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PROFESSOR: OK, let's just
take 10 more seconds.

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00:01:15,493 --> 00:01:15,993
OK.

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00:01:19,860 --> 00:01:23,698
Does someone want to
explain the answer here?

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00:01:32,550 --> 00:01:35,010
I'm not sure if this is on.

12
00:01:35,010 --> 00:01:37,310
Give it a try.

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00:01:37,310 --> 00:01:38,920
AUDIENCE: So it
says in the problem

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that the X-rays have
the same wavelength,

15
00:01:41,000 --> 00:01:43,220
so you know that they also
have the same frequency,

16
00:01:43,220 --> 00:01:46,280
so that discounts
1, 2, and 5 and 6.

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00:01:46,280 --> 00:01:48,100
So then it's just a
choice between 3 and 4.

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00:01:48,100 --> 00:01:50,890
And in the video
the other day, you

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00:01:50,890 --> 00:01:53,300
said in order to
image these proteins,

20
00:01:53,300 --> 00:01:54,640
you need high intensity light.

21
00:01:54,640 --> 00:01:56,380
So, 3.

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00:01:56,380 --> 00:01:57,590
PROFESSOR: Yup.

23
00:01:57,590 --> 00:01:58,750
That's a great explanation.

24
00:01:58,750 --> 00:02:00,850
Here, I don't really
know what these-- these

25
00:02:00,850 --> 00:02:01,950
might come in handy today.

26
00:02:01,950 --> 00:02:02,491
I don't know.

27
00:02:06,190 --> 00:02:06,950
OK.

28
00:02:06,950 --> 00:02:10,050
Yeah, so the trick was
better quality data,

29
00:02:10,050 --> 00:02:12,210
so you probably figured
out that that, then,

30
00:02:12,210 --> 00:02:15,370
was the higher intensity.

31
00:02:15,370 --> 00:02:17,120
So this is a true thing.

32
00:02:17,120 --> 00:02:19,610
So we have data collection.

33
00:02:19,610 --> 00:02:22,620
There's equipment here
at home, and a lot

34
00:02:22,620 --> 00:02:25,370
of universities have what
they call home data collection

35
00:02:25,370 --> 00:02:30,900
equipment, but we often travel
to synchrotrons where we have

36
00:02:30,900 --> 00:02:34,550
higher intensity, i.e.
more photons per second,

37
00:02:34,550 --> 00:02:37,180
and then you get
better quality data.

38
00:02:37,180 --> 00:02:40,100
And so sometimes people
do these things remotely

39
00:02:40,100 --> 00:02:43,600
where you ship your samples
and someone else collects it,

40
00:02:43,600 --> 00:02:45,850
but my lab likes to go.

41
00:02:45,850 --> 00:02:48,300
And you stay up all night
and collect great data,

42
00:02:48,300 --> 00:02:51,280
and it's a bonding experience.

43
00:02:51,280 --> 00:02:53,920
You saw a little bit
of that on the video.

44
00:02:53,920 --> 00:02:55,690
OK.

45
00:02:55,690 --> 00:03:00,030
We ended last time looking
at the Schroedinger equation

46
00:03:00,030 --> 00:03:02,600
and seeing that the
Schroedinger equation could

47
00:03:02,600 --> 00:03:06,100
be solved for a hydrogen
atom, giving information

48
00:03:06,100 --> 00:03:08,300
about binding
energy, the binding

49
00:03:08,300 --> 00:03:11,650
of the electron to
its nucleus, and also

50
00:03:11,650 --> 00:03:14,454
a wave function, which we
haven't talked about yet.

51
00:03:14,454 --> 00:03:15,870
So we're going to
continue talking

52
00:03:15,870 --> 00:03:18,250
about this binding energy,
and then next week we're

53
00:03:18,250 --> 00:03:20,980
going to move into wave
functions, or orbitals.

54
00:03:20,980 --> 00:03:23,270
So the binding
energy that comes out

55
00:03:23,270 --> 00:03:25,270
of the Schroedinger
equation, no one

56
00:03:25,270 --> 00:03:27,100
should ever just believe things.

57
00:03:27,100 --> 00:03:29,830
It looks fancy, but
does it really work?

58
00:03:29,830 --> 00:03:32,880
Is it really doing
this right estimation?

59
00:03:32,880 --> 00:03:35,830
And again, it just came
out of Schroedinger's mind,

60
00:03:35,830 --> 00:03:39,310
so it's always nice to
verify that this equation is

61
00:03:39,310 --> 00:03:40,850
working pretty well.

62
00:03:40,850 --> 00:03:43,160
So today we're going
to talk about how

63
00:03:43,160 --> 00:03:46,100
we were able to verify
that the binding energy

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00:03:46,100 --> 00:03:49,820
that the Schroedinger equation
was predicting actually

65
00:03:49,820 --> 00:03:52,170
agrees with experiment.

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00:03:52,170 --> 00:03:55,640
So we're going to continue
talking about binding energies,

67
00:03:55,640 --> 00:03:58,680
then go on to the
verification, with a demo,

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00:03:58,680 --> 00:04:02,010
of how people were
able to show that there

69
00:04:02,010 --> 00:04:03,650
was good agreement here.

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00:04:03,650 --> 00:04:04,150
All right.

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00:04:04,150 --> 00:04:06,700
So let's continue
with binding energies.

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00:04:06,700 --> 00:04:09,680
So we're still talking about
the hydrogen atom and energy

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00:04:09,680 --> 00:04:14,360
levels, and we saw the last time
that the Schroedinger equation

74
00:04:14,360 --> 00:04:17,560
could be derived
for a hydrogen atom

75
00:04:17,560 --> 00:04:20,810
such that the binding
energy, or e to the n,

76
00:04:20,810 --> 00:04:26,520
was equal to minus this Rydberg
constant, RH, over n squared

77
00:04:26,520 --> 00:04:29,600
were n is the principle
quantum number.

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00:04:29,600 --> 00:04:31,590
And so this is what
we saw last time,

79
00:04:31,590 --> 00:04:34,880
and now we have a graphical
depiction of this.

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00:04:34,880 --> 00:04:39,780
And you'll note that this is
a negative value over here.

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00:04:39,780 --> 00:04:44,200
So if n is 1 and we have
the principle quantum

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00:04:44,200 --> 00:04:49,280
number of one, we have
minus RH over one squared.

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00:04:49,280 --> 00:04:51,550
And so we just have
the negative value

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00:04:51,550 --> 00:04:55,690
for the Rydberg constant,
2.18 times 10 to the minus

85
00:04:55,690 --> 00:04:57,760
18th joules.

86
00:04:57,760 --> 00:05:01,240
And as we go up
here in energy, we

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00:05:01,240 --> 00:05:04,440
would get to an energy of zero.

88
00:05:04,440 --> 00:05:10,240
And if energy here is zero,
what must be true about n?

89
00:05:10,240 --> 00:05:13,840
What kind of number is n here?

90
00:05:13,840 --> 00:05:15,860
Infinity, right.

91
00:05:15,860 --> 00:05:20,700
So if this is infinity,
that number goes to zero.

92
00:05:20,700 --> 00:05:25,020
And so if the electron
is infinitely far away

93
00:05:25,020 --> 00:05:28,550
from the nucleus, it's
basically a free electron.

