1
00:00:00,030 --> 00:00:02,400
The following content is
provided under a Creative

2
00:00:02,400 --> 00:00:03,830
Commons License.

3
00:00:03,830 --> 00:00:06,840
Your support will help MIT
OpenCourseWare continue to

4
00:00:06,840 --> 00:00:10,510
offer high quality educational
resources for free.

5
00:00:10,510 --> 00:00:13,390
To make a donation or view
additional materials from

6
00:00:13,390 --> 00:00:15,840
hundreds of MIT courses, visit
mitopencourseware@ocw.mit.edu.

7
00:00:21,110 --> 00:00:22,570
PROFESSOR: OK, settle down.

8
00:00:22,570 --> 00:00:23,980
Let's get started.

9
00:00:23,980 --> 00:00:29,770
One announcement, yesterday we
had our first weekly I would

10
00:00:29,770 --> 00:00:31,630
say minor celebration.

11
00:00:31,630 --> 00:00:33,580
And by and large,
it went well.

12
00:00:33,580 --> 00:00:36,840
Please make sure that you go to
your assigned recitation.

13
00:00:36,840 --> 00:00:40,760
If you miss your recitation,
you need to get down to see

14
00:00:40,760 --> 00:00:44,400
Hillary so that we make sure
that we have enough copies of

15
00:00:44,400 --> 00:00:46,780
the weekly quizzes on hand.

16
00:00:46,780 --> 00:00:49,490
If you've joined the class, you
have to check in with her.

17
00:00:49,490 --> 00:00:52,910
She's down the hall here
in room 8-201.

18
00:00:52,910 --> 00:00:54,310
And you'll be assigned
to a section.

19
00:00:57,640 --> 00:00:59,560
What else do I have by
way of announcements?

20
00:00:59,560 --> 00:01:00,520
Oh yes.

21
00:01:00,520 --> 00:01:03,460
Just reminding you, this
was from 2003.

22
00:01:03,460 --> 00:01:04,380
See it doesn't change.

23
00:01:04,380 --> 00:01:09,470
It's the same s-block, p-block,
and d-block elements.

24
00:01:09,470 --> 00:01:12,450
So that's coming up a week
from tomorrow, two

25
00:01:12,450 --> 00:01:14,810
celebrations next.

26
00:01:14,810 --> 00:01:20,790
And of course the contests, the
contests with hot prizes.

27
00:01:20,790 --> 00:01:22,320
All right.

28
00:01:22,320 --> 00:01:23,410
Let's get down to business.

29
00:01:23,410 --> 00:01:27,220
Last day we looked at the
Rutherford-Geiger-Marsden

30
00:01:27,220 --> 00:01:28,400
experiment.

31
00:01:28,400 --> 00:01:30,820
Oh there's one other one.

32
00:01:30,820 --> 00:01:33,380
If you look at the readings,
there's this one section

33
00:01:33,380 --> 00:01:34,890
called the archives.

34
00:01:34,890 --> 00:01:39,530
My predecessor, Professor Wit,
wrote a set of lecture notes.

35
00:01:39,530 --> 00:01:41,880
And they look something
like this.

36
00:01:41,880 --> 00:01:44,580
And some students have said that
they find these a little

37
00:01:44,580 --> 00:01:49,080
more expository in certain
sections on certain topics

38
00:01:49,080 --> 00:01:51,260
than the book to be.

39
00:01:51,260 --> 00:01:52,660
And I have no preference.

40
00:01:52,660 --> 00:01:55,520
But if you take a look at
this it'll say LN1,

41
00:01:55,520 --> 00:01:56,810
lecture notes 1.

42
00:01:56,810 --> 00:01:58,170
If you go to this, read this.

43
00:01:58,170 --> 00:02:00,060
If you find that's
helpful, good.

44
00:02:00,060 --> 00:02:03,710
If you don't find it helpful,
than stick with the book.

45
00:02:03,710 --> 00:02:05,280
Just letting you know
what that is.

46
00:02:05,280 --> 00:02:06,950
All right, so last day
we looked at the

47
00:02:06,950 --> 00:02:10,250
Rutherford-Geiger-Marsden
experiment in which a high

48
00:02:10,250 --> 00:02:15,290
energy beam of alpha particles
bombarded a thin, gold foil.

49
00:02:15,290 --> 00:02:18,610
And on the basis of the
scattering results, namely

50
00:02:18,610 --> 00:02:22,890
most of the particles went
through with minor scattering.

51
00:02:22,890 --> 00:02:24,990
And a tiny fraction of
them were scattered

52
00:02:24,990 --> 00:02:27,500
through large angles.

53
00:02:27,500 --> 00:02:31,620
The Thomson plum pudding model
was rejected in favor of

54
00:02:31,620 --> 00:02:34,500
Rutherford's nuclear
model of the atom.

55
00:02:34,500 --> 00:02:38,240
And then subsequently, Bohr came
up with the quantitative

56
00:02:38,240 --> 00:02:41,840
representation off the
Rutherford nuclear model.

57
00:02:41,840 --> 00:02:47,040
And we were partway through the
treatment of Bohr last day

58
00:02:47,040 --> 00:02:47,790
when we adjourned.

59
00:02:47,790 --> 00:02:51,220
So let's right pick up the
thread from where we left off.

60
00:02:51,220 --> 00:02:56,010
And so just to remind you, the
Bohr model is for a 1-electron

61
00:02:56,010 --> 00:02:58,020
atom gas phase.

62
00:02:58,020 --> 00:03:01,280
So this is either atomic
hydrogen, it could be helium

63
00:03:01,280 --> 00:03:07,380
plus lithium 2 plus roentgenium
110 plus Its

64
00:03:07,380 --> 00:03:08,830
doesn't matter how
many protons.

65
00:03:08,830 --> 00:03:11,390
there's always only
want electron.

66
00:03:11,390 --> 00:03:13,500
And it's a planetary model.

67
00:03:13,500 --> 00:03:16,360
The positive charge concentrated
in the nucleus, Z

68
00:03:16,360 --> 00:03:18,160
is the proton number.

69
00:03:18,160 --> 00:03:22,910
And at a distance r from the
nucleus is a circular orbit in

70
00:03:22,910 --> 00:03:25,075
which resides 1 electron.

71
00:03:25,075 --> 00:03:27,780
It has a charge of minus E.

72
00:03:27,780 --> 00:03:30,180
And I just designated
them q1 and q2.

73
00:03:30,180 --> 00:03:31,360
You could have done
it the other way.

74
00:03:31,360 --> 00:03:33,060
But I had to choose something.

75
00:03:33,060 --> 00:03:34,590
So we went through
and looked at the

76
00:03:34,590 --> 00:03:35,950
constitutive equations here.

77
00:03:35,950 --> 00:03:38,670
So first of all, the energy
of the system--

78
00:03:38,670 --> 00:03:40,960
and this is only going to be
the energy the electron.

79
00:03:40,960 --> 00:03:45,480
Because we assume that the
nucleus is far more massive.

80
00:03:45,480 --> 00:03:48,100
And so we don't have to get into
things like reduced mass

81
00:03:48,100 --> 00:03:48,830
or anything like that.

82
00:03:48,830 --> 00:03:51,430
So just measure the energy
of the electron.

83
00:03:51,430 --> 00:03:54,210
1/2 mv squared is the
newtonian component.

84
00:03:54,210 --> 00:03:59,910
And then coulombic energy that's
stored is z times e

85
00:03:59,910 --> 00:04:04,140
squared over 4 pi epsilon zero
r, where epsilon zero is the

86
00:04:04,140 --> 00:04:05,430
permittivity of vacuum.

87
00:04:05,430 --> 00:04:09,160
And it's the factor, the 4 pi
epsilon zero, is the factor

88
00:04:09,160 --> 00:04:12,240
that allows us to take
electrostatic energies and put

89
00:04:12,240 --> 00:04:16,525
them on the same plane as
mechanical energies.

90
00:04:16,525 --> 00:04:19,700
When we run through this, we
always end up in joules.

91
00:04:19,700 --> 00:04:22,480
Then there's a force balanced to
make sure that the electron

92
00:04:22,480 --> 00:04:25,890
neither falls into the
nucleus nor flees and

93
00:04:25,890 --> 00:04:29,490
breaks free of the atom.

94
00:04:29,490 --> 00:04:32,560
And the force balance is if you
put a ball at the end of a

95
00:04:32,560 --> 00:04:35,830
string, and you whip it around
on a tether, you have a

96
00:04:35,830 --> 00:04:38,040
centrifugal force that's trying
to get the ball to

97
00:04:38,040 --> 00:04:38,760
break away.

98
00:04:38,760 --> 00:04:41,260
And then the string
is pulling in.

99
00:04:41,260 --> 00:04:45,270
So the pull in, in this case,
is the coulombic force.

100
00:04:45,270 --> 00:04:49,340
And the force that makes the
ball want to flee is this mv

101
00:04:49,340 --> 00:04:50,360
squared over r.

102
00:04:50,360 --> 00:04:52,510
And that must be net zero.

103
00:04:52,510 --> 00:04:55,380
Otherwise we're going to
have a shift in orbit.

104
00:04:55,380 --> 00:04:57,530
And then lastly we have
the quantum condition.

105
00:04:57,530 --> 00:05:02,270
And this was the breakthrough
of Bohr where he enunciated

106
00:05:02,270 --> 00:05:06,910
that the quantum condition is
going to give us this energy

107
00:05:06,910 --> 00:05:08,500
level quantization.

108
00:05:08,500 --> 00:05:12,010
And this was a big departure
from what had been in the

109
00:05:12,010 --> 00:05:16,150
past. The only antecedent idea
of this nature was the work by

110
00:05:16,150 --> 00:05:18,700
Planck who said that
light is quantized.

111
00:05:18,700 --> 00:05:20,900
But as I told you last
day, who knows what

112
00:05:20,900 --> 00:05:22,070
light really is.

113
00:05:22,070 --> 00:05:26,040
The Newtonian notion of
a ball orbiting was

114
00:05:26,040 --> 00:05:27,780
very compelling here.

115
00:05:27,780 --> 00:05:32,690
And the notion that the movement
of the electron could

116
00:05:32,690 --> 00:05:37,380
in some way be discontinuous was
quite a major departure.

117
00:05:37,380 --> 00:05:38,790
So I left you last
day with three

118
00:05:38,790 --> 00:05:40,420
equations and three unknowns.

119
00:05:40,420 --> 00:05:42,370
And what I'm not going
to do right now

120
00:05:42,370 --> 00:05:44,080
is solve the equations.

121
00:05:44,080 --> 00:05:46,390
Because I've been lecturing long
enough to know that's the

122
00:05:46,390 --> 00:05:49,530
way to kill interest,
quench a lecture.

123
00:05:49,530 --> 00:05:52,570
And so if you really want to go
through the algebra, be my

124
00:05:52,570 --> 00:05:54,250
guest. You're smart
enough to do that.

125
00:05:54,250 --> 00:05:55,650
Instead I'm going to show
you the results.

126
00:05:55,650 --> 00:05:57,790
But those are the three
equations that you need.

127
00:05:57,790 --> 00:05:59,650
So we have an equation in r.

128
00:05:59,650 --> 00:06:01,960
We have an equation at v,
and an equation in e.

129
00:06:01,960 --> 00:06:03,430
So let's go after them.

130
00:06:03,430 --> 00:06:07,020
If you first look at
the solution for r.

131
00:06:07,020 --> 00:06:10,640
This is the radius of the orbit
of the electron, the

132
00:06:10,640 --> 00:06:11,805
orbit of the electron.

133
00:06:11,805 --> 00:06:15,960
If you go through and solve,
you'll end up with this,

134
00:06:15,960 --> 00:06:19,980
Epsilon zero times the square of
the Planck constant divided

135
00:06:19,980 --> 00:06:22,720
by pi times m.

136
00:06:22,720 --> 00:06:23,920
It's always the electron.

137
00:06:23,920 --> 00:06:26,530
So this is the radius of
the electron orbit.

