311
00:24:03,000 --> 00:24:06,000
I will just call it
electron-free,

312
00:24:06,000 --> 00:24:11,000
not bound to the metal anymore.
And the energy that is required

313
00:24:11,000 --> 00:24:15,000
to pull the electron off,
from the bound state to its

314
00:24:15,000 --> 00:24:20,000
free state, is this threshold
energy, h times nu nought.

315
00:24:20,000 --> 00:24:23,000
This threshold energy is like

316
00:24:23,000 --> 00:24:27,000
an ionization potential.
You know what the ionization

317
00:24:27,000 --> 00:24:32,000
potential is.
Just the energy required to

318
00:24:32,000 --> 00:24:35,000
pull an electron off an atom or
a molecule.

319
00:24:35,000 --> 00:24:40,000
However, when we are pulling an
electron off a chunk of a metal,

320
00:24:40,000 --> 00:24:43,000
we actually have another name
for it.

321
00:24:43,000 --> 00:24:47,000
It is called the work function.
That is just historical,

322
00:24:47,000 --> 00:24:51,000
but it is the same thing as an
ionization potential.

323
00:24:51,000 --> 00:24:54,000
And we often give it the symbol
phi.

324
00:24:54,000 --> 00:24:58,000
That threshold energy,
ionization energy for a metal,

325
00:24:58,000 --> 00:25:01,000
is the work function,
here, h times nu,

326
00:25:01,000 --> 00:25:06,000
phi.
The important point here is

327
00:25:06,000 --> 00:25:11,000
this.
In order to get an electron off

328
00:25:11,000 --> 00:25:17,000
of the metal,
what you have to have is

329
00:25:17,000 --> 00:25:24,000
energy, E sub i.
That energy E sub i has to be

330
00:25:24,000 --> 00:25:32,000
equal to at least the threshold
energy, h times nu nought.

331
00:25:32,000 --> 00:25:37,000
If you come in with energy of

332
00:25:37,000 --> 00:25:41,000
this radiation,
of this wavelength and that

333
00:25:41,000 --> 00:25:45,000
frequency, you pulled the
electron off,

334
00:25:45,000 --> 00:25:50,000
and then the electron is off
the metal and it just kind of

335
00:25:50,000 --> 00:25:53,000
stays there.
It doesn't move away.

336
00:25:53,000 --> 00:25:57,000
But you can also come in with
energy here, E sub i,

337
00:25:57,000 --> 00:26:03,000
that is greater than this work
function, than the threshold

338
00:26:03,000 --> 00:26:07,000
energy.
And you can pull the electron

339
00:26:07,000 --> 00:26:09,000
off.
But then, the electron is

340
00:26:09,000 --> 00:26:14,000
actually going to move away from
the metal, and the energy with

341
00:26:14,000 --> 00:26:18,000
which it moves away from the
metal, its kinetic energy,

342
00:26:18,000 --> 00:26:23,000
is just the incident energy
minus this threshold energy.

343
00:26:23,000 --> 00:26:27,000
It is the excess energy here.
And I am going to write it as

344
00:26:27,000 --> 00:26:33,000
the kinetic energy.
From that energy level diagram,

345
00:26:33,000 --> 00:26:37,000
this energy,
the incident energy,

346
00:26:37,000 --> 00:26:43,000
has to be equal to the work
function, h nu nought,

347
00:26:43,000 --> 00:26:48,000
plus the kinetic energy.

348
00:26:48,000 --> 00:26:54,000
Or, if I turned this around,
the kinetic energy is equal to

349
00:26:54,000 --> 00:27:02,000
the incident energy minus h nu
nought.

350
00:27:02,000 --> 00:27:06,000
The actual expression for the
energy that Einstein found,

351
00:27:06,000 --> 00:27:08,000
I just turned that equation
around.

352
00:27:08,000 --> 00:27:11,000
This is an equation that you
have to know.

353
00:27:11,000 --> 00:27:14,000
I will not give this to you on
an exam.