94
00:05:28,550 --> 00:05:30,920
It doesn't feel any
kind of attraction.

95
00:05:30,920 --> 00:05:32,780
It's infinitely far away.

96
00:05:32,780 --> 00:05:36,130
Then your binding energy
would be zero, i.e.

97
00:05:36,130 --> 00:05:38,640
it's not bound,
and that would be

98
00:05:38,640 --> 00:05:42,180
true with this infinitely
far away distance.

99
00:05:42,180 --> 00:05:46,750
And then in between the n
equals 1, 2n equals infinity,

100
00:05:46,750 --> 00:05:49,790
we can use this equation
for the hydrogen atom

101
00:05:49,790 --> 00:05:54,280
to figure out what
these energy levels are.

102
00:05:54,280 --> 00:05:57,990
So when we have the
n equals 2 state,

103
00:05:57,990 --> 00:06:02,670
it would be minus RH
over 2 squared, or 4,

104
00:06:02,670 --> 00:06:05,720
and so we can calculate
what that number is here,

105
00:06:05,720 --> 00:06:12,160
minus 0.545 times 10 to
the minus 18th joules.

106
00:06:12,160 --> 00:06:17,710
N equals 3 so we have
RH over 3 squared.

107
00:06:17,710 --> 00:06:20,610
We can do the math over here.

108
00:06:20,610 --> 00:06:26,280
4-- you get the idea--
minus RH over 4 squared,

109
00:06:26,280 --> 00:06:30,510
and we have then over 5
squared, over 6 squared,

110
00:06:30,510 --> 00:06:35,230
and you can see the energy, and
you can calculate the energy

111
00:06:35,230 --> 00:06:37,750
levels here.

112
00:06:37,750 --> 00:06:38,250
All right.

113
00:06:38,250 --> 00:06:44,800
So when you have an electron in
this n equals 1 state, that's

114
00:06:44,800 --> 00:06:48,280
the lowest energy, it's
the most negative number,

115
00:06:48,280 --> 00:06:51,010
and that's known as
the ground state.

116
00:06:51,010 --> 00:06:54,200
And when you have an electron
in this ground state,

117
00:06:54,200 --> 00:06:59,100
that's the most stable
state for the hydrogen atom.

118
00:06:59,100 --> 00:07:03,070
So again, from these lower
ground state up to this state

119
00:07:03,070 --> 00:07:04,810
here.

120
00:07:04,810 --> 00:07:07,300
Now we're going to
introduce another term which

121
00:07:07,300 --> 00:07:13,370
you'll hear a lot, and
this is ionization energy.

122
00:07:13,370 --> 00:07:16,110
So the ionization energy,
the amount of energy

123
00:07:16,110 --> 00:07:21,580
you need to put in to ionize
an atom or release an electron.

124
00:07:21,580 --> 00:07:26,630
So the ionization energy of a
hydrogen atom in the nth state

125
00:07:26,630 --> 00:07:29,380
is going to be equal
to the binding energy,

126
00:07:29,380 --> 00:07:32,030
but the signs of these
are going to be different.

127
00:07:32,030 --> 00:07:36,480
So we have this equation where
binding energy equals minus IE,

128
00:07:36,480 --> 00:07:39,140
the ionization energy.

129
00:07:39,140 --> 00:07:43,900
So we talked about the fact that
the binding energy is negative,

130
00:07:43,900 --> 00:07:47,800
and the ionization energy
is always positive.

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00:07:47,800 --> 00:07:50,630
So for the binding energy, when
the binding energy is zero,

132
00:07:50,630 --> 00:07:52,520
it means the
electron isn't bound.

133
00:07:52,520 --> 00:07:54,930
So a negative value
for binding energy

134
00:07:54,930 --> 00:07:57,230
means that the
electron's being held

135
00:07:57,230 --> 00:08:00,420
by the nucleus-- the
electron's bound.

136
00:08:00,420 --> 00:08:02,980
For ionization energy,
that's the energy

137
00:08:02,980 --> 00:08:05,905
you need to add to the system
to release the electron,

138
00:08:05,905 --> 00:08:08,030
and you're always going to
need to add some energy,

139
00:08:08,030 --> 00:08:10,000
so that's a positive number.

140
00:08:10,000 --> 00:08:13,060
So when you think about
ionization energy,

141
00:08:13,060 --> 00:08:14,770
it's a positive
number that you're

142
00:08:14,770 --> 00:08:17,570
going to be expecting there.

143
00:08:17,570 --> 00:08:20,940
Now we can consider
this same diagram,

144
00:08:20,940 --> 00:08:23,990
and we already talked
about these energy levels

145
00:08:23,990 --> 00:08:27,850
and now we can think about these
in terms of ionization energies

146
00:08:27,850 --> 00:08:29,070
as well.

147
00:08:29,070 --> 00:08:31,030
So the difference
from this state,

148
00:08:31,030 --> 00:08:35,570
where energy is 0, to the
ground state down here,

149
00:08:35,570 --> 00:08:37,880
the ionization energy--
the energy that's

150
00:08:37,880 --> 00:08:42,070
needed to ionize an electron
that's in n equals 1 here,

151
00:08:42,070 --> 00:08:45,290
is going to be equal
to minus the binding

152
00:08:45,290 --> 00:08:49,310
energy of that electron in
that n equals one state.

153
00:08:49,310 --> 00:08:52,290
So again here, it's
not too hard if you

154
00:08:52,290 --> 00:08:55,190
know this information
and this equation

155
00:08:55,190 --> 00:08:58,530
to figure out what the
ionization energy is.

156
00:08:58,530 --> 00:09:01,960
So that's just, then, going
to be the positive value

157
00:09:01,960 --> 00:09:03,540
of the binding energy.

158
00:09:03,540 --> 00:09:05,880
So binding energy
minus Rydberg's

159
00:09:05,880 --> 00:09:11,310
constant here, 2.18 times
10 to the minus 18th joules.

160
00:09:11,310 --> 00:09:14,920
So the ionization energy,
then, for a hydrogen atom

161
00:09:14,920 --> 00:09:20,070
in the ground state is positive
2.180 times 10 to the minus

162
00:09:20,070 --> 00:09:20,760
18th.

163
00:09:20,760 --> 00:09:22,760
And I'm just going to try
to use the same number

164
00:09:22,760 --> 00:09:24,320
of significant figures.

165
00:09:24,320 --> 00:09:27,930
I always try to pay attention
to my significant figures.

166
00:09:27,930 --> 00:09:28,430
All right.

167
00:09:28,430 --> 00:09:34,530
So we can do this again
for the n equals 2 state,

168
00:09:34,530 --> 00:09:38,480
or the first excited state.

169
00:09:38,480 --> 00:09:41,040
So here's the n equals 2 state.

170
00:09:41,040 --> 00:09:44,290
So now we're going to be talking
about this differential energy

171
00:09:44,290 --> 00:09:46,970
here.

172
00:09:46,970 --> 00:09:50,780
So the ionization
energy for an electron

173
00:09:50,780 --> 00:09:53,120
in this first excited state.