138
00:06:26,530 --> 00:06:29,870
This is the mass of the electron
times the square of

139
00:06:29,870 --> 00:06:31,840
the elementary charge--

140
00:06:31,840 --> 00:06:33,730
that whole thing I'm
going to group--

141
00:06:33,730 --> 00:06:37,540
times the square of the quantum
number divided by z,

142
00:06:37,540 --> 00:06:39,720
the proton number.

143
00:06:39,720 --> 00:06:41,050
So what we see here?

144
00:06:41,050 --> 00:06:45,640
Well, everything inside the
parentheses is constant.

145
00:06:45,640 --> 00:06:46,440
These are all constant.

146
00:06:46,440 --> 00:06:48,750
Pi obviously is geometric
constant.

147
00:06:48,750 --> 00:06:50,970
And the rest of these are
constants you could look up in

148
00:06:50,970 --> 00:06:52,790
your table of constants.

149
00:06:52,790 --> 00:06:56,710
And we noticed that there is
a set of solutions to this.

150
00:06:56,710 --> 00:07:01,260
The radius of the electron can
occupy various discrete values

151
00:07:01,260 --> 00:07:03,100
defined by n.

152
00:07:03,100 --> 00:07:06,680
So we say that the radius takes
on a plurality of values

153
00:07:06,680 --> 00:07:08,550
a function of n.

154
00:07:08,550 --> 00:07:12,170
And furthermore, the
functionality goes as the

155
00:07:12,170 --> 00:07:12,910
square of n.

156
00:07:12,910 --> 00:07:16,330
It's n squared times a constant,
where that constant

157
00:07:16,330 --> 00:07:18,770
is inside those parentheses.

158
00:07:18,770 --> 00:07:21,310
And we notice that because
the r goes as n

159
00:07:21,310 --> 00:07:23,670
squared it's nonlinear.

160
00:07:23,670 --> 00:07:24,920
It's nonlinear.

161
00:07:28,560 --> 00:07:30,350
This is so important I'm
going to write it

162
00:07:30,350 --> 00:07:31,280
down one more time.

163
00:07:31,280 --> 00:07:41,725
So the radius of the electron
orbit takes multiple values.

164
00:07:41,725 --> 00:07:43,310
It takes multiple values.

165
00:07:46,490 --> 00:07:49,280
And they're discreet.

166
00:07:49,280 --> 00:07:51,540
The physicists like to
use a different term.

167
00:07:51,540 --> 00:07:53,070
When something is
discretized, the

168
00:07:53,070 --> 00:07:56,540
physicists say it is quantized.

169
00:07:56,540 --> 00:07:58,380
So these values are quantized.

170
00:07:58,380 --> 00:08:07,610
You cannot continuously vary
the radius and nonlinear

171
00:08:07,610 --> 00:08:12,280
values, multiple values.

172
00:08:12,280 --> 00:08:15,900
So let's plug in.

173
00:08:15,900 --> 00:08:17,990
Because I want to get
a sense of scale.

174
00:08:17,990 --> 00:08:21,280
So let's look at the
simplest one.

175
00:08:21,280 --> 00:08:24,115
The most primitive 1-electron
atom would be hydrogen.

176
00:08:24,115 --> 00:08:26,280
In which case, Z equals 1.

177
00:08:26,280 --> 00:08:29,870
So I've just got a proton
orbited by an electron.

178
00:08:29,870 --> 00:08:35,170
So look at atomic hydrogen.

179
00:08:35,170 --> 00:08:38,950
So in that case, Z equals 1.

180
00:08:38,950 --> 00:08:42,790
And I'm going to look at n
equals 1, which is the lowest

181
00:08:42,790 --> 00:08:43,710
number here, right?

182
00:08:43,710 --> 00:08:45,120
R scales as n squared.

183
00:08:45,120 --> 00:08:49,130
So the lowest value or r is
obtained when n equals 1.

184
00:08:49,130 --> 00:08:52,230
And this is termed
the ground state.

185
00:08:52,230 --> 00:08:55,560
The ground state.

186
00:08:55,560 --> 00:09:01,210
So I want to ask what is the
radius of the electron orbit

187
00:09:01,210 --> 00:09:03,280
ground state in atomic
hydrogen?

188
00:09:03,280 --> 00:09:07,265
And if I plug in these values,
I'll call this r sub 1.

189
00:09:07,265 --> 00:09:16,590
It turns out to be 5.29 times 10
to the minus 11 meters, or

190
00:09:16,590 --> 00:09:22,390
0.529 angstroms. I love
the angstrom.

191
00:09:22,390 --> 00:09:23,640
It's a great unit.

192
00:09:23,640 --> 00:09:24,580
It's a great unit.

193
00:09:24,580 --> 00:09:26,460
It's not an SI unit.

194
00:09:26,460 --> 00:09:28,450
But I like the angstrom.

195
00:09:28,450 --> 00:09:29,510
I'll show you why.

196
00:09:29,510 --> 00:09:34,410
If you try to express this in
SI units, well there's 10 to

197
00:09:34,410 --> 00:09:36,990
the minus 11 meters.

198
00:09:36,990 --> 00:09:43,340
The Si units go in units
of clusters of 1,000.

199
00:09:43,340 --> 00:09:45,200
So for example, you've
got the meter.

200
00:09:45,200 --> 00:09:46,660
You've got the kilometer.

201
00:09:46,660 --> 00:09:48,230
You've got the micrometer.

202
00:09:48,230 --> 00:09:51,160
You've got 10 to the
minus 9 meters,

203
00:09:51,160 --> 00:09:53,650
which is the nanometer.

204
00:09:56,250 --> 00:09:57,520
This is a Goldilocks problem.

205
00:09:57,520 --> 00:09:58,320
This one's too big.

206
00:09:58,320 --> 00:10:01,330
And then the next one down here
is 10 to the minus 12

207
00:10:01,330 --> 00:10:03,350
meters, which is
the picometer.

208
00:10:03,350 --> 00:10:07,960
So this is either 52.9
picometers, or a 0.0529

209
00:10:07,960 --> 00:10:09,970
nanometers.

210
00:10:09,970 --> 00:10:11,000
And that's no good.

211
00:10:11,000 --> 00:10:14,930
I want numbers like 3, 7,
simple to remember.

212
00:10:14,930 --> 00:10:20,740
So 0.529, this is about
1/2 angstrom.

213
00:10:20,740 --> 00:10:21,910
It's good to know.

214
00:10:21,910 --> 00:10:24,280
But you try to publish, you
know what happens in a

215
00:10:24,280 --> 00:10:25,910
scientific literature today?

216
00:10:25,910 --> 00:10:28,710
The Literary Lions that control
the journals, they'll

217
00:10:28,710 --> 00:10:31,510
circle that and say you have
to convert to SI units.

218
00:10:31,510 --> 00:10:32,930
And so they have to
right some goofy

219
00:10:32,930 --> 00:10:34,680
nanometer thing or something.

220
00:10:34,680 --> 00:10:37,430
I know you think I'm crazy,
but I love the angstrom.

221
00:10:37,430 --> 00:10:38,100
So there.

222
00:10:38,100 --> 00:10:39,890
Anyway, so here it is.

223
00:10:39,890 --> 00:10:43,770
Once you know that this is
0.529, this is on your table

224
00:10:43,770 --> 00:10:44,660
of constants.

225
00:10:44,660 --> 00:10:46,550
It's right on your table
of constants.

226
00:10:46,550 --> 00:10:48,880
So you don't have to go and
calculate all this stuff.

227
00:10:48,880 --> 00:10:52,110
Which means if you do your
homework with your table of

228
00:10:52,110 --> 00:10:56,080
constants, you will know where
those numbers lie, as opposed

229
00:10:56,080 --> 00:10:59,450
to opening this thing up for
the first time on the first

230
00:10:59,450 --> 00:11:02,800
celebration of learning on
October the 7th, and with 47

231
00:11:02,800 --> 00:11:04,910
entries and they're
tiny, tiny font.

232
00:11:04,910 --> 00:11:08,060
And you're wondering where
is that thing.

233
00:11:08,060 --> 00:11:09,140
Just a word to wise.

234
00:11:09,140 --> 00:11:10,860
So now we know what this is.

235
00:11:10,860 --> 00:11:14,650
We know this is 0.529 angstroms.
So now I can write

236
00:11:14,650 --> 00:11:17,770
an equation for the radius
of a 1-electron

237
00:11:17,770 --> 00:11:20,330
atom anywhere, anytime.

238
00:11:20,330 --> 00:11:26,600
r of n is going to be equal
to a naught which

239
00:11:26,600 --> 00:11:29,620
is this value here.

240
00:11:29,620 --> 00:11:31,460
And it is termed the
Bohr radius.

241
00:11:34,790 --> 00:11:37,050
So you can write it as a
function of the Bohr radius,

242
00:11:37,050 --> 00:11:41,750
times the square of
n divided by Z.

243
00:11:41,750 --> 00:11:45,230
So that's for all 1-electron
atoms, gas phase.

244
00:11:45,230 --> 00:11:50,930
And you can see that as Z goes
up, the r goes down, which

245
00:11:50,930 --> 00:11:51,520
makes sense.

246
00:11:51,520 --> 00:11:56,100
So suppose instead of hydrogen,
we talk helium plus

247
00:11:56,100 --> 00:11:57,020
What's the only difference?

248
00:11:57,020 --> 00:11:59,580
Helium plus has 2 protons
in the nucleus.

249
00:11:59,580 --> 00:12:03,090
Which means that the coulombic
force of attraction between

250
00:12:03,090 --> 00:12:07,010
the same 1-electron and now a
doubly charged nucleus is

251
00:12:07,010 --> 00:12:09,340
going to be stronger.

252
00:12:09,340 --> 00:12:11,320
So the first orbit is going
to get pulled in.

253
00:12:11,320 --> 00:12:14,210
And all the other orbits are
going to get pulled in.

254
00:12:14,210 --> 00:12:16,200
By how much are they going
to get pulled in?

255
00:12:16,200 --> 00:12:17,100
By that much.

256
00:12:17,100 --> 00:12:19,900
So this is the functional
representation

257
00:12:19,900 --> 00:12:21,730
of all of that physics.

258
00:12:21,730 --> 00:12:23,540
All right, there's three
equations, three unknowns.

259
00:12:23,540 --> 00:12:24,930
Let's look at energy.

260
00:12:24,930 --> 00:12:27,960
So if you go through and solve
for energy, you get this one.

261
00:12:27,960 --> 00:12:31,840
Minus this big monstrosity, mass
of the electron to the

262
00:12:31,840 --> 00:12:37,390
fourth power of the elementary
charge times 8 times the

263
00:12:37,390 --> 00:12:41,470
square of the permittivity of
vacuum times the square of the

264
00:12:41,470 --> 00:12:47,740
Planck constant, all times the
square of the Proton number

265
00:12:47,740 --> 00:12:52,630
divided by the square of
the quantum number.

266
00:12:52,630 --> 00:12:56,080
And I just to make sure
everybody is with me here.

267
00:12:56,080 --> 00:13:01,430
I always want to write n here.
n equals 1, 2, 3, takes on

268
00:13:01,430 --> 00:13:02,710
integer values.

269
00:13:02,710 --> 00:13:04,090
And we'll say it again here.

270
00:13:04,090 --> 00:13:08,530
N equals 1, 2, 3, et
cetera, et cetera.

271
00:13:08,530 --> 00:13:15,020
So again we say we see that
e is a function of n.

272
00:13:15,020 --> 00:13:15,720
It's discretized.

273
00:13:15,720 --> 00:13:17,890
It's quantized.

274
00:13:17,890 --> 00:13:18,580
Why?

275
00:13:18,580 --> 00:13:22,330
Because once you impose the
quantum condition here on

276
00:13:22,330 --> 00:13:24,470
angular momentum, it propagates

277
00:13:24,470 --> 00:13:25,880
through the entire model.