354
00:27:14,000 --> 00:27:17,000
Now, you don't have to memorize
it.

355
00:27:17,000 --> 00:27:21,000
You just have to reason it.
Draw yourself an energy

356
00:27:21,000 --> 00:27:23,000
diagram.
You know conservation of

357
00:27:23,000 --> 00:27:26,000
energy.
The sum of these two energies

358
00:27:26,000 --> 00:27:30,000
has to equal the incident
energy.

359
00:27:30,000 --> 00:27:37,000
Then you will be all set.
Now, what is very important

360
00:27:37,000 --> 00:27:44,000
here is the following.
If I come in with radiation

361
00:27:44,000 --> 00:27:50,000
that is, say,
a half of the threshold energy.

362
00:27:50,000 --> 00:27:58,000
Suppose I come in with two
photons, where each photon is

363
00:27:58,000 --> 00:28:03,000
one half h nu --

364
00:28:08,000 --> 00:28:12,000
The bottom line is that you are
not going to get an electron

365
00:28:12,000 --> 00:28:15,000
off.
Even though you are coming in

366
00:28:15,000 --> 00:28:19,000
with two photons,
which together are going to

367
00:28:19,000 --> 00:28:23,000
give you the threshold energy,
you won't get a photon off.

368
00:28:23,000 --> 00:28:28,000
You have to come in with at
least the energy of the work

369
00:28:28,000 --> 00:28:33,000
function.
A photon has to have at least

370
00:28:33,000 --> 00:28:37,000
this energy to get an electron
off.

371
00:28:37,000 --> 00:28:42,000
That is the particle-like
nature of radiation.

372
00:28:42,000 --> 00:28:47,000
Energy comes in chunks,
in particles of energy,

373
00:28:47,000 --> 00:28:53,000
in quanta of energy.
Likewise, if I came in here

374
00:28:53,000 --> 00:29:00,000
with a photon that had twice the
energy of the work function or

375
00:29:00,000 --> 00:29:05,000
the threshold energy,
I would still only get one

376
00:29:05,000 --> 00:29:11,000
electron off.
I would not get two electrons

377
00:29:11,000 --> 00:29:15,000
off, even though energetically
you would be able,

378
00:29:15,000 --> 00:29:19,000
in principle,
to get two electrons off.

379
00:29:19,000 --> 00:29:23,000
But you won't.
You will only get one electron

380
00:29:23,000 --> 00:29:26,000
off.
Whenever you send a photon in,

381
00:29:26,000 --> 00:29:31,000
if it has enough energy,
that is if its energy is equal

382
00:29:31,000 --> 00:29:35,000
to or greater than the work
function, you will get an

383
00:29:35,000 --> 00:29:40,000
electron off.
There is one electron for every

384
00:29:40,000 --> 00:29:44,000
photon.
You never get two electrons for

385
00:29:44,000 --> 00:29:48,000
every photon,
or you can never get one

386
00:29:48,000 --> 00:29:52,000
electron for two photons that
are lower energy.

387
00:29:52,000 --> 00:29:56,000
That is the particle quantum
nature of radiation.

388
00:29:56,000 --> 00:30:00,000
That is important.
Yes?

389
00:30:08,000 --> 00:30:18,000
What is the form of the photon?
What do you mean by form?

390
00:30:18,000 --> 00:30:25,000
Oh, you want a picture of the
photon.

391
00:30:25,000 --> 00:30:33,000
You're looking at them.
You cannot draw a picture of a

392
00:30:33,000 --> 00:30:39,000
photon because you want to
relate it to something that is

393
00:30:39,000 --> 00:30:42,000
within your classical
experience.

394
00:30:42,000 --> 00:30:48,000
And you cannot do that.
It isn't a classical particle.

395
00:30:48,000 --> 00:30:53,000
That is what you're working
with right here.