174
00:09:53,120 --> 00:09:57,080
Again, that will be ionization
energy equals minus the binding

175
00:09:57,080 --> 00:10:00,490
energy for that state,
and so that's going to be,

176
00:10:00,490 --> 00:10:02,640
then, the positive value here.

177
00:10:02,640 --> 00:10:09,110
So the binding energy was minus,
if we change this to-- this

178
00:10:09,110 --> 00:10:14,910
is 18.5 to the 18, or 5.0
to the minus 19th joules.

179
00:10:14,910 --> 00:10:18,190
Try to keep the significant
figures the same.

180
00:10:18,190 --> 00:10:18,690
All right.

181
00:10:18,690 --> 00:10:21,155
So why don't you
give this a try now

182
00:10:21,155 --> 00:10:23,170
and we'll have a
clicker question.

183
00:11:14,440 --> 00:11:14,940
OK.

184
00:11:14,940 --> 00:11:15,606
10 more seconds.

185
00:11:34,870 --> 00:11:38,440
A very long one second.

186
00:11:38,440 --> 00:11:40,814
OK.

187
00:11:40,814 --> 00:11:41,314
Interesting.

188
00:11:44,220 --> 00:11:51,990
So maybe you can talk to
your neighbor and someone can

189
00:11:51,990 --> 00:11:53,590
tell me what the trick is here.

190
00:12:10,900 --> 00:12:11,440
OK.

191
00:12:11,440 --> 00:12:14,530
We have someone who is going
to tell us what the trick is.

192
00:12:19,360 --> 00:12:21,560
AUDIENCE: The ground
state is n equals one,

193
00:12:21,560 --> 00:12:24,830
and from there, the
excited states go up one.

194
00:12:24,830 --> 00:12:27,900
So the first excited
state is n equals 2,

195
00:12:27,900 --> 00:12:31,220
and then the third one
will be n equals 4.

196
00:12:31,220 --> 00:12:33,760
And since you're looking
for the ionization energy,

197
00:12:33,760 --> 00:12:37,950
you go to the energy
for n equals 4,

198
00:12:37,950 --> 00:12:42,810
and you multiply by negative
one, which is 40.14 10

199
00:12:42,810 --> 00:12:45,120
to the negative 18th.

200
00:12:45,120 --> 00:12:46,430
PROFESSOR: Great.

201
00:12:46,430 --> 00:12:49,520
Yeah, so let's see what I have.

202
00:12:49,520 --> 00:12:51,086
I need to get some more stuff.

203
00:12:51,086 --> 00:12:52,310
Sorry.

204
00:12:52,310 --> 00:12:52,900
OK.

205
00:12:52,900 --> 00:12:56,481
So the trick.

206
00:12:56,481 --> 00:12:57,480
It's not a hard problem.

207
00:12:57,480 --> 00:13:00,660
You just had to figure out what
the third excited state meant,

208
00:13:00,660 --> 00:13:03,610
so once you've figured
that out, it was

209
00:13:03,610 --> 00:13:05,350
pretty easy to get it right.

210
00:13:05,350 --> 00:13:06,120
OK.

211
00:13:06,120 --> 00:13:07,930
So keep that in mind.

212
00:13:07,930 --> 00:13:10,190
Now that you've potentially
made that mistake,

213
00:13:10,190 --> 00:13:12,600
you will not make
that one again.

214
00:13:12,600 --> 00:13:13,460
All right.

215
00:13:13,460 --> 00:13:17,540
So now we can think about this
also in more general terms--

216
00:13:17,540 --> 00:13:19,630
only slightly more
general terms,

217
00:13:19,630 --> 00:13:28,660
frankly-- which is to consider,
for other one electron ions,

218
00:13:28,660 --> 00:13:31,180
we can have a more
general equation.

219
00:13:31,180 --> 00:13:34,840
So we had, for
the hydrogen atom,

220
00:13:34,840 --> 00:13:39,640
the binding energy, En, is minus
Rydberg's constant, RH, over

221
00:13:39,640 --> 00:13:40,560
n squared.

222
00:13:40,560 --> 00:13:45,260
And now I've added z squared,
which is the atomic number.

223
00:13:45,260 --> 00:13:48,670
And for hydrogen, it's
1, so it wasn't around.

224
00:13:48,670 --> 00:13:50,330
We didn't need it before.

225
00:13:50,330 --> 00:13:55,470
But we can consider other ions
that also have one electron.

226
00:13:55,470 --> 00:13:59,370
They will also work
with this equation.

227
00:13:59,370 --> 00:14:02,530
So there's a couple of things
that kind of fall out of this.

228
00:14:02,530 --> 00:14:06,140
One, that an electron is
going to be bound more weakly

229
00:14:06,140 --> 00:14:12,150
when n is a big number here, and
so that makes sense from what

230
00:14:12,150 --> 00:14:14,500
we were looking at before.

231
00:14:14,500 --> 00:14:17,130
And that an electron
is also going

232
00:14:17,130 --> 00:14:21,254
to be bound more
tightly when z is big,

233
00:14:21,254 --> 00:14:23,670
and we haven't really talked
about that because we've just

234
00:14:23,670 --> 00:14:25,970
been talking about
the hydrogen atom,

235
00:14:25,970 --> 00:14:28,450
and so it always has the same z.

236
00:14:28,450 --> 00:14:30,280
But if you have a
different z, you're

237
00:14:30,280 --> 00:14:34,100
going to have a bigger
positively charged nucleus,

238
00:14:34,100 --> 00:14:37,490
and so it makes sense that
you would then have a tighter

239
00:14:37,490 --> 00:14:39,200
bonding electron.

240
00:14:39,200 --> 00:14:39,970
All right.

241
00:14:39,970 --> 00:14:42,560
So you might think, what
are other things that

242
00:14:42,560 --> 00:14:46,020
have just one electron that
this is going to apply to?

243
00:14:46,020 --> 00:14:47,450
And so far, of
course, we've just

244
00:14:47,450 --> 00:14:49,730
been talking about
our friend, hydrogen,

245
00:14:49,730 --> 00:14:52,720
that has its one
electron and z equals 1.

246
00:14:52,720 --> 00:14:57,400
But we have ions that can
also have one electron.

247
00:14:57,400 --> 00:15:02,510
So helium plus, and it has a z
of 2, but when it's helium plus

248
00:15:02,510 --> 00:15:05,200
it only has one electron.

249
00:15:05,200 --> 00:15:09,470
Lithium, plus 2, also
only has one electron,

250
00:15:09,470 --> 00:15:12,730
and it has a z of three.

251
00:15:12,730 --> 00:15:17,570
And then what about something
that's a one electron

252
00:15:17,570 --> 00:15:21,250
system with a plus 64.

253
00:15:21,250 --> 00:15:23,840
Without looking at your
periodic table, what does

254
00:15:23,840 --> 00:15:26,520
the z have to be here?

255
00:15:26,520 --> 00:15:27,590
Yeah.

256
00:15:27,590 --> 00:15:29,330
So, 65.

257
00:15:29,330 --> 00:15:31,450
So in working these
kinds of problems,

258
00:15:31,450 --> 00:15:36,410
if you're talking about a
one electron ion or atom

259
00:15:36,410 --> 00:15:39,280
and it's not hydrogen,
don't forget about z.