278
00:13:25,880 --> 00:13:28,470
So radius this quantized, energy
is quantized, you're

279
00:13:28,470 --> 00:13:29,970
going to see velocity
is quantized.

280
00:13:29,970 --> 00:13:33,740
Because the quantum condition
is pervasive.

281
00:13:33,740 --> 00:13:38,110
So e to the n, and I'm going to
take this whole quantity in

282
00:13:38,110 --> 00:13:42,810
parentheses and just
call it giant K.

283
00:13:42,810 --> 00:13:44,600
These are all positive
quantities.

284
00:13:44,600 --> 00:13:45,720
Mass is positive.

285
00:13:45,720 --> 00:13:49,010
And squares and fourth powers
of numbers must be positive.

286
00:13:49,010 --> 00:13:56,650
So this is K times Z squared
over n squared That's good.

287
00:13:56,650 --> 00:13:59,210
And we can go and evaluate K.

288
00:13:59,210 --> 00:14:05,990
And when we evaluate L in SI
units, we get 2.18 times 10 to

289
00:14:05,990 --> 00:14:10,500
the minus 18 joules.

290
00:14:10,500 --> 00:14:13,450
This is joules per atom.

291
00:14:13,450 --> 00:14:16,750
Or you can multiply this
by Avogadro's number.

292
00:14:16,750 --> 00:14:19,230
If you multiply it by Avogadro's
number, then that

293
00:14:19,230 --> 00:14:28,270
will give you 1.312 megajoules
per mol.

294
00:14:28,270 --> 00:14:32,700
So that's the energy of the
electron in the ground state

295
00:14:32,700 --> 00:14:34,730
of atomic hydrogen.

296
00:14:34,730 --> 00:14:39,000
And then we can mediate that
with Z and n, and go to

297
00:14:39,000 --> 00:14:41,870
electrons that are outside the
ground state, above the ground

298
00:14:41,870 --> 00:14:45,160
state, or ground state electrons
in atoms that have

299
00:14:45,160 --> 00:14:47,800
more than 1 proton, or both.

300
00:14:47,800 --> 00:14:50,630
And so let's take a look
at the graphical

301
00:14:50,630 --> 00:14:51,790
representation of that.

302
00:14:51,790 --> 00:14:55,030
So instead of Cartesian
coordinates, because this is

303
00:14:55,030 --> 00:14:57,450
spatial distribution, I'm
going to go to energy

304
00:14:57,450 --> 00:15:00,080
coordinates and give you an
energy level diagram.

305
00:15:00,080 --> 00:15:05,700
So again, not to scale.

306
00:15:05,700 --> 00:15:08,940
Because this thing goes
is 1 over the square.

307
00:15:08,940 --> 00:15:10,300
So that's going to be messy.

308
00:15:10,300 --> 00:15:12,360
So let's start here.

309
00:15:12,360 --> 00:15:15,535
And on the left side I'm going
to designate the energy.

310
00:15:15,535 --> 00:15:17,590
And on the right side
I'm going to

311
00:15:17,590 --> 00:15:18,950
designate the quantum number.

312
00:15:18,950 --> 00:15:20,280
I'm going to start down here.

313
00:15:20,280 --> 00:15:21,470
That's the lowest energy.

314
00:15:21,470 --> 00:15:23,810
You see these are all negative
values, first of all.

315
00:15:23,810 --> 00:15:25,670
They're all negative values.

316
00:15:25,670 --> 00:15:27,910
Because Z is a square,
n is a square, and K

317
00:15:27,910 --> 00:15:29,750
is a positive quantity.

318
00:15:29,750 --> 00:15:31,600
So n equals 1 is the
lowest state.

319
00:15:31,600 --> 00:15:32,770
It's the ground state.

320
00:15:32,770 --> 00:15:37,680
It has a value of minus K.

321
00:15:37,680 --> 00:15:40,660
So I'm going to do this one
just for atomic hydrogen.

322
00:15:40,660 --> 00:15:44,440
So I'm going to write
atomic H.

323
00:15:44,440 --> 00:15:47,900
So now Z equals 1.

324
00:15:47,900 --> 00:15:51,520
You can do it later for Z
equals 2, 3, whatever.

325
00:15:51,520 --> 00:15:52,850
So this is atomic hydrogen.

326
00:15:52,850 --> 00:15:56,580
So ground state energy
is minus K.

327
00:15:56,580 --> 00:15:59,700
What happens if we go to n
equals 2? n equals 2 it

328
00:15:59,700 --> 00:16:02,460
becomes K divided
by 2 squared 4.

329
00:16:02,460 --> 00:16:04,000
So it should be 3/4
of the way up.

330
00:16:04,000 --> 00:16:06,180
I'm not going to go quite
3/4 of the way.

331
00:16:06,180 --> 00:16:08,710
Because I want to leave room
for some fine structure.

332
00:16:08,710 --> 00:16:10,380
That's why it's not to scale.

333
00:16:10,380 --> 00:16:13,200
All right so this is
minus L over 4.

334
00:16:13,200 --> 00:16:15,060
What if we go to n equals 3?

335
00:16:15,060 --> 00:16:16,430
Well it's not symmetric here.

336
00:16:16,430 --> 00:16:17,150
It's nonlinear.

337
00:16:17,150 --> 00:16:18,940
But this should be
really what?

338
00:16:18,940 --> 00:16:21,880
Minus K over 3 squared is 9.

339
00:16:21,880 --> 00:16:22,720
You get the picture.

340
00:16:22,720 --> 00:16:27,170
3, you can go 4, 5, and so on
until n equals infinity.

341
00:16:27,170 --> 00:16:29,450
What happens when n
equals infinity?

342
00:16:29,450 --> 00:16:33,210
I've got minus K over infinity,
which is vanishingly

343
00:16:33,210 --> 00:16:34,840
small, zero.

344
00:16:34,840 --> 00:16:38,590
Where is the electron when
n equals infinity?

345
00:16:38,590 --> 00:16:42,740
r is n squared times
the Bohr radius.

346
00:16:42,740 --> 00:16:46,830
That's a great, great
distance away.

347
00:16:46,830 --> 00:16:47,870
What does it mean?

348
00:16:47,870 --> 00:16:50,810
Physically it means that the
electron is so far away that

349
00:16:50,810 --> 00:16:52,190
it is no longer bound.

350
00:16:52,190 --> 00:16:55,710
It's no longer part
of the atom.

351
00:16:55,710 --> 00:16:58,910
And when it's no longer part of
the atom, and the potential

352
00:16:58,910 --> 00:17:01,920
energy that's stored is a result
of the charges coming

353
00:17:01,920 --> 00:17:03,630
together from infinity.

354
00:17:03,630 --> 00:17:05,800
I'm starting to talk like
someone out of 802.

355
00:17:05,800 --> 00:17:09,480
What's the energy if I take 2
charged particles at infinite

356
00:17:09,480 --> 00:17:10,210
separation?

357
00:17:10,210 --> 00:17:12,510
I bring them into some
finite separation.

358
00:17:12,510 --> 00:17:13,170
Voila.

359
00:17:13,170 --> 00:17:13,970
There it is.

360
00:17:13,970 --> 00:17:15,590
So when they're in infinite
separation

361
00:17:15,590 --> 00:17:17,030
there's no energy stored.

362
00:17:17,030 --> 00:17:18,850
Hence, you are at that point.

363
00:17:18,850 --> 00:17:25,000
So n equals infinity means r
equals infinity, which means E

364
00:17:25,000 --> 00:17:25,780
equal zero.

365
00:17:25,780 --> 00:17:27,590
There's no stored energy.

366
00:17:27,590 --> 00:17:30,570
So this means the electron
is no longer bound.

367
00:17:33,940 --> 00:17:37,080
And therefore, if it's
no longer bound, we

368
00:17:37,080 --> 00:17:37,930
have a term for it.

369
00:17:37,930 --> 00:17:39,440
It's called free.

370
00:17:39,440 --> 00:17:42,290
It's a free electron.

371
00:17:42,290 --> 00:17:44,480
And if the electron
is free, then the

372
00:17:44,480 --> 00:17:48,565
atom is electron deficient.

373
00:17:48,565 --> 00:17:50,780
So if the electron is
free, that means the

374
00:17:50,780 --> 00:17:54,810
atom is now an ion.

375
00:17:54,810 --> 00:17:56,225
Because it's lost an electron.

376
00:17:56,225 --> 00:17:57,990
It's no longer net neutral.

377
00:17:57,990 --> 00:18:03,800
Or we say an atom hasn't
turned into an ion.

378
00:18:03,800 --> 00:18:06,200
Or the electron has
been ionized.

379
00:18:12,900 --> 00:18:14,130
What's the energy for that?

380
00:18:14,130 --> 00:18:15,740
We can calculate what
that energy is.

381
00:18:15,740 --> 00:18:17,760
It would be called the
ionization energy.

382
00:18:17,760 --> 00:18:20,620
So if I started with an electron
down in here, and I

383
00:18:20,620 --> 00:18:23,090
sent it all the way
to infinity.

384
00:18:23,090 --> 00:18:24,490
See that's an energy space.

385
00:18:24,490 --> 00:18:27,410
Which is the equivalent in
Cartesian space to go from

386
00:18:27,410 --> 00:18:30,510
here to infinity, same idea.

387
00:18:30,510 --> 00:18:32,040
Do you see the models?

388
00:18:32,040 --> 00:18:34,460
This is Cartesian.

389
00:18:34,460 --> 00:18:34,900
It's like a.

390
00:18:34,900 --> 00:18:37,450
Map This is energy
coordinates.

391
00:18:37,450 --> 00:18:38,740
It's different.

392
00:18:38,740 --> 00:18:40,210
And you're going to be
able to think from

393
00:18:40,210 --> 00:18:41,600
one model to another.

394
00:18:41,600 --> 00:18:43,050
What's the energy
consequences?

395
00:18:43,050 --> 00:18:44,980
What are the Cartesian
consequences?

396
00:18:44,980 --> 00:18:46,980
Until we get to the point where
there is no Cartesian

397
00:18:46,980 --> 00:18:47,790
representation.

398
00:18:47,790 --> 00:18:50,560
Because the abstraction level
is too high, we'll have to

399
00:18:50,560 --> 00:18:51,720
content ourselves with this.

400
00:18:51,720 --> 00:18:54,000
So get comfortable moving
from there to there.

401
00:18:54,000 --> 00:18:56,550
And then some day we're going
to say it's too complicated.

402
00:18:56,550 --> 00:18:58,240
There's no Cartesian thing.

403
00:18:58,240 --> 00:18:59,800
We'll be comfortable
by then with this.

404
00:18:59,800 --> 00:19:02,580
OK so now we're taking an
electron from here up to here.

405
00:19:02,580 --> 00:19:06,600
While we ask, what is the
ionization energy?

406
00:19:06,600 --> 00:19:10,370
The ionization energy must
equal the delta E of the

407
00:19:10,370 --> 00:19:11,620
transition.

408
00:19:14,440 --> 00:19:15,230
So what's that?

409
00:19:15,230 --> 00:19:18,560
The delta E of the transition
is going to equal always E

410
00:19:18,560 --> 00:19:22,360
final minus E initial.

411
00:19:22,360 --> 00:19:25,290
E final minus E initial.

412
00:19:25,290 --> 00:19:29,530
Which is equal to E
at infinity minus

413
00:19:29,530 --> 00:19:32,000
E1, the ground state.

414
00:19:32,000 --> 00:19:34,540
Well E infinity, we just
said, is zero.

415
00:19:34,540 --> 00:19:38,630
And the ground state energy
is equal to minus K.

416
00:19:38,630 --> 00:19:40,860
So minus minus K is K.

417
00:19:40,860 --> 00:19:44,120
So you also get the energy.

418
00:19:44,120 --> 00:19:47,090
From infinity down to
ground state is

419
00:19:47,090 --> 00:19:48,960
the ionization energy.