396
00:30:53,000 --> 00:30:59,000
You are trying to use your
experiences, that are everyday

397
00:30:59,000 --> 00:31:05,000
experiences, to explain
something that isn't within your

398
00:31:05,000 --> 00:31:13,000
everyday experiences.
You don't have a frame or a

399
00:31:13,000 --> 00:31:18,000
format to do that.
Yeah?

400
00:31:30,000 --> 00:31:33,000
Yes.
If you have a constant flux of

401
00:31:33,000 --> 00:31:39,000
photons onto the surface,
you will have a constant flux

402
00:31:39,000 --> 00:31:44,000
of electrons.
Now, there is a probability.

403
00:31:44,000 --> 00:31:50,000
It is not necessarily the case
that every photon gets in,

404
00:31:50,000 --> 00:31:56,000
will eject electrons,
because there are other kinds

405
00:31:56,000 --> 00:32:02,000
of competing processes.
Whatever the rate with which

406
00:32:02,000 --> 00:32:07,000
the photons come in.
It depends on the flux of the

407
00:32:07,000 --> 00:32:11,000
photons.
And we will have some problems

408
00:32:11,000 --> 00:32:17,000
like that, where we are going to
assume that the probability of

409
00:32:17,000 --> 00:32:23,000
the electron coming off is going
to be one, so one electron for

410
00:32:23,000 --> 00:32:26,000
every photon.
But, in reality,

411
00:32:26,000 --> 00:32:32,000
there are competing processes.
Are all electrons being

412
00:32:32,000 --> 00:32:35,000
ejected?
Actually, some electrons.

413
00:32:35,000 --> 00:32:39,000
Again, this goes to the
probability.

414
00:32:39,000 --> 00:32:47,000
Some are actually kind of going
in, too, into deeper the metal.

415
00:32:53,000 --> 00:32:55,000
Not the probability,
right.

416
00:32:55,000 --> 00:33:01,000
The rate at which the electrons
come out with is dependent on

417
00:33:01,000 --> 00:33:06,000
the intensity.
The more photons you send in,

418
00:33:06,000 --> 00:33:12,000
the larger the number of
photons per second coming in,

419
00:33:12,000 --> 00:33:18,000
the larger the number of
electrons per second coming out.

420
00:33:18,000 --> 00:33:23,000
This is a plot,
here, of the energy of the

421
00:33:23,000 --> 00:33:26,000
electrons.
That's all right.

422
00:33:26,000 --> 00:33:30,000
Other questions?
Yeah?

423
00:33:35,000 --> 00:33:36,000
Eventually.
Yes.

424
00:33:36,000 --> 00:33:39,000
Absolutely.
There are other problems that

425
00:33:39,000 --> 00:33:43,000
will come in.
Usually, your light source

426
00:33:43,000 --> 00:33:48,000
isn't so energetic that you
could possibly do that.

427
00:33:48,000 --> 00:33:53,000
Now, also usually what happens
is that you've got your metal

428
00:33:53,000 --> 00:33:58,000
grounded, so that as you lose
electrons, new electrons come in

429
00:33:58,000 --> 00:34:03,000
and fill it up to the fermi
level.

430
00:34:03,000 --> 00:34:06,000
And so you don't charge up your
sample.

431
00:34:06,000 --> 00:34:10,000
In an experiment,
if you had your metal just not

432
00:34:10,000 --> 00:34:15,000
grounded and you did shine some
radiation, what would happen is

433
00:34:15,000 --> 00:34:18,000
the metal would start to charge
up.

434
00:34:18,000 --> 00:34:23,000
Then, that would make it
difficult to get electrons off.

435
00:34:23,000 --> 00:34:25,000
Yes?

436
00:34:35,000 --> 00:34:37,000
Yes.
How strongly those electrons

437
00:34:37,000 --> 00:34:42,000
are bound to the metal depends
on the electronic structure of

438
00:34:42,000 --> 00:34:44,000
the metal.
And we are going to talk a

439
00:34:44,000 --> 00:34:49,000
little bit about what determines
the strength of the interaction

440
00:34:49,000 --> 00:34:53,000
for electrons on atoms and
molecules, but it is similar to

441
00:34:53,000 --> 00:34:57,000
what it is for metals.
That is coming in a few days.