260
00:15:39,280 --> 00:15:41,546
And we need to have
that in our equation.

261
00:15:43,990 --> 00:15:44,490
All right.

262
00:15:44,490 --> 00:15:49,860
So talking about these
binding energies now,

263
00:15:49,860 --> 00:15:51,650
out of the
Schroedinger equation,

264
00:15:51,650 --> 00:15:53,960
you can calculate
ionization energies

265
00:15:53,960 --> 00:15:55,280
if you know the binding energy.

266
00:15:55,280 --> 00:15:56,990
All of this is
good, but how do we

267
00:15:56,990 --> 00:15:59,660
know that we can trust
the Schroedinger equation,

268
00:15:59,660 --> 00:16:02,460
that equations
really are working?

269
00:16:02,460 --> 00:16:04,790
So the way that they
figured this out

270
00:16:04,790 --> 00:16:08,630
is from experiment, and
particularly, experimentally

271
00:16:08,630 --> 00:16:12,830
figuring out what the energy
levels were, and thinking,

272
00:16:12,830 --> 00:16:15,380
does this match with the
Schroedinger equation?

273
00:16:15,380 --> 00:16:20,240
So they were able to use photon
emission to be able to do this.

274
00:16:20,240 --> 00:16:24,720
So let's consider what
photon emission is,

275
00:16:24,720 --> 00:16:28,570
and then we're going to prove
that this equation that I've

276
00:16:28,570 --> 00:16:31,430
been showing you actually holds.

277
00:16:31,430 --> 00:16:35,570
So photon emission,
this is a situation

278
00:16:35,570 --> 00:16:38,320
that occurs when
you have an electron

279
00:16:38,320 --> 00:16:44,590
going from a higher energy
initial state going to a lower

280
00:16:44,590 --> 00:16:46,660
energy state.

281
00:16:46,660 --> 00:16:50,070
And as it goes from
this high energy state

282
00:16:50,070 --> 00:16:54,320
to the low energy state, there's
a difference between these two

283
00:16:54,320 --> 00:16:56,870
energy states,
delta E, and that's

284
00:16:56,870 --> 00:16:59,710
going to be equal
to the higher energy

285
00:16:59,710 --> 00:17:03,940
initial state minus the
energy in the final state.

286
00:17:03,940 --> 00:17:07,670
So there's this difference in
energy between the two states,

287
00:17:07,670 --> 00:17:12,750
and the photon that gets
emitted when this energy

288
00:17:12,750 --> 00:17:17,310
transition happens has the
same energy as the difference

289
00:17:17,310 --> 00:17:18,359
between those.

290
00:17:18,359 --> 00:17:23,140
So the energy of the emitted
photon is also delta E.

291
00:17:23,140 --> 00:17:28,079
So you emit all of that energy
as you have that change.

292
00:17:28,079 --> 00:17:33,310
So the difference here-- we
can consider an actual case

293
00:17:33,310 --> 00:17:36,360
where we're going from
an energy difference of n

294
00:17:36,360 --> 00:17:41,660
equals 6 to an energy
level of an equals 2,

295
00:17:41,660 --> 00:17:44,880
and we can think about what
the energy difference is

296
00:17:44,880 --> 00:17:49,060
between these two and we can
just write that equation out.

297
00:17:49,060 --> 00:17:55,940
So the initial energy, the
electron started at n equals 6,

298
00:17:55,940 --> 00:17:58,090
the energy of the
n equals 6 state,

299
00:17:58,090 --> 00:18:02,130
and it goes to the energy
of the n equals 2 state.

300
00:18:02,130 --> 00:18:08,040
So energy n equals 6
minus energy n equals 2.

301
00:18:08,040 --> 00:18:09,360
All right.

302
00:18:09,360 --> 00:18:11,690
So of course if you
know energy, you

303
00:18:11,690 --> 00:18:15,300
can know a lot of other
things about the photon.

304
00:18:15,300 --> 00:18:20,120
So you can calculate frequency
of that emitted photon.

305
00:18:20,120 --> 00:18:23,410
So again, we have our
energy difference here

306
00:18:23,410 --> 00:18:27,170
and we can then solve
for the frequency

307
00:18:27,170 --> 00:18:31,040
of the emitted photon, which is
equal to the energy difference.

308
00:18:31,040 --> 00:18:35,070
That energy, divided
by Planck's constant,

309
00:18:35,070 --> 00:18:39,150
and you could also write
it out, the initial energy

310
00:18:39,150 --> 00:18:41,780
minus the final energy over h.

311
00:18:41,780 --> 00:18:43,900
All of these are
equivalent things.

312
00:18:43,900 --> 00:18:46,630
And when you know
frequency, we're

313
00:18:46,630 --> 00:18:50,290
talking about light here, so you
can calculate the wavelength.

314
00:18:52,890 --> 00:18:55,850
So let's think now about
what we might expect

315
00:18:55,850 --> 00:18:58,520
in terms of frequencies
and wavelengths,

316
00:18:58,520 --> 00:19:02,470
depending on the energy
difference between the two

317
00:19:02,470 --> 00:19:04,790
different states.

318
00:19:04,790 --> 00:19:08,490
So here, if we think
first about this electron

319
00:19:08,490 --> 00:19:12,700
with the purple line, we have
a large energy difference

320
00:19:12,700 --> 00:19:16,300
here between this
state and this state

321
00:19:16,300 --> 00:19:20,530
down here, between n
equals 5 to n equals 1.

322
00:19:20,530 --> 00:19:23,500
So when we have a large
difference in energy,

323
00:19:23,500 --> 00:19:26,080
what do we expect
about the frequency

324
00:19:26,080 --> 00:19:27,910
of the emitted photon?

325
00:19:27,910 --> 00:19:32,010
Is it going to be a high
frequency or low frequency?

326
00:19:32,010 --> 00:19:33,010
High.

327
00:19:33,010 --> 00:19:33,910
Yep.

328
00:19:33,910 --> 00:19:36,840
So large energy, high frequency.

329
00:19:36,840 --> 00:19:40,150
And so then what would be
true about the wavelength

330
00:19:40,150 --> 00:19:42,780
of that emitted photon?

331
00:19:42,780 --> 00:19:43,920
Short.

332
00:19:43,920 --> 00:19:46,020
Right.

333
00:19:46,020 --> 00:19:49,800
Now if we had a small
difference, say n equals 3 to n

334
00:19:49,800 --> 00:19:53,400
equals 1, which is a smaller
difference in energy, what's

335
00:19:53,400 --> 00:19:56,421
true about the frequency here?

336
00:19:56,421 --> 00:19:56,920
Right.

337
00:19:56,920 --> 00:19:58,120
Low frequency.

338
00:19:58,120 --> 00:20:00,150
And wavelength?

339
00:20:00,150 --> 00:20:03,050
Right, long wavelength.

340
00:20:03,050 --> 00:20:04,850
Right.

341
00:20:04,850 --> 00:20:10,310
So now we're actually going to
see some photons being emitted,

342
00:20:10,310 --> 00:20:16,140
and let me just build in to
this experiment a little bit.

343
00:20:16,140 --> 00:20:22,270
So we have an evacuated glass
tube filled with hydrogen.