420
00:19:48,960 --> 00:19:58,050
So we can define the ionization
energy in terms of

421
00:19:58,050 --> 00:19:59,610
this transition.

422
00:19:59,610 --> 00:20:06,280
Define ionization energy as the
minimum energy to remove

423
00:20:06,280 --> 00:20:23,430
an electron from the
ground state of an

424
00:20:23,430 --> 00:20:24,733
atom in a gas phase.

425
00:20:31,020 --> 00:20:32,640
So that means there's no
solids, no liquids.

426
00:20:32,640 --> 00:20:33,980
There's no work function here.

427
00:20:33,980 --> 00:20:36,410
There's no lattice energy,
and so on.

428
00:20:36,410 --> 00:20:40,340
So there's a definition of
the ionization energy.

429
00:20:40,340 --> 00:20:42,880
And we can be a little
bit more elaborate.

430
00:20:42,880 --> 00:20:44,300
Even though right now I'm
just going to do a

431
00:20:44,300 --> 00:20:45,380
little break here.

432
00:20:45,380 --> 00:20:46,620
I don't want to mislead
people.

433
00:20:46,620 --> 00:20:49,620
But just an aside.

434
00:20:49,620 --> 00:20:51,110
I'm nonlinear.

435
00:20:51,110 --> 00:20:53,070
I can have multiple
conversations at once.

436
00:20:53,070 --> 00:20:54,910
And you are capable
of stacking.

437
00:20:54,910 --> 00:20:56,130
So we're going to break now.

438
00:20:56,130 --> 00:20:58,160
We're not going to talk
about 1-electron atom.

439
00:20:58,160 --> 00:21:01,900
We're going to follow the thread
of ionization energy.

440
00:21:01,900 --> 00:21:03,310
I'm going to take lithium.

441
00:21:03,310 --> 00:21:08,250
Lithium in its normal state has
3 protons, 3 electrons.

442
00:21:08,250 --> 00:21:10,140
So I'm going to take
lithium gas.

443
00:21:10,140 --> 00:21:13,800
And I'm going to ionize it
and make lithium plus.

444
00:21:13,800 --> 00:21:16,230
So this is a lithium plus
ion in the gas phase.

445
00:21:16,230 --> 00:21:17,760
It's still got 2 electrons.

446
00:21:17,760 --> 00:21:19,330
So this isn't Bohr
model stuff.

447
00:21:19,330 --> 00:21:21,880
But anyway, here we are.

448
00:21:21,880 --> 00:21:26,470
So the energy for this action
would be called

449
00:21:26,470 --> 00:21:27,690
the ionization energy.

450
00:21:27,690 --> 00:21:31,437
Because I took a neutral atom,
and I pulled an electron out

451
00:21:31,437 --> 00:21:32,910
of the ground state,
and so on.

452
00:21:32,910 --> 00:21:34,140
So this is an ionization
energy.

453
00:21:34,140 --> 00:21:36,790
But now I can continue
this process.

454
00:21:36,790 --> 00:21:39,860
And I can take Lithium plus.

455
00:21:39,860 --> 00:21:42,900
And I can lose an electron from
that, which will than

456
00:21:42,900 --> 00:21:45,970
give me lithium 2 plus.

457
00:21:45,970 --> 00:21:48,150
And this is called also
an ionization energy.

458
00:21:48,150 --> 00:21:50,710
This is called the second
ionization energy.

459
00:21:50,710 --> 00:21:52,320
So this is the first
ionization energy.

460
00:21:52,320 --> 00:21:55,650
But just as when you write an
equation, when the coefficient

461
00:21:55,650 --> 00:21:59,450
is 1, you don't write the 1.

462
00:21:59,450 --> 00:22:01,110
I don't write 1 lithium here.

463
00:22:01,110 --> 00:22:02,360
I know it's 1.

464
00:22:02,360 --> 00:22:04,460
This is the second ionization
energy.

465
00:22:04,460 --> 00:22:06,700
And then I can keep stripping
away electrons.

466
00:22:06,700 --> 00:22:11,010
And I can take lithium 2 plus
in the gas phase, and take

467
00:22:11,010 --> 00:22:16,120
away that electron leaving me
with just the lithium nucleus,

468
00:22:16,120 --> 00:22:19,060
lithium 3 plus, plus electron.

469
00:22:19,060 --> 00:22:23,260
And that's called the third
ionization energy.

470
00:22:23,260 --> 00:22:25,340
OK, now what can we say?

471
00:22:25,340 --> 00:22:29,530
What's the relationship here
between any of this except the

472
00:22:29,530 --> 00:22:31,860
definition and the Bohr model?

473
00:22:31,860 --> 00:22:32,250
well?

474
00:22:32,250 --> 00:22:35,810
The Bohr model applies only to
1-electron atoms. Are there

475
00:22:35,810 --> 00:22:40,270
any 1-electron atoms
on this board?

476
00:22:40,270 --> 00:22:42,460
So we can calculate
the energy, the

477
00:22:42,460 --> 00:22:43,820
third ionization energy.

478
00:22:43,820 --> 00:22:45,730
We can get that from
the Bohr model.

479
00:22:48,330 --> 00:22:49,820
You can do it in your head.

480
00:22:49,820 --> 00:22:51,360
You can do it in your
head right?

481
00:22:51,360 --> 00:22:55,520
It's just K times Z squared
right here.

482
00:22:55,520 --> 00:22:56,630
It's going from 1.

483
00:22:56,630 --> 00:23:02,480
So if this is 2.18, it's going
to be 9 times that trivially.

484
00:23:02,480 --> 00:23:08,040
OK, so this is just
3 squared times K.

485
00:23:08,040 --> 00:23:11,860
And this when you have to
get from the literature.

486
00:23:11,860 --> 00:23:14,000
So you have to go to
primary sources.

487
00:23:14,000 --> 00:23:15,060
Which is why you're going
to learn how to

488
00:23:15,060 --> 00:23:17,530
use the proper database.

489
00:23:17,530 --> 00:23:20,070
And this one here also you
get from the literature.

490
00:23:20,070 --> 00:23:23,020
But this is on your
periodic table.

491
00:23:23,020 --> 00:23:26,040
Your periodic table, one of the
data points it gives is

492
00:23:26,040 --> 00:23:28,960
the first ionization energy
of all of the elements.

493
00:23:28,960 --> 00:23:31,790
And so even though lithium
normally is a solid at room

494
00:23:31,790 --> 00:23:35,140
temperature, the ionization
energy for lithium as given on

495
00:23:35,140 --> 00:23:36,945
your periodic table is
for this reaction.

496
00:23:36,945 --> 00:23:40,100
It's for the gas.

497
00:23:40,100 --> 00:23:40,400
Anyway.

498
00:23:40,400 --> 00:23:42,660
So that's little aside.

499
00:23:42,660 --> 00:23:46,410
All right, the last quantity
that we could get from the

500
00:23:46,410 --> 00:23:49,690
Bohr model is v, the velocity.

501
00:23:49,690 --> 00:23:50,730
And I solve for the velocity.

502
00:23:50,730 --> 00:23:52,240
We don't talk about
this very much.

503
00:23:52,240 --> 00:23:56,950
But we're going to
do so once today.

504
00:23:56,950 --> 00:23:58,210
And here it is.

505
00:23:58,210 --> 00:23:59,820
So I went through the algebra.

506
00:23:59,820 --> 00:24:05,780
And you get nh over 2 pi mr,
where r is the radius.

507
00:24:05,780 --> 00:24:07,020
There's the quantum number.

508
00:24:07,020 --> 00:24:08,600
This is quantized as well.

509
00:24:08,600 --> 00:24:09,830
So I regrouped this.

510
00:24:09,830 --> 00:24:12,800
And I already have a nice, cool
expression for r in terms

511
00:24:12,800 --> 00:24:14,070
of the Bohr radius.

512
00:24:14,070 --> 00:24:16,910
So I use that because
that's on the table.

513
00:24:16,910 --> 00:24:20,690
So this is 2 pi times the mass
of the electron times the Bohr

514
00:24:20,690 --> 00:24:28,240
radius, 1/2 angstrom, times Z
proton number divided by n,

515
00:24:28,240 --> 00:24:32,810
where n equals 1,
2, 3, and so on.

516
00:24:32,810 --> 00:24:34,980
So let's again get
a sense of scale.

517
00:24:34,980 --> 00:24:38,160
So let's try for
sense of scale.

518
00:24:41,540 --> 00:24:45,950
Let's do velocity of the ground
state electron in

519
00:24:45,950 --> 00:24:47,350
atomic hydrogen.

520
00:24:47,350 --> 00:24:51,080
So that means Z equals
1, n equals 1.

521
00:24:51,080 --> 00:24:52,760
So I plug in the numbers.

522
00:24:52,760 --> 00:24:59,800
And I get v1 for hydrogen,
atomic hydrogen, gives me 2.18

523
00:24:59,800 --> 00:25:02,870
times 10 to the 6 meters
for second.

524
00:25:06,870 --> 00:25:07,180
I don't know.

525
00:25:07,180 --> 00:25:07,950
Is that fast?

526
00:25:07,950 --> 00:25:08,880
Is that slow?

527
00:25:08,880 --> 00:25:09,260
I don't know.

528
00:25:09,260 --> 00:25:10,490
But I do know this much.

529
00:25:10,490 --> 00:25:14,890
I know that the speed of light
is equal to 3 times 10 to the

530
00:25:14,890 --> 00:25:16,943
8 meters per second.

531
00:25:20,500 --> 00:25:24,080
So 10 to the 8 divided
by 10 to the 6.

532
00:25:24,080 --> 00:25:27,280
2 and 3, that's roughly 1,
speaking as an engineer.

533
00:25:27,280 --> 00:25:28,620
Who cares?

534
00:25:28,620 --> 00:25:32,540
So this is about 1% of
the speed of light.

535
00:25:35,840 --> 00:25:36,790
That's pretty good.

536
00:25:36,790 --> 00:25:38,960
That gives me something
I can hang on to.

537
00:25:38,960 --> 00:25:42,900
I would say that if this thing
is zipping around at 1% of the

538
00:25:42,900 --> 00:25:50,090
speed of light, I would say
that's relatively fast. One

539
00:25:50,090 --> 00:25:52,060
more time, 1% of the
speed of light.

540
00:25:52,060 --> 00:25:58,030
That's relatively fast.

541
00:25:58,030 --> 00:26:01,560
Remember last day I told you
that Bohr simply dismissed the

542
00:26:01,560 --> 00:26:06,850
concept of the use of classical
electrodynamics down

543
00:26:06,850 --> 00:26:08,270
to atomic dimensions.

544
00:26:08,270 --> 00:26:11,840
Well here's another example of
why a lot of these assumptions

545
00:26:11,840 --> 00:26:13,250
aren't going to work so well.

546
00:26:13,250 --> 00:26:17,330
We're talking about the ground
state electron velocity in

547
00:26:17,330 --> 00:26:21,140
this putative planetary model
of a 1-electron atom.

548
00:26:21,140 --> 00:26:23,010
You're already getting into
relativistic effects.

549
00:26:23,010 --> 00:26:25,120
So, just another example.

550
00:26:25,120 --> 00:26:29,592
By the way, why do we use the
letter c for speed of light?

551
00:26:29,592 --> 00:26:31,420
It comes from the latin word

552
00:26:31,420 --> 00:26:35,530
celeritas, which means swiftness.

553
00:26:35,530 --> 00:26:38,200
And we get the modern
word acceleration,

554
00:26:38,200 --> 00:26:40,150
deceleration from that.

555
00:26:40,150 --> 00:26:41,150
OK.

556
00:26:41,150 --> 00:26:41,430
All right.

557
00:26:41,430 --> 00:26:45,430
So the Bohr model, we've
now rolled it all out.

558
00:26:45,430 --> 00:26:46,890
We have the energy portrait.

559
00:26:46,890 --> 00:26:49,230
We have the radii, discrete.

560
00:26:49,230 --> 00:26:50,750
We have quantization.