442
00:34:57,000 --> 00:34:59,000
Yes?

443
00:35:04,000 --> 00:35:05,000
Yes, there is.
Right.

444
00:35:05,000 --> 00:35:08,000
You don't actually have to have
a metal.

445
00:35:08,000 --> 00:35:11,000
You could do it.
There are usually higher

446
00:35:11,000 --> 00:35:14,000
frequencies on insulators and
semiconductors,

447
00:35:14,000 --> 00:35:17,000
right.
It is harder to see the effect,

448
00:35:17,000 --> 00:35:19,000
but it can be done and has been
done.

449
00:35:19,000 --> 00:35:24,000
Well, what I want to do right
now is to show you an experiment

450
00:35:24,000 --> 00:35:27,000
we are going to do.
We are going to do a

451
00:35:27,000 --> 00:35:30,000
photoelectron experiment.

452
00:35:45,000 --> 00:35:53,000
And the experiment is this.
We have a device up here.

453
00:35:53,000 --> 00:36:00,000
What we have is an aluminum
plate.

454
00:36:00,000 --> 00:36:05,000
And that aluminum plate is
mounted on this blue metal rod.

455
00:36:05,000 --> 00:36:10,000
And in the middle of this rod
is a needle on a pivot.

456
00:36:10,000 --> 00:36:14,000
And this is a fairly
frictionless pivot.

457
00:36:14,000 --> 00:36:17,000
This black ring,
here, is just a support

458
00:36:17,000 --> 00:36:22,000
structure, an insulating support
structure.

459
00:36:22,000 --> 00:36:27,000
What we are going to do is put
some excess charge on this

460
00:36:27,000 --> 00:36:32,000
aluminum plate.
And that excess charge is going

461
00:36:32,000 --> 00:36:35,000
to run down this metal rod and
then onto this needle.

462
00:36:35,000 --> 00:36:40,000
And because that excess charge,
the electrons on the needle and

463
00:36:40,000 --> 00:36:43,000
the electrons on the metal rod
are repulsive,

464
00:36:43,000 --> 00:36:45,000
since this is rather
frictionless,

465
00:36:45,000 --> 00:36:49,000
that needle is going to move
because of the repulsive

466
00:36:49,000 --> 00:36:52,000
interactions between these
electrons.

467
00:36:52,000 --> 00:36:56,000
What we're then going to do is
try to do the photoelectron

468
00:36:56,000 --> 00:37:00,000
experiment.
We are going to take some UV

469
00:37:00,000 --> 00:37:07,000
radiation and shine it on this
metal and drive the electrons

470
00:37:07,000 --> 00:37:09,000
off.
And we should see,

471
00:37:09,000 --> 00:37:14,000
then, the needle swing back to
its original position.

472
00:37:14,000 --> 00:37:20,000
I need a couple of volunteers
in order to do this experiment

473
00:37:20,000 --> 00:37:22,000
here.
Come on up.

474
00:37:22,000 --> 00:37:24,000
All right.
Fantastic.

475
00:37:24,000 --> 00:37:27,000
I think that is all right.
Good.

476
00:37:27,000 --> 00:37:32,000
Okay.
One of you needs to be the

477
00:37:32,000 --> 00:37:35,000
charger, and the other needs to
be the discharger.

478
00:37:35,000 --> 00:37:38,000
Which one?
You want to discharge?

479
00:37:38,000 --> 00:37:41,000
Discharge, okay.
You come over here.

480
00:37:41,000 --> 00:37:45,000
And what you are going to do is
discharge the aluminum plate

481
00:37:45,000 --> 00:37:48,000
after we get some excess charge
on it.