344
00:20:22,270 --> 00:20:26,160
And if you have negative
and positive electrodes,

345
00:20:26,160 --> 00:20:30,670
you can emit light from
this and then analyze

346
00:20:30,670 --> 00:20:32,930
the different wavelengths.

347
00:20:32,930 --> 00:20:37,560
So we are not going to be
the first people to see this,

348
00:20:37,560 --> 00:20:40,400
but we're going
to try this and we

349
00:20:40,400 --> 00:20:44,190
should observe these different
wavelengths coming off.

350
00:20:44,190 --> 00:20:46,840
And after we observe
them, we will

351
00:20:46,840 --> 00:20:49,650
try to calculate
what they're due to,

352
00:20:49,650 --> 00:20:54,910
and then if the experimental
results of the wavelength

353
00:20:54,910 --> 00:20:57,860
and frequency observed can be
explained by the Schroedinger

354
00:20:57,860 --> 00:20:58,520
equation.

355
00:20:58,520 --> 00:21:03,100
But first, let's actually
see the visible spectra

356
00:21:03,100 --> 00:21:07,310
that is created by hydrogen.
And so we have our demo TAs,

357
00:21:07,310 --> 00:21:10,390
and actually if all our
TAs can help pass out

358
00:21:10,390 --> 00:21:13,840
some little glasses to
help everyone see this.

359
00:21:13,840 --> 00:21:18,530
And when we're ready, we're
going to do lights down.

360
00:21:18,530 --> 00:21:20,350
But let's get everything
handed out first.

361
00:21:24,430 --> 00:21:24,930
All right.

362
00:21:24,930 --> 00:21:25,745
I got the lights.

363
00:21:28,600 --> 00:21:33,230
TA: So this is a hydrogen
lamp, and when you turn it on,

364
00:21:33,230 --> 00:21:36,310
the electricity excites
all the hydrogen inside

365
00:21:36,310 --> 00:21:40,730
and then you see this glow from
the electromagnetic radiation

366
00:21:40,730 --> 00:21:44,420
being emitted by these excited
hydrogens relaxing down

367
00:21:44,420 --> 00:21:45,496
to the ground state.

368
00:21:53,432 --> 00:21:54,920
PROFESSOR: Want
to try the light?

369
00:21:57,920 --> 00:22:00,050
TA: So we're going to
try this for those of you

370
00:22:00,050 --> 00:22:04,042
who don't have the glasses,
but let's see if this works.

371
00:22:08,040 --> 00:22:11,440
It was kind of there.

372
00:22:11,440 --> 00:22:13,792
Is that what we're
supposed to see?

373
00:22:13,792 --> 00:22:15,250
You're supposed to
see all of them.

374
00:22:15,250 --> 00:22:16,333
I guess you can't, really.

375
00:22:18,515 --> 00:22:20,390
I guess depending on
how you move this thing,

376
00:22:20,390 --> 00:22:23,234
maybe you end up
seeing all of them.

377
00:22:23,234 --> 00:22:25,704
Is it working?

378
00:22:25,704 --> 00:22:26,870
PROFESSOR: It's not working.

379
00:22:32,486 --> 00:22:34,996
TA: It's not working?

380
00:22:34,996 --> 00:22:35,496
No?

381
00:22:38,970 --> 00:22:39,630
Yeah, I know.

382
00:22:42,792 --> 00:22:45,000
It kind of works, depending
on how I move this thing.

383
00:22:48,824 --> 00:22:50,574
PROFESSOR: Sometimes
it works really well.

384
00:22:59,770 --> 00:23:03,098
Should we just try walking?

385
00:23:03,098 --> 00:23:06,180
Can we hold it up and see
whether people also can see it?

386
00:23:06,180 --> 00:23:06,930
TA: All rights.

387
00:23:06,930 --> 00:23:08,220
So we're going to hold it up.

388
00:23:08,220 --> 00:23:09,830
See if you guys--

389
00:23:09,830 --> 00:23:12,521
PROFESSOR: Can just see
it without the camera.

390
00:23:15,785 --> 00:23:16,285
TA: OK.

391
00:23:19,650 --> 00:23:21,174
So what you should
be able to see,

392
00:23:21,174 --> 00:23:22,840
for those of you that
have your glasses,

393
00:23:22,840 --> 00:23:27,220
is a continuous spectrum
with the various colors.

394
00:23:33,394 --> 00:23:35,435
PROFESSOR: You might have
to get the angle right.

395
00:23:35,435 --> 00:23:37,940
Are people in the middle
of the room able to see it?

396
00:23:47,710 --> 00:23:50,130
Can anyone see it?

397
00:23:50,130 --> 00:23:51,150
Yeah?

398
00:23:51,150 --> 00:23:53,620
People on the edge of
the room, can you see it?

399
00:23:53,620 --> 00:23:57,660
I think it's harder
from-- and the camera's

400
00:23:57,660 --> 00:24:00,900
blocking people a little bit.

401
00:24:00,900 --> 00:24:01,450
TA: It works.

402
00:24:01,450 --> 00:24:03,032
I can see it.

403
00:24:03,032 --> 00:24:05,490
PROFESSOR: Do you want to move
it up farther, like in front

404
00:24:05,490 --> 00:24:05,990
of that?

405
00:24:16,244 --> 00:24:17,160
Try turning it around.

406
00:24:19,842 --> 00:24:21,190
All right.

407
00:24:21,190 --> 00:24:23,840
Maybe we'll turn it
slightly, and then we

408
00:24:23,840 --> 00:24:26,690
can come down, maybe,
and try it after class

409
00:24:26,690 --> 00:24:28,070
if it's not working very well.

410
00:24:41,700 --> 00:24:44,567
When it's tilted, are you
having better luck over here?

411
00:24:51,046 --> 00:24:51,696
All right.

412
00:24:51,696 --> 00:24:53,320
I guess we'll bring
the lights back up,

413
00:24:53,320 --> 00:24:55,153
and I'll show you what
you should have seen,

414
00:24:55,153 --> 00:24:56,924
if it didn't work for you.

415
00:24:59,890 --> 00:25:04,280
So how many people were
able to see the spectra?

416
00:25:04,280 --> 00:25:04,780
OK.

417
00:25:04,780 --> 00:25:05,279
All right.

418
00:25:05,279 --> 00:25:06,410
So a good number of people.

419
00:25:06,410 --> 00:25:09,080
Great.

420
00:25:09,080 --> 00:25:11,415
I feel like this room is
not as perfect for this

421
00:25:11,415 --> 00:25:13,370
as some other rooms.

422
00:25:13,370 --> 00:25:16,510
But there are some rooms that
actually don't get dark at all,

423
00:25:16,510 --> 00:25:19,043
and then you can't
really see anything.

424
00:25:19,043 --> 00:25:20,770
All right.

425
00:25:20,770 --> 00:25:28,090
So maybe if we have a chance,
we can try again at the end.

426
00:25:28,090 --> 00:25:28,600
All right.

427
00:25:28,600 --> 00:25:33,160
So this is what you
should have seen.

428
00:25:33,160 --> 00:25:36,820
You should have seen these
different series of lights,

429
00:25:36,820 --> 00:25:42,440
or series of colors coming off,
and we're not the first people

430
00:25:42,440 --> 00:25:43,870
to see it.