561
00:26:50,750 --> 00:26:52,660
And we have velocities
if we ever want to

562
00:26:52,660 --> 00:26:53,550
look at those again.

563
00:26:53,550 --> 00:26:56,120
Now what's the next thing
we do in science?

564
00:26:56,120 --> 00:27:00,110
We compare the predictions of
the Bohr model with data.

565
00:27:00,110 --> 00:27:01,640
Are there any data
to support this?

566
00:27:01,640 --> 00:27:04,370
Because remember, all Rutherford
said was plum

567
00:27:04,370 --> 00:27:05,690
pudding doesn't make sense.

568
00:27:05,690 --> 00:27:08,070
Instead I'm going to concentrate
the positive mass

569
00:27:08,070 --> 00:27:08,950
in the center.

570
00:27:08,950 --> 00:27:12,030
And then Bohr came along and
said, not only is it going to

571
00:27:12,030 --> 00:27:15,350
be a planetary model, I'm going
to have circular orbits.

572
00:27:15,350 --> 00:27:17,600
So now we've gone a long way
from Geiger-Marsden.

573
00:27:17,600 --> 00:27:19,700
So is there any data?

574
00:27:19,700 --> 00:27:23,620
Well there were data in 1853.

575
00:27:23,620 --> 00:27:26,500
Remember, Bohr published
this in 1913.

576
00:27:26,500 --> 00:27:30,820
In 1853 there was a
spectroscopist by the name--

577
00:27:30,820 --> 00:27:32,570
I'm going to tell
you his name--

578
00:27:32,570 --> 00:27:36,360
in Uppsala, Sweden.

579
00:27:36,360 --> 00:27:38,570
And his name was Angstrom.

580
00:27:42,720 --> 00:27:45,710
Angstrom was doing experiments
on hydrogen in

581
00:27:45,710 --> 00:27:48,140
gas discharge tubes.

582
00:27:48,140 --> 00:27:58,680
So he measured emissions from
gas discharge tube.

583
00:28:01,200 --> 00:28:04,810
And it was filled with
various gases

584
00:28:04,810 --> 00:28:08,890
including atomic hydrogen.

585
00:28:08,890 --> 00:28:12,550
And in order to take his
data, what he used

586
00:28:12,550 --> 00:28:15,050
was this device here--

587
00:28:15,050 --> 00:28:17,330
there's the Bohr radius,
just an example.

588
00:28:17,330 --> 00:28:19,740
He used the prism
spectrograph.

589
00:28:19,740 --> 00:28:21,230
So here's a gas discharge
tube.

590
00:28:21,230 --> 00:28:23,300
And I'm going to show you the
physics of that in a second.

591
00:28:23,300 --> 00:28:24,890
Basically you've got a
pair of electrodes.

592
00:28:24,890 --> 00:28:26,135
You've got gas in the tube.

593
00:28:26,135 --> 00:28:30,080
And as this cartoon shows, you
apply a potential across the

594
00:28:30,080 --> 00:28:30,750
electrodes.

595
00:28:30,750 --> 00:28:33,170
And beyond a certain threshold
potential, the

596
00:28:33,170 --> 00:28:34,860
tube begins to glow.

597
00:28:34,860 --> 00:28:36,530
And the glow goes in
all directions.

598
00:28:36,530 --> 00:28:38,110
And a blinds you when
you're in the lab.

599
00:28:38,110 --> 00:28:40,410
So what you do, is you
cover this up a bit.

600
00:28:40,410 --> 00:28:41,760
You have a narrow slit.

601
00:28:41,760 --> 00:28:44,260
And then you force the light
to come through in a thin

602
00:28:44,260 --> 00:28:46,880
ribbon, and then expose
it to a prism.

603
00:28:46,880 --> 00:28:50,850
What the prism does, is it takes
the light and breaks it

604
00:28:50,850 --> 00:28:54,490
into its components, sort of
rainbow-like, and magnifies

605
00:28:54,490 --> 00:28:56,630
the difference.

606
00:28:56,630 --> 00:28:59,560
As refraction goes, different
wavelengths will refract

607
00:28:59,560 --> 00:29:00,550
different amounts.

608
00:29:00,550 --> 00:29:02,420
And then you shoot this
across the room.

609
00:29:05,280 --> 00:29:06,430
There's two counters.

610
00:29:06,430 --> 00:29:09,340
One is a scintillation screen
and an army of graduate

611
00:29:09,340 --> 00:29:10,980
students who sit there
in the dark.

612
00:29:10,980 --> 00:29:13,690
But they're no good because you
can't stick them into the

613
00:29:13,690 --> 00:29:14,570
publication.

614
00:29:14,570 --> 00:29:17,120
You need to have data that
people will rely upon.

615
00:29:17,120 --> 00:29:19,460
So instead you use a
photographic plate.

616
00:29:19,460 --> 00:29:23,740
And if you put even a tiny,
tiny angle of separation

617
00:29:23,740 --> 00:29:26,380
across a great enough distance,
you start to get

618
00:29:26,380 --> 00:29:28,090
enough line splitting
that you can see.

619
00:29:28,090 --> 00:29:29,030
And then you go backwards.

620
00:29:29,030 --> 00:29:30,230
And you know the
geometry here.

621
00:29:30,230 --> 00:29:32,870
And you can figure out what the
wavelength must have been

622
00:29:32,870 --> 00:29:34,710
to go this distance, et
cetera, et cetera.

623
00:29:34,710 --> 00:29:38,070
And these are all color coded,
not because they had color

624
00:29:38,070 --> 00:29:41,400
film in those days, but just
to let you know that 656

625
00:29:41,400 --> 00:29:45,150
nanometers, if you were the
graduate student sitting

626
00:29:45,150 --> 00:29:47,470
there, you'd see a red line, a
green line, a blue line, and a

627
00:29:47,470 --> 00:29:49,330
violent line.

628
00:29:49,330 --> 00:29:50,580
So that's how he made
the measurements.

629
00:29:54,070 --> 00:29:56,140
And he published those
measurements.

630
00:29:56,140 --> 00:30:00,510
And so they lay.

631
00:30:00,510 --> 00:30:03,620
And then the story gets
a little thicker.

632
00:30:03,620 --> 00:30:09,310
In 1885, there's a Swiss high
school math teacher.

633
00:30:09,310 --> 00:30:10,720
I mean, I can't make
this stuff.

634
00:30:10,720 --> 00:30:12,030
This is true story.

635
00:30:12,030 --> 00:30:15,040
There's a Swiss high school math
teacher by the name of J.

636
00:30:15,040 --> 00:30:15,310
J.

637
00:30:15,310 --> 00:30:16,290
Balmer.

638
00:30:16,290 --> 00:30:16,720
We had J.

639
00:30:16,720 --> 00:30:16,940
J.

640
00:30:16,940 --> 00:30:17,440
Thomson.

641
00:30:17,440 --> 00:30:18,070
Now we've got J.

642
00:30:18,070 --> 00:30:18,280
J.

643
00:30:18,280 --> 00:30:19,300
Balmer.

644
00:30:19,300 --> 00:30:19,630
And J.

645
00:30:19,630 --> 00:30:19,770
J.

646
00:30:19,770 --> 00:30:22,620
Balmer, he loved to
play with numbers.

647
00:30:22,620 --> 00:30:25,640
And he was studying
this set of lines.

648
00:30:25,640 --> 00:30:27,730
And he was trying to come
up with a pattern.

649
00:30:27,730 --> 00:30:28,840
Can you see a pattern there?

650
00:30:28,840 --> 00:30:33,160
410 434 486, 656, do
they go squares?

651
00:30:33,160 --> 00:30:35,180
Are they primes?

652
00:30:35,180 --> 00:30:36,380
What's the pattern there?

653
00:30:36,380 --> 00:30:39,440
So Balmer puzzled over
this for awhile.

654
00:30:39,440 --> 00:30:42,480
And he finally came up with
the equation to represent

655
00:30:42,480 --> 00:30:43,650
those lines.

656
00:30:43,650 --> 00:30:49,640
So he studied Angstrom's
data found the pattern.

657
00:30:53,150 --> 00:30:54,870
And here's the pattern
that he found.

658
00:30:54,870 --> 00:30:58,450
He said that those
are wavelengths.

659
00:30:58,450 --> 00:31:04,720
If I take instead wave number,
nu bar is called wave number,

660
00:31:04,720 --> 00:31:09,660
which is the reciprocal
of the wavelength.

661
00:31:09,660 --> 00:31:13,430
So if I take the reciprocal of
the wavelength, I end up with

662
00:31:13,430 --> 00:31:17,980
those 4 lines conforming to a
series that goes like this.

663
00:31:17,980 --> 00:31:22,780
1 over 2 squared minus 1
over n squared, where n

664
00:31:22,780 --> 00:31:27,260
equals 3, 4, 5, 6.

665
00:31:27,260 --> 00:31:30,510
And there's a constant here
which we're going

666
00:31:30,510 --> 00:31:32,330
to designate r.

667
00:31:32,330 --> 00:31:34,790
And the value of R--

668
00:31:34,790 --> 00:31:37,480
I'm going to put that
on the next board--

669
00:31:37,480 --> 00:31:43,040
the value of R as expressed in
SI units today, would be 1.1

670
00:31:43,040 --> 00:31:46,740
times 10 to the 7 reciprocal
meters.

671
00:31:46,740 --> 00:31:48,390
Wavelength is a meter.

672
00:31:48,390 --> 00:31:50,370
Reciprocal wavelength
or wave number must

673
00:31:50,370 --> 00:31:52,120
be reciprocal meters.

674
00:31:52,120 --> 00:31:56,160
So how this all of this support
the Bohr model?

675
00:31:56,160 --> 00:31:58,450
Well in order to explain it,
I've got a first tell you what

676
00:31:58,450 --> 00:32:01,200
the physics of the gas
discharge tube are.

677
00:32:01,200 --> 00:32:06,520
So let's go inside the gas
discharge tube and understand

678
00:32:06,520 --> 00:32:07,200
those physics.

679
00:32:07,200 --> 00:32:09,410
So here's the gas
discharge tube.

680
00:32:09,410 --> 00:32:12,830
It's made are borosilicate
glass.

681
00:32:12,830 --> 00:32:15,390
And we fill it with gas.

682
00:32:15,390 --> 00:32:19,530
And in this case, the gas is
going to contain among other

683
00:32:19,530 --> 00:32:21,660
things hydrogen.

684
00:32:21,660 --> 00:32:25,120
So this is a hydrogen
gas phase atom.

685
00:32:25,120 --> 00:32:27,340
And this is probably
at low pressure.

686
00:32:27,340 --> 00:32:29,330
And then I said I
need electrode.

687
00:32:29,330 --> 00:32:31,200
I'll get the electrodes
inside.

688
00:32:31,200 --> 00:32:33,320
So I've got to have a really
good glass blower who can make

689
00:32:33,320 --> 00:32:35,330
a glass to metal seal,
and have a

690
00:32:35,330 --> 00:32:37,670
feedthrough to an electrode.

691
00:32:37,670 --> 00:32:39,800
So this is still
a vacuum seal.

692
00:32:39,800 --> 00:32:41,420
How do they get the gas
in the first place?

693
00:32:41,420 --> 00:32:42,550
We don't show you this
in the books.

694
00:32:42,550 --> 00:32:44,430
I'll tell you because I
did this in my Ph.D.

695
00:32:44,430 --> 00:32:47,430
What you do is you have a
little side tube here.

696
00:32:47,430 --> 00:32:49,380
You evacuate.

697
00:32:49,380 --> 00:32:52,300
This goes to a vacuum pump.

698
00:32:52,300 --> 00:32:54,190
And then over here you
have a gas source.

699
00:32:54,190 --> 00:32:55,440
You evacuate.

700
00:32:55,440 --> 00:32:57,520
Put in the gas to whatever
pressure you want.

701
00:32:57,520 --> 00:33:00,230
And then the glass blower
disconnects.