482
00:37:48,000 --> 00:37:52,000
You are going to do it just by
holding it up to here.

483
00:37:52,000 --> 00:37:57,000
You have to get it kind of
close because it is not a very

484
00:37:57,000 --> 00:38:03,000
intense UV source.
Could you get the video cam on

485
00:38:03,000 --> 00:38:09,000
the side or on the center to get
where we are putting it?

486
00:38:09,000 --> 00:38:13,000
I guess we are putting it on
the side, right?

487
00:38:13,000 --> 00:38:15,000
Okay.
There we go.

488
00:38:15,000 --> 00:38:19,000
There is the device.
You are the charger.

489
00:38:19,000 --> 00:38:24,000
What we are going to do,
to get the excess charge,

490
00:38:24,000 --> 00:38:30,000
we are taking a piece of
natural fur.

491
00:38:30,000 --> 00:38:33,000
We are going to rub it on this
Lucite rod.

492
00:38:33,000 --> 00:38:37,000
You have to keep your fingers
on the yellow tape here.

493
00:38:37,000 --> 00:38:41,000
And we are going to transfer
some of the natural oils here

494
00:38:41,000 --> 00:38:44,000
onto this rod.
And there are plenty of

495
00:38:44,000 --> 00:38:47,000
negative ions around here and
free electrons.

496
00:38:47,000 --> 00:38:52,000
That oil likes those negative
charges, and so there are going

497
00:38:52,000 --> 00:38:57,000
to be excess negative charges on
this Lucite rod.

498
00:38:57,000 --> 00:39:03,000
And then you are going to come
over here and just touch the

499
00:39:03,000 --> 00:39:08,000
edge of this and let the
electrons flow onto there.

500
00:39:08,000 --> 00:39:13,000
Are you right-handed?
You have to rub that really,

501
00:39:13,000 --> 00:39:16,000
really hard.
[LAUGHTER] Great.

502
00:39:16,000 --> 00:39:19,000
Go over there.
Touch the end.

503
00:39:19,000 --> 00:39:23,000
Cool.
Why don't you give it another

504
00:39:23,000 --> 00:39:30,000
jolt here and we will really
move that needle over.

505
00:39:30,000 --> 00:39:31,000
Okay.
Discharger.

506
00:39:31,000 --> 00:39:33,000
We have to give it another
jolt.

507
00:39:33,000 --> 00:39:36,000
That is okay.
You may have touched it with

508
00:39:36,000 --> 00:39:40,000
something else and discharged it
a little bit.

509
00:39:40,000 --> 00:39:43,000
No, that's okay.
You have to get the hang of

510
00:39:43,000 --> 00:39:46,000
this, here.
You are doing fantastic.

511
00:39:46,000 --> 00:39:49,000
Take it off.
That's what it is.

512
00:39:49,000 --> 00:39:53,000
You are holding it on too long.
Okay, that is pretty good.

513
00:39:53,000 --> 00:39:57,000
Put it in front there.
Get it a little bit closer.

514
00:39:57,000 --> 00:40:02,000
Here comes the UV radiation.
We did it.

515
00:40:02,000 --> 00:40:06,000
Try it again really hard.
Just touch it.

516
00:40:06,000 --> 00:40:09,000
Take it off.
Do it again.

517
00:40:09,000 --> 00:40:14,000
You need to do it again.
You've got to get it right

518
00:40:14,000 --> 00:40:16,000
here.
Not too much,

519
00:40:16,000 --> 00:40:18,000
not too little.
Okay.

520
00:40:18,000 --> 00:40:22,000
It is doing it.
Discharge in front.

521
00:40:22,000 --> 00:40:27,000
Electrons off.
Now we have to do a control

522
00:40:27,000 --> 00:40:33,000
experiment.
That is, you have got to charge

523
00:40:33,000 --> 00:40:38,000
it up again, but now,
when you put the light there,

524
00:40:38,000 --> 00:40:44,000
what I am going to do is hold
up a Pyrex plate in between the

525
00:40:44,000 --> 00:40:49,000
light and the metal.
It is going to block the

526
00:40:49,000 --> 00:40:53,000
radiation, and it should not
discharge.