431
00:25:43,870 --> 00:25:51,420
So J.J. Balmer, in 1885,
reported seeing these colors,

432
00:25:51,420 --> 00:25:55,180
and he wanted to calculate
the frequencies of the lights

433
00:25:55,180 --> 00:25:58,010
that you were seeing
emitted from this.

434
00:25:58,010 --> 00:26:01,420
And so he did calculate
the frequency,

435
00:26:01,420 --> 00:26:04,470
and then he tried to figure out
the mathematical relationship

436
00:26:04,470 --> 00:26:06,440
between the different
frequencies of light

437
00:26:06,440 --> 00:26:07,800
that he was observing.

438
00:26:07,800 --> 00:26:12,660
And he found that the
frequency equaled 3.29 times 10

439
00:26:12,660 --> 00:26:17,610
to the 15th per second,
times 1 over 4 minus 1

440
00:26:17,610 --> 00:26:23,540
over some number, n, where
n was either 3, 4, or 5.

441
00:26:23,540 --> 00:26:26,390
And he really didn't understand
what the significance of this

442
00:26:26,390 --> 00:26:28,320
was, but it was pretty.

443
00:26:28,320 --> 00:26:30,760
You had hydrogen in
this sealed tube,

444
00:26:30,760 --> 00:26:35,780
and there were colors that came
off, and they had frequencies.

445
00:26:35,780 --> 00:26:39,370
So that's kind of where that
stood for a little while.

446
00:26:39,370 --> 00:26:43,080
So now let's think about what
those different colored lights

447
00:26:43,080 --> 00:26:44,600
were due to.

448
00:26:44,600 --> 00:26:51,070
So we have here energy
levels, and the transitions

449
00:26:51,070 --> 00:26:56,000
that we were observing
are all going to be n

450
00:26:56,000 --> 00:26:58,550
equals 2 final state.

451
00:26:58,550 --> 00:27:02,110
And we can think about why you
didn't see any transitions to n

452
00:27:02,110 --> 00:27:02,680
equals one.

453
00:27:02,680 --> 00:27:03,560
Think about that.

454
00:27:03,560 --> 00:27:05,791
We'll come back to
that in a minute.

455
00:27:05,791 --> 00:27:07,540
But there were these
different transitions

456
00:27:07,540 --> 00:27:12,180
that were being observed
from 3 to 2, 4 to 2, 5 to 2,

457
00:27:12,180 --> 00:27:13,540
and 6 to 2.

458
00:27:13,540 --> 00:27:18,340
So now let's think about which
colors-- which wavelengths--

459
00:27:18,340 --> 00:27:21,730
are due to which
of the transitions.

460
00:27:21,730 --> 00:27:25,740
So for the red one,
what do you think?

461
00:27:25,740 --> 00:27:29,890
3, 4, or 5 transitioned to 2?

462
00:27:29,890 --> 00:27:31,300
3.

463
00:27:31,300 --> 00:27:32,520
It is 3.

464
00:27:32,520 --> 00:27:36,420
And you could think about that
in terms of the smaller energy.

465
00:27:36,420 --> 00:27:39,210
That's the smallest
energy, so that

466
00:27:39,210 --> 00:27:43,470
would be a low frequency
and a long wavelength.

467
00:27:43,470 --> 00:27:46,540
So the one with the longest
wavelength-- and red

468
00:27:46,540 --> 00:27:48,820
is the longest
wavelength-- so that

469
00:27:48,820 --> 00:27:55,160
must be the transition from an
initial n of 3 to n equal 2.

470
00:27:55,160 --> 00:27:59,700
And then we can fill in the
rest, so this one over here

471
00:27:59,700 --> 00:28:03,850
must have been n equals 4 to 2.

472
00:28:03,850 --> 00:28:09,990
This one here, then, would
be the blue, n equals 5 to 2.

473
00:28:09,990 --> 00:28:15,240
And then the purple or indigo
at the end, n equals 6 to n

474
00:28:15,240 --> 00:28:16,810
equals 2.

475
00:28:16,810 --> 00:28:19,970
So they saw these
four colors, there

476
00:28:19,970 --> 00:28:22,040
were these different
transitions,

477
00:28:22,040 --> 00:28:24,720
and so then, now,
we can calculate

478
00:28:24,720 --> 00:28:27,680
what the frequencies
of these are and think

479
00:28:27,680 --> 00:28:32,040
about this, then, in terms
of Schroedinger's equation

480
00:28:32,040 --> 00:28:37,090
and test Schroedinger's equation
to see if it predicts this.

481
00:28:37,090 --> 00:28:39,740
So we can calculate
the frequency, then,

482
00:28:39,740 --> 00:28:43,320
of the emitted
photons, and we had

483
00:28:43,320 --> 00:28:48,860
frequency equals the initial
energy minus the final energy

484
00:28:48,860 --> 00:28:54,940
state, or this delta E,
over Planck's constant.

485
00:28:54,940 --> 00:28:57,350
And from the
Schroedinger equation,

486
00:28:57,350 --> 00:29:01,500
we know about what these energy
levels are from Schroedinger.

487
00:29:01,500 --> 00:29:05,090
And this is, again, for
hydrogen, so z equals 1, so z

488
00:29:05,090 --> 00:29:06,360
isn't shown.

489
00:29:06,360 --> 00:29:11,530
We have the binding energy
equals minus RH, Rydberg

490
00:29:11,530 --> 00:29:14,080
constant over n squared.

491
00:29:14,080 --> 00:29:17,200
And now we can put these
equations together.

492
00:29:17,200 --> 00:29:22,200
So we can substitute these
energies in using these,

493
00:29:22,200 --> 00:29:24,920
and so we can do that here.

494
00:29:24,920 --> 00:29:29,680
We'll pull out Planck's
constant, so 1 over h.

495
00:29:29,680 --> 00:29:38,980
And then we can substitute in
minus RH over the initial n

496
00:29:38,980 --> 00:29:47,820
level squared minus minus
RH over the final n squared.

497
00:29:47,820 --> 00:29:51,180
And we can also simplify
this a little more,

498
00:29:51,180 --> 00:29:57,560
pull out RH over here, and now
we just have 1 over the final--

499
00:29:57,560 --> 00:29:59,920
we have minus a minus,
so we've rearranged

500
00:29:59,920 --> 00:30:06,950
this-- 1 over n final squared
minus 1 over n initial squared.

501
00:30:06,950 --> 00:30:10,510
And we have an
equation that solves

502
00:30:10,510 --> 00:30:15,490
for the frequency in terms of
Rydberg, Planck's constant,

503
00:30:15,490 --> 00:30:20,450
and what the principle quantum
numbers are, what n is.

504
00:30:20,450 --> 00:30:22,380
So let's look at
this a little more.

505
00:30:22,380 --> 00:30:28,470
Now remember, this is all
going to n final of 2,

506
00:30:28,470 --> 00:30:31,720
and so we can put that
equation up here again.

507
00:30:31,720 --> 00:30:35,290
So when this is
2, 2 squared is 4.