702
00:33:00,230 --> 00:33:02,170
This pulls this down
to a reduced

703
00:33:02,170 --> 00:33:05,200
pressure, and seals it.

704
00:33:05,200 --> 00:33:06,880
But the books don't
show you that.

705
00:33:06,880 --> 00:33:09,650
That's a secret.

706
00:33:09,650 --> 00:33:11,310
So we've got a gas
at low pressure.

707
00:33:11,310 --> 00:33:13,320
And I've got an electrode
over here and an

708
00:33:13,320 --> 00:33:14,270
electrode over here.

709
00:33:14,270 --> 00:33:18,055
And they're connected to a
variable voltage power supply.

710
00:33:18,055 --> 00:33:20,200
So I'm going to put an arrow
with the V meaning it's

711
00:33:20,200 --> 00:33:21,070
variable voltage.

712
00:33:21,070 --> 00:33:22,650
I can change the voltage.

713
00:33:22,650 --> 00:33:24,730
And this convention, this
is the negative side.

714
00:33:24,730 --> 00:33:26,680
So this means the electrons
leave the power

715
00:33:26,680 --> 00:33:27,950
supply and go like this.

716
00:33:27,950 --> 00:33:30,300
Which means this electrode
will be negative.

717
00:33:30,300 --> 00:33:32,530
And this electrode
will be positive.

718
00:33:32,530 --> 00:33:35,390
And thanks to Michael Faraday,
we will call

719
00:33:35,390 --> 00:33:37,270
this one the cathode.

720
00:33:37,270 --> 00:33:39,100
And this one we will
call the anode.

721
00:33:41,880 --> 00:33:43,080
Now what happens?

722
00:33:43,080 --> 00:33:45,660
We start turning up the
pressure, turning up the

723
00:33:45,660 --> 00:33:46,650
voltage rather.

724
00:33:46,650 --> 00:33:47,820
Low pressure here, but

725
00:33:47,820 --> 00:33:49,890
electrical pressure is voltage.

726
00:33:49,890 --> 00:33:53,760
The voltage gets high enough,
eventually the electrons will

727
00:33:53,760 --> 00:33:56,170
boil off the cathode.

728
00:33:56,170 --> 00:33:58,030
And this is a gas
at low pressure.

729
00:33:58,030 --> 00:34:00,690
And they will accelerate from
rest and go all the way across

730
00:34:00,690 --> 00:34:03,120
the tube and crash
into the anode.

731
00:34:03,120 --> 00:34:05,130
And we complete the circuit.

732
00:34:05,130 --> 00:34:07,770
But if there's a gas in here,
some of these electrons are

733
00:34:07,770 --> 00:34:10,000
going to hit the
gas molecules.

734
00:34:10,000 --> 00:34:12,330
And when they hit the gas
molecules, if they have enough

735
00:34:12,330 --> 00:34:17,760
energy to do so, they will cause
electrons inside the gas

736
00:34:17,760 --> 00:34:19,730
molecules to be excited.

737
00:34:23,170 --> 00:34:26,740
And if they're excited enough,
the electrons will jump up to

738
00:34:26,740 --> 00:34:28,100
a higher energy level.

739
00:34:28,100 --> 00:34:30,180
But they can't be sustained.

740
00:34:30,180 --> 00:34:32,410
Because this is a ballistic
collision.

741
00:34:32,410 --> 00:34:33,220
It's a one of.

742
00:34:33,220 --> 00:34:34,520
It's like a bowling alley.

743
00:34:34,520 --> 00:34:37,910
One ball, one pin, one impact.

744
00:34:37,910 --> 00:34:39,030
Now the pin is in the air.

745
00:34:39,030 --> 00:34:40,490
What happens to the pin?

746
00:34:40,490 --> 00:34:41,540
It falls back down.

747
00:34:41,540 --> 00:34:41,870
Why?

748
00:34:41,870 --> 00:34:43,690
Because gravity pulls it down.

749
00:34:43,690 --> 00:34:47,030
In this case, you've got the
energetics pulling the

750
00:34:47,030 --> 00:34:48,170
electron back down.

751
00:34:48,170 --> 00:34:50,760
Now the electron goes from high
energy to low energy.

752
00:34:50,760 --> 00:34:54,380
And when that happens, the
energy difference is given off

753
00:34:54,380 --> 00:34:57,200
in the form of a photon.

754
00:34:57,200 --> 00:35:01,690
So I get photon emission when
this falls back down.

755
00:35:01,690 --> 00:35:05,730
And this photon has
a wavelength.

756
00:35:05,730 --> 00:35:09,820
What I'm going to show you is
that the set of lines that you

757
00:35:09,820 --> 00:35:14,860
get from exactly this
configuration using this

758
00:35:14,860 --> 00:35:19,100
equation give you the
Balmer series.

759
00:35:19,100 --> 00:35:23,710
So now you've got a model that
Bohr postulated for atomic

760
00:35:23,710 --> 00:35:28,460
hydrogen on 1-electron atom that
exactly predicts that set

761
00:35:28,460 --> 00:35:29,680
of 4 lines.

762
00:35:29,680 --> 00:35:33,670
Which were measured
50 years before.

763
00:35:33,670 --> 00:35:35,160
So let's go.

764
00:35:35,160 --> 00:35:38,520
So first of all let's
get the energy here.

765
00:35:38,520 --> 00:35:40,220
And I'm going to get the energy
of this electron.

766
00:35:40,220 --> 00:35:44,110
This electron I'm going to call
a ballistic electron.

767
00:35:44,110 --> 00:35:46,080
Why do I call it a ballistic
electron?

768
00:35:46,080 --> 00:35:47,580
Because it's not bound.

769
00:35:47,580 --> 00:35:48,240
It's free.

770
00:35:48,240 --> 00:35:51,790
It boils off the cathode, flies
through free space, and

771
00:35:51,790 --> 00:35:52,850
crashes into an anode.

772
00:35:52,850 --> 00:35:55,050
Clearly it's not part
of an atom.

773
00:35:55,050 --> 00:35:57,270
But there's a second electron
in this story.

774
00:35:57,270 --> 00:35:59,950
And it's the ground state
electron in hydrogen.

775
00:35:59,950 --> 00:36:01,200
And it lives here.

776
00:36:04,080 --> 00:36:06,070
So what's the energy of the
ballistic electron?

777
00:36:10,490 --> 00:36:14,750
Well that's just 1/2 mv squared
And where did it get

778
00:36:14,750 --> 00:36:15,640
its energy from?

779
00:36:15,640 --> 00:36:18,070
It got its energy from
the power supply.

780
00:36:18,070 --> 00:36:20,330
And what's the electrostatic
energy?

781
00:36:20,330 --> 00:36:24,200
It's the product of the charge
on the species times the

782
00:36:24,200 --> 00:36:27,270
voltage through which
it was accelerated.

783
00:36:27,270 --> 00:36:29,710
So away we go.

784
00:36:29,710 --> 00:36:32,190
I know the charge on the
electron is minus E.

785
00:36:32,190 --> 00:36:34,300
Whatever the voltage is
there, 1 volt, 10

786
00:36:34,300 --> 00:36:35,960
volts, 100 volts, whatever.

787
00:36:35,960 --> 00:36:37,560
Away we go.

788
00:36:37,560 --> 00:36:40,630
By the way, I'm going to show
you just one other thing in

789
00:36:40,630 --> 00:36:42,580
terms of order of magnitude.

790
00:36:42,580 --> 00:36:46,290
The kinds of voltages you see
along here are 1 volt, 10

791
00:36:46,290 --> 00:36:47,650
volts, that sort of thing.

792
00:36:47,650 --> 00:36:57,160
So suppose, to get an order of
magnitude, suppose we had a

793
00:36:57,160 --> 00:37:02,070
species of charge E.

794
00:37:02,070 --> 00:37:05,255
So in other words, it's only 1
times the elementary charge.

795
00:37:05,255 --> 00:37:14,370
A species of charge
E influenced by

796
00:37:14,370 --> 00:37:18,350
voltage of 1 volt.

797
00:37:18,350 --> 00:37:23,040
So this is 1 in the voltage
units, and 1 in the elementary

798
00:37:23,040 --> 00:37:24,000
charge units.

799
00:37:24,000 --> 00:37:25,310
How much energy would that be?

800
00:37:25,310 --> 00:37:28,260
That's equivalent to making
1 volt and accelerate an

801
00:37:28,260 --> 00:37:33,110
electron from rest
across this gap.

802
00:37:33,110 --> 00:37:37,400
And the result would be, the
energy then would simply equal

803
00:37:37,400 --> 00:37:46,260
1.6 times 10 to the minus 19
coulombs times 1 volt.

804
00:37:46,260 --> 00:37:47,720
And what's the energy
going to be?

805
00:37:47,720 --> 00:37:49,330
Well I've got coulombs
times volts.

806
00:37:49,330 --> 00:37:51,550
And I don't know how I convert
one to the other.

807
00:37:51,550 --> 00:37:52,200
I don't have to.

808
00:37:52,200 --> 00:37:53,170
Why not?

809
00:37:53,170 --> 00:37:54,570
Because that's an SI unit.

810
00:37:54,570 --> 00:37:56,040
And that's an SI unit.

811
00:37:56,040 --> 00:37:57,110
This is an energy.

812
00:37:57,110 --> 00:37:59,576
So with impunity, I write
1.6 times 10 to

813
00:37:59,576 --> 00:38:01,400
the minus 19 joules.

814
00:38:01,400 --> 00:38:04,820
That's the beauty of SI units.

815
00:38:04,820 --> 00:38:05,820
So that's a good news.

816
00:38:05,820 --> 00:38:06,560
I know it's joules.

817
00:38:06,560 --> 00:38:08,640
The bad news is I hate
this number.

818
00:38:08,640 --> 00:38:10,850
It's a stupid number, 1.6 times
10 to the minus 19.

819
00:38:10,850 --> 00:38:11,450
it's crazy.

820
00:38:11,450 --> 00:38:14,920
Why don't I come up with
a number like 3, 7?

821
00:38:14,920 --> 00:38:17,440
So what I could do,
is I could define.

822
00:38:17,440 --> 00:38:21,070
I could define a unit such
that when the elementary

823
00:38:21,070 --> 00:38:26,300
charge is accelerated across the
unit voltage, I would call

824
00:38:26,300 --> 00:38:30,470
that unit 1 electron volt.

825
00:38:30,470 --> 00:38:32,650
And so somebody thought
of this before me.

826
00:38:32,650 --> 00:38:35,190
And hence, this is the unit
of the electron volt.

827
00:38:35,190 --> 00:38:38,790
It takes these crazy things that
we've been spewing here

828
00:38:38,790 --> 00:38:42,510
up until now, and rationalizes
them into numbers that people

829
00:38:42,510 --> 00:38:44,060
can carry around
in their heads.

830
00:38:44,060 --> 00:38:45,380
So what's K now?

831
00:38:45,380 --> 00:38:48,990
K is 2.18 times 10 to
the minus 18 joules.

832
00:38:48,990 --> 00:38:49,960
Yuck!

833
00:38:49,960 --> 00:38:51,700
Let's convert that to
electron volts.

834
00:38:51,700 --> 00:38:55,100
So I divide by 1.6 times
10 to the minus 19.

835
00:38:55,100 --> 00:38:58,600
And I got 13.6 electron volts.

836
00:38:58,600 --> 00:39:02,090
You'll remember that on your
death bed, ionization energy

837
00:39:02,090 --> 00:39:04,440
of atomic hydrogen.

838
00:39:04,440 --> 00:39:06,980
Maybe we don't have to give
out tables of constants.

839
00:39:06,980 --> 00:39:08,300
You just know this stuff.

840
00:39:08,300 --> 00:39:09,510
It's OK.

841
00:39:09,510 --> 00:39:10,430
All right.

842
00:39:10,430 --> 00:39:14,380
Now one last thing about this.

843
00:39:14,380 --> 00:39:16,380
So this has got gas in it.

844
00:39:16,380 --> 00:39:17,720
This is the cathode.