527
00:40:53,000 --> 00:40:57,000
You need to get on there.
Fantastic.

528
00:40:57,000 --> 00:41:02,000
There it goes.
Here is the plate.

529
00:41:02,000 --> 00:41:07,000
Get it to a little bit lower.
Do a good discharge.

530
00:41:07,000 --> 00:41:12,000
[APPLAUSE] Fantastic.
Thank you very much.

531
00:41:12,000 --> 00:41:15,000
Thank you for being a good
sport.

532
00:41:15,000 --> 00:41:19,000
That is the photoelectron
experiment.

533
00:41:19,000 --> 00:41:24,000
Hey, it works.
Well, what I want to do now is

534
00:41:24,000 --> 00:41:32,000
just spend a few minutes working
on a few problems.

535
00:41:32,000 --> 00:41:36,000
I think these are pretty
straightforward,

536
00:41:36,000 --> 00:41:42,000
but I just want to make sure
that everybody is on the same

537
00:41:42,000 --> 00:41:47,000
page here in terms of being able
to do the homework.

538
00:41:47,000 --> 00:41:53,000
Here is the first problem.
The first problem says,

539
00:41:53,000 --> 00:41:57,000
how many photons?
And remember what we said a

540
00:41:57,000 --> 00:42:02,000
photon was?
E equals h nu.

541
00:42:02,000 --> 00:42:07,000
This is the number of joules.
Implied is the number of joules

542
00:42:07,000 --> 00:42:11,000
per photon, although we don't
usually write this,

543
00:42:11,000 --> 00:42:15,000
but that is what that is,
joules per photon.

544
00:42:15,000 --> 00:42:20,000
You may want to write it as you
do these problems.

545
00:42:20,000 --> 00:42:28,000
How many photons associated
with radiation of a wavelength

546
00:42:28,000 --> 00:42:35,000
lambda equals one picometer,
which is 1.0x10^-12 meters,

547
00:42:35,000 --> 00:42:42,000
how many of these do you need
in order to create,

548
00:42:42,000 --> 00:42:49,000
say, a laser pulse of energy
that is one joule?

549
00:42:49,000 --> 00:42:55,000
Lasers are pulsed,
so I am talking about a pulse

550
00:42:55,000 --> 00:43:02,000
of energy, one joule.
You want to draw yourself a

551
00:43:02,000 --> 00:43:06,000
picture, here.
We are drawing a picture of one

552
00:43:06,000 --> 00:43:08,000
pulse of energy,
one joule.

553
00:43:08,000 --> 00:43:13,000
Now, we have not been given the
frequency, here,

554
00:43:13,000 --> 00:43:17,000
of this radiation,
but we know the wavelength,

555
00:43:17,000 --> 00:43:21,000
and we know the relationship
between frequency and

556
00:43:21,000 --> 00:43:25,000
wavelength.
It is just c over lambda.

557
00:43:25,000 --> 00:43:30,000
I know what lambda is.
I can calculate nu.

558
00:43:30,000 --> 00:43:34,000
And, when I do that,
I find that the energy of the

559
00:43:34,000 --> 00:43:40,000
photon, hc over lambda,
that energy of the

560
00:43:40,000 --> 00:43:44,000
photon is 1.99x10^-13 joules per
photon.

561
00:43:44,000 --> 00:43:50,000
And I am using one more figure
than is significant since this

562
00:43:50,000 --> 00:43:55,000
an intermediate step in the
calculation.

563
00:43:55,000 --> 00:44:02,000
If I want a pulse of one joule
of energy and I am asked how

564
00:44:02,000 --> 00:44:10,000
many photons do I need to get
that, and each photon is

565
00:44:10,000 --> 00:44:16,000
1.99x10^-13 joules,
well, that means that I am

566
00:44:16,000 --> 00:44:24,000
going to need 5.0x10^12 photons.
There was a question here?