508
00:30:35,290 --> 00:30:37,960
And if you remember
back, Balmer had

509
00:30:37,960 --> 00:30:41,430
a 4-- had this part
of the expression--

510
00:30:41,430 --> 00:30:44,640
but he had a strange
number over here

511
00:30:44,640 --> 00:30:47,470
that he experimentally
determined.

512
00:30:47,470 --> 00:30:51,300
But if you take RH and divide
by Planck's constant, Rydberg

513
00:30:51,300 --> 00:30:53,420
constant divided
by Planck's, you

514
00:30:53,420 --> 00:30:56,980
get that number that
Balmer had found back

515
00:30:56,980 --> 00:31:03,710
in 1885-- 3.29 times 10
to the 15th per second.

516
00:31:03,710 --> 00:31:08,330
So when we plug in the values
from Schroedinger's equations,

517
00:31:08,330 --> 00:31:11,300
you come up with the
experimentally determined

518
00:31:11,300 --> 00:31:13,830
values for frequencies,
or wavelength,

519
00:31:13,830 --> 00:31:15,480
of the emitted light.

520
00:31:15,480 --> 00:31:17,210
And of course,
from the frequency,

521
00:31:17,210 --> 00:31:19,100
you can calculate
the wavelength,

522
00:31:19,100 --> 00:31:22,560
and the wavelengths that
were observed experimentally

523
00:31:22,560 --> 00:31:25,280
agreed with the wavelength
you would calculate

524
00:31:25,280 --> 00:31:29,020
from the Schroedinger's
equation to one part, n times 10

525
00:31:29,020 --> 00:31:29,900
to the 8th.

526
00:31:29,900 --> 00:31:33,070
So the agreement was
absolutely amazing.

527
00:31:33,070 --> 00:31:34,950
So Schroedinger's
equation, which

528
00:31:34,950 --> 00:31:38,280
was taking into account
the wavelike properties

529
00:31:38,280 --> 00:31:41,090
of the electrons,
were able to predict,

530
00:31:41,090 --> 00:31:43,890
for a hydrogen atom,
what wavelengths

531
00:31:43,890 --> 00:31:47,980
you should see emitted in
that hydrogen atom spectra.

532
00:31:47,980 --> 00:31:50,330
So this was really exciting.

533
00:31:50,330 --> 00:31:52,630
Schroedinger
equation was working,

534
00:31:52,630 --> 00:31:55,700
we had a way of
describing the behavior

535
00:31:55,700 --> 00:31:58,300
that we were observing
for these electrons,

536
00:31:58,300 --> 00:32:00,730
and that was really incredible.

537
00:32:00,730 --> 00:32:03,940
And I think Balmer should
get a lot of credit as well

538
00:32:03,940 --> 00:32:05,450
for all of this.

539
00:32:05,450 --> 00:32:07,720
And the people who were doing
these early experiments,

540
00:32:07,720 --> 00:32:09,090
they didn't know
what it was meaning,

541
00:32:09,090 --> 00:32:11,200
but they were coming up
with the data that allowed

542
00:32:11,200 --> 00:32:13,500
to test theories later on.

543
00:32:13,500 --> 00:32:14,000
OK.

544
00:32:14,000 --> 00:32:18,760
So this was a series
going to a final n of 2,

545
00:32:18,760 --> 00:32:20,630
and so we have
the Balmer series.

546
00:32:20,630 --> 00:32:24,620
That was the visible
series that we were seeing.

547
00:32:24,620 --> 00:32:30,701
So what about, why wasn't
anything going to n equals 1?

548
00:32:30,701 --> 00:32:31,950
And that's a clicker question.

549
00:33:17,354 --> 00:33:19,770
So at the end, I'm going to
ask you to put up the winners.

550
00:33:27,090 --> 00:33:28,460
Is my number good?

551
00:33:28,460 --> 00:33:29,010
OK.

552
00:33:29,010 --> 00:33:29,890
10 more seconds.

553
00:33:48,750 --> 00:33:50,420
OK.

554
00:33:50,420 --> 00:33:54,090
So 71%.

555
00:33:54,090 --> 00:33:56,970
So the trick here is to
think about-- well, actually,

556
00:33:56,970 --> 00:33:58,210
someone can tell me, maybe.

557
00:33:58,210 --> 00:34:00,392
What was the trick
here to think about?

558
00:34:04,800 --> 00:34:06,090
I'll get a little exercise.

559
00:34:06,090 --> 00:34:07,320
I'll come up.

560
00:34:07,320 --> 00:34:08,650
How's everyone doing up here?

561
00:34:12,989 --> 00:34:15,050
AUDIENCE: So for
the Lyman series,

562
00:34:15,050 --> 00:34:17,580
there's a more difference
from the Balmer series,

563
00:34:17,580 --> 00:34:20,199
so there's more energy in
the transition when it goes

564
00:34:20,199 --> 00:34:21,690
down back to the ground state.

565
00:34:21,690 --> 00:34:23,150
So for that, with
more energy, it's

566
00:34:23,150 --> 00:34:24,870
going to be a
shorter wavelength,

567
00:34:24,870 --> 00:34:27,489
and that's ultraviolet.

568
00:34:27,489 --> 00:34:30,050
PROFESSOR: So here it would
be convenient to remember

569
00:34:30,050 --> 00:34:34,139
your orders of what are short
and long wavelength kinds

570
00:34:34,139 --> 00:34:37,233
of light.

571
00:34:37,233 --> 00:34:37,732
OK.

572
00:34:41,260 --> 00:34:44,080
So we have the UV range, then.

573
00:34:44,080 --> 00:34:46,790
And so that's why you
didn't observe it.

574
00:34:46,790 --> 00:34:49,090
It was happening,
but you didn't see it

575
00:34:49,090 --> 00:34:52,719
because it was in the UV.

576
00:34:52,719 --> 00:34:53,219
All right.

577
00:34:53,219 --> 00:34:56,580
So then we can go on and
look at the other things that

578
00:34:56,580 --> 00:34:58,230
can happen here.

579
00:34:58,230 --> 00:35:02,910
So we can have n
final of 3, and you

580
00:35:02,910 --> 00:35:05,420
don't need to know the
names of these series,

581
00:35:05,420 --> 00:35:08,930
but that would be near IR.

582
00:35:08,930 --> 00:35:12,730
N equals 4 would
be in the IR range.

583
00:35:12,730 --> 00:35:17,720
So only some of what's happening
is actually visible to us.

584
00:35:17,720 --> 00:35:21,140
We see beautiful colors
from transitions,

585
00:35:21,140 --> 00:35:23,010
but there's other
things happening, too,

586
00:35:23,010 --> 00:35:27,430
that are not visible to us.

587
00:35:27,430 --> 00:35:31,960
So at this point, we're feeling
pretty good about those energy

588
00:35:31,960 --> 00:35:35,190
levels, about the
Schroedinger equation being

589
00:35:35,190 --> 00:35:40,310
able to successfully predict
what kind of energy levels

590
00:35:40,310 --> 00:35:41,850
you have, that binding energy.

591
00:35:44,570 --> 00:35:48,850
And now, this
verification was good,

592
00:35:48,850 --> 00:35:50,990
from your photon emission.

593
00:35:50,990 --> 00:35:53,390
But there's another
property that you can have,

594
00:35:53,390 --> 00:35:56,480
which is photon absorption.