845
00:39:17,720 --> 00:39:23,270
And this beam of electrons, back
in the 1800s, there was a

846
00:39:23,270 --> 00:39:25,750
popular term, it was
called the ray.

847
00:39:25,750 --> 00:39:28,410
So instead of a beam of
light, people refer

848
00:39:28,410 --> 00:39:30,460
to the ray of light.

849
00:39:30,460 --> 00:39:33,700
So then when they got to
particle beams, they talk to

850
00:39:33,700 --> 00:39:35,210
them as rays.

851
00:39:35,210 --> 00:39:39,890
So this is now not an electron
beam, it's an electron ray.

852
00:39:39,890 --> 00:39:41,550
And it comes off the cathode.

853
00:39:41,550 --> 00:39:43,500
And it's in a vacuum tube.

854
00:39:43,500 --> 00:39:49,715
So this could be called a
cathode ray tube, a CRT.

855
00:39:49,715 --> 00:39:51,650
Now see, I could flatten this.

856
00:39:51,650 --> 00:39:53,450
And I could spray it
with phosphors.

857
00:39:53,450 --> 00:39:56,880
And then I could put some
charge plates here.

858
00:39:56,880 --> 00:39:58,670
The electrons have a
negative charge.

859
00:39:58,670 --> 00:40:01,440
So if I charge these plates, and
I was clever about how I

860
00:40:01,440 --> 00:40:04,490
charge them and varied the
charge, I could raster the

861
00:40:04,490 --> 00:40:07,920
electron beam like this about
30 times a second all up and

862
00:40:07,920 --> 00:40:08,850
down the screen.

863
00:40:08,850 --> 00:40:11,370
And then I could put some
program signal in there.

864
00:40:11,370 --> 00:40:12,430
And I could sit here.

865
00:40:12,430 --> 00:40:13,680
And I could watch TV.

866
00:40:17,630 --> 00:40:21,830
It all started with the
gas discharge tube.

867
00:40:21,830 --> 00:40:25,930
It says nothing about the
content unfortunately.

868
00:40:25,930 --> 00:40:28,660
Very nice physics,
but no content.

869
00:40:28,660 --> 00:40:29,030
All right.

870
00:40:29,030 --> 00:40:32,940
So now we've got the electron.

871
00:40:32,940 --> 00:40:35,060
The electron is moving, the
ballistic electron.

872
00:40:35,060 --> 00:40:36,690
Now I want to look at what
happens when the ballistic

873
00:40:36,690 --> 00:40:39,640
electron smashes into one of
those hydrogen atoms. So let's

874
00:40:39,640 --> 00:40:41,340
go back over here.

875
00:40:41,340 --> 00:40:44,330
So here's the incident
particle.

876
00:40:44,330 --> 00:40:47,250
And it's going to be an
electron in this case.

877
00:40:47,250 --> 00:40:48,900
So I'm going to designate
this electron.

878
00:40:48,900 --> 00:40:52,860
This is my ballistic electron.

879
00:40:52,860 --> 00:40:57,810
So here's the incident
electron.

880
00:40:57,810 --> 00:41:00,500
And this is ballistic,
just to be clear.

881
00:41:00,500 --> 00:41:02,800
It's the ballistic incident
electron.

882
00:41:02,800 --> 00:41:04,750
Now this is a mixed
metaphor here.

883
00:41:04,750 --> 00:41:08,390
Because I'm representing this
in Cartesian space.

884
00:41:08,390 --> 00:41:10,790
But I've moved into
energy space.

885
00:41:10,790 --> 00:41:12,360
So some people are going
to get really upset.

886
00:41:12,360 --> 00:41:13,430
Because they're going to say,
well this is Cartesian, but

887
00:41:13,430 --> 00:41:14,480
this isn't.

888
00:41:14,480 --> 00:41:15,615
It doesn't matter.

889
00:41:15,615 --> 00:41:17,060
It's my lecture.

890
00:41:17,060 --> 00:41:17,800
It's my model.

891
00:41:17,800 --> 00:41:19,050
It works.

892
00:41:21,180 --> 00:41:22,860
I'm the professor.

893
00:41:22,860 --> 00:41:24,700
So we've got this mixed
metaphor here.

894
00:41:24,700 --> 00:41:26,300
But anyways, it helps a lot.

895
00:41:26,300 --> 00:41:28,565
So what happens when this
thing comes in?

896
00:41:28,565 --> 00:41:32,610
It depends on how much
energy it has.

897
00:41:32,610 --> 00:41:38,680
Now if the incident energy,
if E incident is

898
00:41:38,680 --> 00:41:40,400
tiny, nothing happens.

899
00:41:40,400 --> 00:41:43,470
This thing just zooms
right on through.

900
00:41:43,470 --> 00:41:47,860
But if the incident energy, if
E of the incident ballistic

901
00:41:47,860 --> 00:41:52,830
electron is greater than
delta E for any

902
00:41:52,830 --> 00:41:54,900
transition that's feasible--

903
00:41:54,900 --> 00:41:57,470
and in this case I'm going to
assume I don't have thermal

904
00:41:57,470 --> 00:41:58,700
distribution of electrons.

905
00:41:58,700 --> 00:42:00,890
If I gave you Avogadro's number
of hydrogen atoms

906
00:42:00,890 --> 00:42:02,810
because of the thermal
distribution of energies-- and

907
00:42:02,810 --> 00:42:04,310
we'll come back to
this later--

908
00:42:04,310 --> 00:42:07,740
there might actually be, at
any moment, some electrons

909
00:42:07,740 --> 00:42:10,110
that are thermally excited
above the ground state.

910
00:42:10,110 --> 00:42:11,710
We're going to forget
about that for now.

911
00:42:11,710 --> 00:42:15,590
We're going to spiral up the
learning curve here.

912
00:42:15,590 --> 00:42:17,920
So first time we're going to
assume all the electrons are

913
00:42:17,920 --> 00:42:19,270
in the ground state.

914
00:42:19,270 --> 00:42:24,520
If I don't enough energy to go
from n equals 1 to n equals 2,

915
00:42:24,520 --> 00:42:25,330
nothing happens.

916
00:42:25,330 --> 00:42:27,760
If I have more than enough
energy to go for n equals 1 to

917
00:42:27,760 --> 00:42:30,200
n equals 2, I will
take that energy.

918
00:42:30,200 --> 00:42:33,530
And the electron will jump,
steal that amount of energy,

919
00:42:33,530 --> 00:42:36,010
and then this thing moves on--

920
00:42:36,010 --> 00:42:38,700
and I'm purposely making this
vector shorter than the

921
00:42:38,700 --> 00:42:39,800
incident vector--

922
00:42:39,800 --> 00:42:41,510
with that amount
of energy raw.

923
00:42:41,510 --> 00:42:43,820
And this is called the
scattered electron.

924
00:42:43,820 --> 00:42:45,590
Go back to the bowling
ball analogy.

925
00:42:45,590 --> 00:42:48,440
The bowling ball comes in with
a certain energy, hits the

926
00:42:48,440 --> 00:42:50,190
pin, continues to roll.

927
00:42:50,190 --> 00:42:53,420
But you know that there's a loss
of kinetic energy in the

928
00:42:53,420 --> 00:42:54,100
bowling ball.

929
00:42:54,100 --> 00:42:55,040
That's what we're seeing here.

930
00:42:55,040 --> 00:42:57,920
It's purely ballistic.

931
00:42:57,920 --> 00:43:00,680
Now let's say we do have more
than enough energy.

932
00:43:00,680 --> 00:43:04,620
Suppose I have enough energy to
go from n equals 1 halfway

933
00:43:04,620 --> 00:43:07,560
between n equals 2
and n equals 3.

934
00:43:07,560 --> 00:43:10,340
There's only n equals
1, n equals 2.

935
00:43:10,340 --> 00:43:14,850
I can't take the electron
up to n equals 2.3.

936
00:43:14,850 --> 00:43:15,630
It's unallowed.

937
00:43:15,630 --> 00:43:17,460
These are the only
allowed states.

938
00:43:17,460 --> 00:43:21,390
So that differential amount of
energy then resides with the

939
00:43:21,390 --> 00:43:23,380
electron that's ballistic.

940
00:43:23,380 --> 00:43:24,610
And it moves on here.

941
00:43:24,610 --> 00:43:26,690
So we've got conservation
of energy here.

942
00:43:26,690 --> 00:43:32,370
We can say that E incident will
then equal the energy

943
00:43:32,370 --> 00:43:36,570
that's lost in the transition
plus the energy that's still

944
00:43:36,570 --> 00:43:40,070
left with the scattered
electron.

945
00:43:40,070 --> 00:43:43,880
And we can calculate what that
transitional energy is.

946
00:43:43,880 --> 00:43:46,530
That transitional energy
is going to equal

947
00:43:46,530 --> 00:43:51,840
1/2 mv squared incident.

948
00:43:51,840 --> 00:43:55,160
This is the velocity, the
incident electron.

949
00:43:55,160 --> 00:43:58,670
What's the energy to go from
n equals 1 to n equals n?

950
00:43:58,670 --> 00:44:03,990
Whatever it is, its minus K
times Z squared If it's

951
00:44:03,990 --> 00:44:05,470
hydrogen, Z is 1.

952
00:44:05,470 --> 00:44:08,280
It's going to be 1 over nf.

953
00:44:08,280 --> 00:44:11,780
The final quantum number squared
minus 1 over the

954
00:44:11,780 --> 00:44:14,690
square of the initial
quantum number.

955
00:44:14,690 --> 00:44:17,860
And then, what's left over after
this has been robbed

956
00:44:17,860 --> 00:44:22,260
from the incident ballistic
energy is 1/2 mv squared of

957
00:44:22,260 --> 00:44:25,890
the scattered ballistic
electron.

958
00:44:25,890 --> 00:44:39,490
And the quantization dictates
that only if E incident is

959
00:44:39,490 --> 00:44:44,720
greater than delta E going 1
up to n-- here I'm assuming

960
00:44:44,720 --> 00:44:45,950
everything is in its
ground state.

961
00:44:45,950 --> 00:44:47,630
Later on we're going to
be more sophisticated.

962
00:44:47,630 --> 00:44:49,980
But for first time
through, all are

963
00:44:49,980 --> 00:44:50,830
ground state electrons.

964
00:44:50,830 --> 00:44:54,040
I have to have enough energy to
go at least to n equals 2.

965
00:44:54,040 --> 00:44:55,760
I can go to n equals
3, m equals 4.

966
00:44:55,760 --> 00:44:59,490
In principle, if this thing had
more than 13.6 electron

967
00:44:59,490 --> 00:45:01,320
volts, what would happen?

968
00:45:01,320 --> 00:45:03,060
It would kick this
electron out.

969
00:45:03,060 --> 00:45:04,350
Gone!

970
00:45:04,350 --> 00:45:08,110
And you'd have 2
free electrons.

971
00:45:08,110 --> 00:45:13,620
So if it's greater than this,
then the consequence is

972
00:45:13,620 --> 00:45:14,870
electron promotion.

973
00:45:19,850 --> 00:45:22,490
So we're moving along.

974
00:45:22,490 --> 00:45:24,890
But this excited state
is unstable.

975
00:45:24,890 --> 00:45:28,600
This excited state is unstable
because it's like the bowling

976
00:45:28,600 --> 00:45:29,450
pin that got thrown up.

977
00:45:29,450 --> 00:45:30,070
So what happens?

978
00:45:30,070 --> 00:45:32,460
The electron standing up there
on n equals 2, for example,

979
00:45:32,460 --> 00:45:34,310
looking down to n equals 1.

980
00:45:34,310 --> 00:45:35,080
And it falls.

981
00:45:35,080 --> 00:45:38,290
When it falls it gives
off radiation.

982
00:45:38,290 --> 00:45:41,170
And that radiation is
conservation of energy there.