567
00:44:24,000 --> 00:44:30,000
All right.
Let's work another one.

568
00:44:30,000 --> 00:44:34,000
Here, we want to define what we
mean by power.

569
00:44:34,000 --> 00:44:40,000
This says the power of
radiation from the continuous

570
00:44:40,000 --> 00:44:44,000
laser is three milliwatts.

571
00:44:44,000 --> 00:44:50,000
We have some laser,
and the power of that radiation

572
00:44:50,000 --> 00:44:55,000
coming out is three milliwatts.
Well, what is power?

573
00:44:55,000 --> 00:45:02,000
Power is energy per unit time.
It is the energy delivered or

574
00:45:02,000 --> 00:45:06,000
the energy expended per unit
time.

575
00:45:06,000 --> 00:45:11,000
The unit of power that we are
going to use is a watt.

576
00:45:11,000 --> 00:45:16,000
A watt is a joule per second.
We are told that we have

577
00:45:16,000 --> 00:45:22,000
radiation of three milliwatts.
That is 3.0x10^-3 joules per

578
00:45:22,000 --> 00:45:25,000
second.
And the question asks,

579
00:45:25,000 --> 00:45:30,000
how long will it take for a
total energy of one joule to be

580
00:45:30,000 --> 00:45:36,000
supplied?
Well, one joule.

581
00:45:36,000 --> 00:45:47,000
And we have the rate of energy
supply as 3x10^-3 joules per

582
00:45:47,000 --> 00:45:54,000
second.
That gives us 330 seconds.

583
00:45:54,000 --> 00:46:04,000
That is straightforward.
Finally, we have one more.

584
00:46:04,000 --> 00:46:11,000
It says, how many photons per
second of, again,

585
00:46:11,000 --> 00:46:17,000
the same radiation,
of the wavelength of one

586
00:46:17,000 --> 00:46:22,000
picometer.
That means, again,

587
00:46:22,000 --> 00:46:29,000
we are dealing with photons
that have an energy of

588
00:46:29,000 --> 00:46:39,000
1.99x10^-13 joules per photon.
How many photons per second,

589
00:46:39,000 --> 00:46:45,000
the rate of photons at the
wavelength do you have to have,

590
00:46:45,000 --> 00:46:49,000
or do you have,
if the power of the radiation

591
00:46:49,000 --> 00:46:54,000
is three milliwatts?
Well, the power of the

592
00:46:54,000 --> 00:47:00,000
radiation is 3.0x10^-3 joules
per second, --

593
00:47:00,000 --> 00:47:06,000
-- and we have 1.99x10^-13
joules per photon.

594
00:47:11,000 --> 00:47:18,000
In order to have this kind of
power, what we have to have

595
00:47:18,000 --> 00:47:25,000
being emitted is 1.5x10^10
photons per second.

596
00:47:34,000 --> 00:47:38,000
All right.
The photoelectric effect is one

597
00:47:38,000 --> 00:47:43,000
of the experiments that
demonstrated the particle-like

598
00:47:43,000 --> 00:47:46,000
nature of light,
of radiation.

599
00:47:46,000 --> 00:47:52,000
Particle-like nature because
you have to have these chunks of

600
00:47:52,000 --> 00:47:57,000
energy to make some process
occur.

601
00:47:57,000 --> 00:48:03,000
Next time, we are going to look
at and will just talk briefly

602
00:48:03,000 --> 00:48:09,000
about the other experiments that
demonstrated the particle-like

603
00:48:09,000 --> 00:48:14,000
nature of radiation.
And that other experiment is

604
00:48:14,000 --> 00:48:18,000
the demonstration that a photon
has momentum,

605
00:48:18,000 --> 00:48:22,000
even though it doesn't have any
mass.

606
00:48:22,562 --> 00:48:25,000
See you Wednesday.
See you Friday.