595
00:35:56,480 --> 00:35:58,810
So why don't we do yet
another clicker question

596
00:35:58,810 --> 00:36:02,834
as a competition, after
all, about absorption.

597
00:36:51,640 --> 00:36:53,046
OK, 10 seconds.

598
00:37:09,000 --> 00:37:11,350
OK.

599
00:37:11,350 --> 00:37:15,300
So now we're talking
about a different process.

600
00:37:15,300 --> 00:37:18,730
We were talking before
about electrons.

601
00:37:18,730 --> 00:37:21,515
They're starting up in a higher
energy level, going lower.

602
00:37:21,515 --> 00:37:23,160
But with photon
absorption, we're

603
00:37:23,160 --> 00:37:27,240
going the other direction, so
we're going from a lower state.

604
00:37:27,240 --> 00:37:28,860
We're being excited.

605
00:37:28,860 --> 00:37:31,760
They're absorbing energy
and being excited,

606
00:37:31,760 --> 00:37:35,420
so we can have a final
state that is higher,

607
00:37:35,420 --> 00:37:39,505
and the energy is gained in this
process, so it's being excited.

608
00:37:43,011 --> 00:37:43,510
All right.

609
00:37:43,510 --> 00:37:45,370
So we can think about
the same things,

610
00:37:45,370 --> 00:37:48,190
then, in terms of absorption.

611
00:37:48,190 --> 00:37:51,430
So if we have a big
energy difference,

612
00:37:51,430 --> 00:37:57,160
if it's absorbing a lot of
energy, big energy difference,

613
00:37:57,160 --> 00:38:01,780
it's going to be absorbing
light with a high frequency

614
00:38:01,780 --> 00:38:04,210
and a short wavelength.

615
00:38:04,210 --> 00:38:06,680
If there's a small
energy difference,

616
00:38:06,680 --> 00:38:12,370
it'll absorb a photon with a low
frequency or a long wavelength.

617
00:38:12,370 --> 00:38:14,570
And we'll come back to
some of these ideas,

618
00:38:14,570 --> 00:38:16,760
actually, well into the
course, and we'll actually

619
00:38:16,760 --> 00:38:19,360
look at some pretty colors.

620
00:38:19,360 --> 00:38:23,460
So in this case now, we can
calculate frequency again,

621
00:38:23,460 --> 00:38:26,270
but our equation is a
little bit different.

622
00:38:26,270 --> 00:38:30,390
So we have the Rydberg constant
and Planck's constant again,

623
00:38:30,390 --> 00:38:37,220
but now we have 1 over initial
n squared minus final n squared,

624
00:38:37,220 --> 00:38:41,160
and so this term should
be a positive term.

625
00:38:41,160 --> 00:38:43,623
We should be getting out
a positive frequency.

626
00:38:46,350 --> 00:38:50,020
So if I take this again
and put it up here,

627
00:38:50,020 --> 00:38:51,900
you want to think about
whether, if you're

628
00:38:51,900 --> 00:38:55,040
talking about
absorption or emission,

629
00:38:55,040 --> 00:38:59,310
that's what's telling you if the
energy is being gained or lost.

630
00:38:59,310 --> 00:39:02,171
So you're not going to have
negative frequencies in one

631
00:39:02,171 --> 00:39:02,670
case.

632
00:39:02,670 --> 00:39:05,610
You're going to be
absorbing the light

633
00:39:05,610 --> 00:39:09,980
of a particular frequency, or
emitting light of a frequency.

634
00:39:09,980 --> 00:39:12,297
So pay attention
to your equations,

635
00:39:12,297 --> 00:39:14,130
and think about whether
your answer actually

636
00:39:14,130 --> 00:39:16,040
make sense when you do them.

637
00:39:16,040 --> 00:39:17,810
And again, all
these equations are

638
00:39:17,810 --> 00:39:20,841
going to be provided to
you in an equation sheet.

639
00:39:20,841 --> 00:39:21,340
OK.

640
00:39:21,340 --> 00:39:25,720
So let's consider the summary
of both of these things now.

641
00:39:25,720 --> 00:39:28,910
So we're talking about
admission versus absorption.

642
00:39:28,910 --> 00:39:31,090
And so we have this
Rydberg formula,

643
00:39:31,090 --> 00:39:33,590
which is what this
is called, and it

644
00:39:33,590 --> 00:39:36,220
can be used to
calculate the frequency

645
00:39:36,220 --> 00:39:42,370
of either emitted photons
or absorbed photons, so

646
00:39:42,370 --> 00:39:44,450
from either process.

647
00:39:44,450 --> 00:39:46,490
And if we want to
make it more general,

648
00:39:46,490 --> 00:39:48,600
again, it's just a
one electron case,

649
00:39:48,600 --> 00:39:53,530
but we can put our z in
for any one electron ion.

650
00:39:53,530 --> 00:39:57,910
So frequency equals Z squared,
Rydberg constant over Planck's

651
00:39:57,910 --> 00:40:04,780
constant, and we have 1 over
the final minus initial,

652
00:40:04,780 --> 00:40:08,450
or initial minus final,
depending on which

653
00:40:08,450 --> 00:40:10,730
process you're talking about.

654
00:40:10,730 --> 00:40:14,730
And over here, we'd be
talking, then, about emission.

655
00:40:14,730 --> 00:40:19,612
So our initial energy is
higher going to lower,

656
00:40:19,612 --> 00:40:21,070
and when that
happens, you're going

657
00:40:21,070 --> 00:40:26,470
to be releasing light with
the energy difference that

658
00:40:26,470 --> 00:40:30,460
is due to the difference
between these states.

659
00:40:30,460 --> 00:40:32,630
So we're going to
have our electron is

660
00:40:32,630 --> 00:40:35,220
going to emit this energy.

661
00:40:35,220 --> 00:40:38,690
In the absorption process
for this equation,

662
00:40:38,690 --> 00:40:41,910
we're going to go from
an initial state that's

663
00:40:41,910 --> 00:40:45,020
lower to a higher state.

664
00:40:45,020 --> 00:40:49,110
So we'll have a final state
that's higher than initial.

665
00:40:49,110 --> 00:40:50,020
That's absorption.

666
00:40:50,020 --> 00:40:51,190
It's absorbing energy.

667
00:40:51,190 --> 00:40:54,450
It's getting excited,
and so the electron

668
00:40:54,450 --> 00:40:58,490
is absorbing that energy.

669
00:40:58,490 --> 00:41:01,850
So this really summarizes,
now, what we need

670
00:41:01,850 --> 00:41:04,820
to know about binding energies.

671
00:41:04,820 --> 00:41:07,570
Schroedinger equation
also tells us

672
00:41:07,570 --> 00:41:12,440
about wave functions, which is
what we're moving into next.

673
00:41:12,440 --> 00:41:14,970
So that's all for
today, except we

674
00:41:14,970 --> 00:41:20,710
have a very important
announcement, which is

675
00:41:20,710 --> 00:41:23,430
congratulation to recitation 6.

676
00:41:23,430 --> 00:41:27,624
Lisa, you are the first winner
of the clicker competition.

677
00:41:30,530 --> 00:41:33,040
Have a great weekend, everybody.