983
00:45:41,170 --> 00:45:45,640
And what we know is when it
gives off an energy of the

984
00:45:45,640 --> 00:45:51,240
emitted photon, the energy of
the emitted photon must equal

985
00:45:51,240 --> 00:45:55,895
delta E of the transition
falling from 2 to 1.

986
00:45:55,895 --> 00:45:57,630
And we know how to
calculate that.

987
00:45:57,630 --> 00:45:59,890
That's just that thing
flipped around.

988
00:45:59,890 --> 00:46:02,290
And this thing is
equal to what?

989
00:46:02,290 --> 00:46:04,570
This is equal to h nu.

990
00:46:04,570 --> 00:46:08,700
According to Planck it's
hc over lambda is

991
00:46:08,700 --> 00:46:11,620
equal to hc nu bar.

992
00:46:11,620 --> 00:46:12,720
You know what this one is.

993
00:46:12,720 --> 00:46:18,070
This is minus KZ squared
1 over-- in this case

994
00:46:18,070 --> 00:46:19,200
it's going to be--

995
00:46:19,200 --> 00:46:23,700
1 over nf squared 1 over 1
squared minus 1 over, in this

996
00:46:23,700 --> 00:46:29,350
case, 1 over 2 squared And you
can generalize this 1 over nf.

997
00:46:29,350 --> 00:46:30,980
So where am I going with this?

998
00:46:30,980 --> 00:46:33,275
Well I'm going to flip
all of this around.

999
00:46:33,275 --> 00:46:36,780
And when I flip it all around,
what I'm going to end up with

1000
00:46:36,780 --> 00:46:38,900
is this equation here.

1001
00:46:38,900 --> 00:46:40,660
And better than that,
I'm going to end

1002
00:46:40,660 --> 00:46:41,980
up with this equation.

1003
00:46:41,980 --> 00:46:45,260
And I'm going to end up with
this as the constant.

1004
00:46:45,260 --> 00:46:49,080
And when I get that, we're going
to say Bohr has done it.

1005
00:46:49,080 --> 00:46:53,070
The data support the theory.

1006
00:46:53,070 --> 00:46:55,920
So that's what we're
going to do.

1007
00:46:55,920 --> 00:47:01,020
But I think we're going to
stop at this point today.

1008
00:47:01,020 --> 00:47:03,900
So let me just jump here.

1009
00:47:03,900 --> 00:47:06,660
I mentioned to you that if you
go here on your periodic

1010
00:47:06,660 --> 00:47:09,120
table, there's the 13.6
electron volts.

1011
00:47:09,120 --> 00:47:15,310
In the case of lithium, this
is 5.4 electron volts.

1012
00:47:15,310 --> 00:47:17,330
So you can see all the
various values.

1013
00:47:17,330 --> 00:47:19,720
This by the way, people
no noise.

1014
00:47:19,720 --> 00:47:20,210
No noise.

1015
00:47:20,210 --> 00:47:22,100
It's 11:52.

1016
00:47:22,100 --> 00:47:24,190
I'm holding court until 11:55.

1017
00:47:24,190 --> 00:47:26,360
I'm simply changing topics.

1018
00:47:26,360 --> 00:47:28,060
It's not, oh this is
the part where I

1019
00:47:28,060 --> 00:47:29,290
can talk to my neighbor.

1020
00:47:29,290 --> 00:47:30,820
What are the rules?

1021
00:47:30,820 --> 00:47:31,880
No talking.

1022
00:47:31,880 --> 00:47:32,880
No food.

1023
00:47:32,880 --> 00:47:37,160
No horseplay until 11:55.

1024
00:47:37,160 --> 00:47:39,580
Then, still no horseplay,
gentle

1025
00:47:39,580 --> 00:47:42,910
talking, no food, no drink.

1026
00:47:42,910 --> 00:47:46,290
This is a sacred space.

1027
00:47:46,290 --> 00:47:47,390
I'm not kidding you.

1028
00:47:47,390 --> 00:47:48,490
Do you know why?

1029
00:47:48,490 --> 00:47:53,400
In this secular America, this
is sacred space because this

1030
00:47:53,400 --> 00:47:55,750
is where people learn.

1031
00:47:55,750 --> 00:47:59,530
The lecture hall is
sacred space.

1032
00:47:59,530 --> 00:48:03,020
Now, here's the 13.6
electron volts.

1033
00:48:03,020 --> 00:48:05,430
And there's the 1.6 times 10
to the minus 19 joules.

1034
00:48:05,430 --> 00:48:09,770
And if you multiply those 2,
you'll get the 2.18 over here.

1035
00:48:09,770 --> 00:48:10,970
All right.

1036
00:48:10,970 --> 00:48:13,760
Here's a cartoon showing the
photon, higher energy orbit,

1037
00:48:13,760 --> 00:48:17,020
lower energy orbit, electron
emission transition, right out

1038
00:48:17,020 --> 00:48:17,900
of your book.

1039
00:48:17,900 --> 00:48:20,130
And there's a postulate 6.

1040
00:48:20,130 --> 00:48:23,340
And we're going to finish this
up at the beginning of the

1041
00:48:23,340 --> 00:48:24,410
Friday lecture.

1042
00:48:24,410 --> 00:48:32,830
So here's the whole series from
n equals 3 to 2, n equals

1043
00:48:32,830 --> 00:48:34,920
4 to 2, and so on.

1044
00:48:34,920 --> 00:48:37,280
See how that works.

1045
00:48:37,280 --> 00:48:38,530
OK.

1046
00:48:41,310 --> 00:48:44,210
One of the things that we've
learned here, is that it

1047
00:48:44,210 --> 00:48:47,730
doesn't matter what the incident
energy is here.

1048
00:48:47,730 --> 00:48:51,360
The emission is characteristic
of the energy

1049
00:48:51,360 --> 00:48:52,920
levels inside the gas.

1050
00:48:55,680 --> 00:48:57,730
Instead of using an incident
electron, I could use an

1051
00:48:57,730 --> 00:48:58,710
incident proton.

1052
00:48:58,710 --> 00:49:01,260
I could use an incident
alpha particle.

1053
00:49:01,260 --> 00:49:03,130
I could use an incident
neutron.

1054
00:49:03,130 --> 00:49:06,020
Anything that has enough energy
to kick this up from n

1055
00:49:06,020 --> 00:49:09,250
equals 1 to n equals 2 will
result in photon emission of

1056
00:49:09,250 --> 00:49:10,320
this frequency.

1057
00:49:10,320 --> 00:49:15,830
That means the set of those
lines is unique to the target.

1058
00:49:15,830 --> 00:49:18,720
And this is the beginning
of chemical analysis.

1059
00:49:18,720 --> 00:49:23,050
I can use this to characterize
species, to it, stars.

1060
00:49:23,050 --> 00:49:25,960
How do we analyze the
composition a stars?

1061
00:49:25,960 --> 00:49:29,550
Well, do we send a NASA
spaceship out 25 light-years

1062
00:49:29,550 --> 00:49:32,390
and grab some gas and bring
it back to the lab?

1063
00:49:32,390 --> 00:49:32,920
No.

1064
00:49:32,920 --> 00:49:36,480
All we've got is the
spectrograph.

1065
00:49:36,480 --> 00:49:37,620
The star is hot.

1066
00:49:37,620 --> 00:49:43,120
That means thermal excitation
and cascading

1067
00:49:43,120 --> 00:49:44,760
down with photon emission.

1068
00:49:44,760 --> 00:49:48,760
And the lines we get are related
to the energy levels

1069
00:49:48,760 --> 00:49:49,470
within the stars.

1070
00:49:49,470 --> 00:49:52,220
So from a distance of a 100
light-years, I can tell you

1071
00:49:52,220 --> 00:49:53,680
what the composition is.

1072
00:49:53,680 --> 00:49:56,330
And if there's two gases
there, what if there's

1073
00:49:56,330 --> 00:49:58,060
hydrogen and helium?

1074
00:49:58,060 --> 00:49:59,650
the helium lines
will be there.

1075
00:49:59,650 --> 00:50:02,410
And they'll be superimposed on
the hydrogen lines unless they

1076
00:50:02,410 --> 00:50:04,380
lie directly on top
of one another.

1077
00:50:04,380 --> 00:50:06,990
I'm going to be able to figure
out what's there.

1078
00:50:06,990 --> 00:50:08,920
That's how it works.

1079
00:50:08,920 --> 00:50:14,190
Now here's a story about an
astronomer, Cecilia Payne.

1080
00:50:14,190 --> 00:50:15,830
She's the first woman
graduate student in

1081
00:50:15,830 --> 00:50:17,116
astronomy at Harvard.

1082
00:50:17,116 --> 00:50:20,900
She went on to chair the Faculty
of Arts and Sciences,

1083
00:50:20,900 --> 00:50:24,480
awarded tenure, but denied a
professorship for 18 years

1084
00:50:24,480 --> 00:50:26,150
because she was a woman.

1085
00:50:26,150 --> 00:50:28,690
And in her thesis, she was the
first person to figure out to

1086
00:50:28,690 --> 00:50:32,830
the sun is dominantly hydrogen,
not iron, which is

1087
00:50:32,830 --> 00:50:34,270
what most astronomers thought.

1088
00:50:34,270 --> 00:50:34,520
Why?

1089
00:50:34,520 --> 00:50:37,110
Well, because the earth
is made of iron.

1090
00:50:37,110 --> 00:50:39,180
Meteorites are made of iron.

1091
00:50:39,180 --> 00:50:40,590
The whole universe must
be made of iron.

1092
00:50:40,590 --> 00:50:42,300
Never mind the fact that
the sun is glowing.

1093
00:50:45,310 --> 00:50:46,950
So here's how spectroscopy
works.

1094
00:50:46,950 --> 00:50:47,700
Look at this.

1095
00:50:47,700 --> 00:50:48,830
See, what does this mean?

1096
00:50:48,830 --> 00:50:50,580
This is an analogy.

1097
00:50:50,580 --> 00:50:51,490
What could that mean?

1098
00:50:51,490 --> 00:50:52,700
Well, they said iron again.

1099
00:50:52,700 --> 00:50:53,770
I know this is misspelled.

1100
00:50:53,770 --> 00:50:56,610
But maybe it's just a glitch
in the instrumentation.

1101
00:50:56,610 --> 00:50:58,600
So most people would look
at that and say,

1102
00:50:58,600 --> 00:50:59,900
the message is iron.

1103
00:50:59,900 --> 00:51:01,560
But it's not about the word.

1104
00:51:01,560 --> 00:51:03,180
It's about the pattern.

1105
00:51:03,180 --> 00:51:05,350
It's about the pattern.

1106
00:51:05,350 --> 00:51:06,820
And that's what's
spectroscopy is.

1107
00:51:06,820 --> 00:51:11,700
By the way, if you somehow
didn't catch this lecture.

1108
00:51:11,700 --> 00:51:14,340
And you walked in, and all you
saw was those four lines.

1109
00:51:14,340 --> 00:51:16,040
You know those four lines.

1110
00:51:16,040 --> 00:51:18,390
That set of lines is
characteristic of atomic

1111
00:51:18,390 --> 00:51:20,220
hydrogen, and nothing else.

1112
00:51:20,220 --> 00:51:21,700
By the way, those lines
are very faint.

1113
00:51:21,700 --> 00:51:23,220
This is not to scale.

1114
00:51:23,220 --> 00:51:25,390
And they're so faint,
they're ghostlike.

1115
00:51:25,390 --> 00:51:27,790
And what is the latin
word for ghost?

1116
00:51:27,790 --> 00:51:28,820
Specter.

1117
00:51:28,820 --> 00:51:30,260
So what is a spectrum?

1118
00:51:30,260 --> 00:51:32,940
It is a set of ghostlike
lines.

1119
00:51:32,940 --> 00:51:35,730
To this day, the term
spectroscopy refers to the

1120
00:51:35,730 --> 00:51:40,540
ability to study data that are
so faint they're ghostlike.

1121
00:51:40,540 --> 00:51:42,710
All right, we'll see
you on Friday.