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PROFESSOR: So, a couple
of announcements.

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00:00:24,650 --> 00:00:27,750
Tomorrow we've got Quiz Two.

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00:00:27,750 --> 00:00:30,360
Based on Homework Two
And then, Thursday,

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00:00:30,360 --> 00:00:33,230
we'll have the
periodic table quiz.

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00:00:33,230 --> 00:00:35,680
I give you the numbers,
you give me the letters.

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00:00:35,680 --> 00:00:39,850
And Friday is the last
day for the contest.

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00:00:39,850 --> 00:00:40,930
I'll have office hours.

15
00:00:40,930 --> 00:00:42,471
I know when others
have office hours.

16
00:00:42,471 --> 00:00:46,520
I'll be available 4:30 to 5:30
down the hall in my office.

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00:00:46,520 --> 00:00:49,170
Where is Grant's, who's
buried in Grant's Tomb?

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00:00:49,170 --> 00:00:49,730
Grant.

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00:00:49,730 --> 00:00:51,880
Where are my office hours held?

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00:00:51,880 --> 00:00:53,492
In my office.

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00:00:53,492 --> 00:00:55,260
Good.

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00:00:55,260 --> 00:00:56,645
Last day.

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00:00:56,645 --> 00:00:57,145
Last day.

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00:00:57,145 --> 00:00:58,103
It was a rough weekend.

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00:00:58,103 --> 00:01:00,030
I can't get a smile,
can't get a laugh.

26
00:01:04,030 --> 00:01:06,850
So, last day we looked at the
validation of the Bohr model.

27
00:01:06,850 --> 00:01:10,190
And we had two pieces
of experimental data.

28
00:01:10,190 --> 00:01:13,540
First were the hydrogen
spectrum lines,

29
00:01:13,540 --> 00:01:17,760
measured in 1853 by Angstrom
and fit to an equation by J.J.

30
00:01:17,760 --> 00:01:20,000
Balmer in 1885.

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00:01:20,000 --> 00:01:22,800
And, secondly, we saw the
Franck-Hertz experiment,

32
00:01:22,800 --> 00:01:26,910
in which we were able to
get the sense that energy

33
00:01:26,910 --> 00:01:30,000
levels within a multi-electron
atom, like, mercury,

34
00:01:30,000 --> 00:01:32,020
those energy levels
are also quantized,

35
00:01:32,020 --> 00:01:34,240
which gave credence to
the quantum condition.

36
00:01:34,240 --> 00:01:38,700
Which said that the movement
of an electron, the movement

37
00:01:38,700 --> 00:01:41,340
of an electron, is quantized.

38
00:01:41,340 --> 00:01:45,210
And then we started looking
at the limitations of the Bohr

39
00:01:45,210 --> 00:01:47,350
model, problems
with the Bohr model.

40
00:01:47,350 --> 00:01:50,370
And I said, in two
words, fine structure.

41
00:01:50,370 --> 00:01:52,230
And we started looking
at fine structure.

42
00:01:52,230 --> 00:01:56,340
We see that the 656
nanometer line in hydrogen,

43
00:01:56,340 --> 00:01:58,040
in point of fact, is a doublet.

44
00:01:58,040 --> 00:02:01,300
It's actually two lines
very closely spaced.

45
00:02:01,300 --> 00:02:05,050
Bohr model is incapable
of explaining this.

46
00:02:05,050 --> 00:02:07,810
Zeeman looked at
gas discharge tube,

47
00:02:07,810 --> 00:02:11,470
measured hydrogen spectrum
in a magnetic field,

48
00:02:11,470 --> 00:02:13,280
and found line
splitting proportional

49
00:02:13,280 --> 00:02:14,940
to the intensity of the field.

50
00:02:14,940 --> 00:02:18,090
Stark did similar experiments
only in an electric field,

51
00:02:18,090 --> 00:02:21,300
and also found line
splitting, the degree of which

52
00:02:21,300 --> 00:02:24,345
was proportional to the
intensity of the field.

53
00:02:24,345 --> 00:02:27,390
And the Bohr model is
incapable of explaining this.

54
00:02:27,390 --> 00:02:31,150
Sommerfeld, in 1916, put
a patch on the Bohr model

55
00:02:31,150 --> 00:02:33,790
and proposed that
the electron moves

56
00:02:33,790 --> 00:02:38,820
not only in a circular orbit
but also in elliptical orbits.

57
00:02:38,820 --> 00:02:40,860
And there's a plurality
of these orbits.

58
00:02:40,860 --> 00:02:46,565
But overall, the distance from
the nucleus to the electron

59
00:02:46,565 --> 00:02:51,320
orbits is more or less given by
the principal quantum number n,

60
00:02:51,320 --> 00:02:54,725
and the degree of
eccentricity is tiny.

61
00:02:54,725 --> 00:02:58,110
But, more or less,
described by n.

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00:02:58,110 --> 00:03:01,360
And then to further
depict what's going on,

63
00:03:01,360 --> 00:03:03,800
he introduced the
orbital quantum number

64
00:03:03,800 --> 00:03:06,900
or, as your book calls it,
the azimuthal quantum number.

65
00:03:06,900 --> 00:03:09,310
And the magnetic quantum number.

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00:03:09,310 --> 00:03:11,420
And further said that the
energy of the electron

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00:03:11,420 --> 00:03:15,410
is given by the specifications
according to all three quantum

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00:03:15,410 --> 00:03:16,310
numbers.

69
00:03:16,310 --> 00:03:19,410
And then, lastly, in
order to get completeness,

70
00:03:19,410 --> 00:03:22,100
we jumped ahead in
time to 1922 with

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00:03:22,100 --> 00:03:25,870
the Stern-Gerlach experiment,
which was the beam of silver.

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00:03:25,870 --> 00:03:30,110
Atoms through a divergent
magnetic field, the beam

73
00:03:30,110 --> 00:03:35,070
split in two symmetrically
about the point

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00:03:35,070 --> 00:03:39,850
at which the beam would land
on the slide in the absence

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00:03:39,850 --> 00:03:40,980
of a magnetic field.

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00:03:40,980 --> 00:03:43,080
And that can led to
some deeper thinking

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00:03:43,080 --> 00:03:47,700
by two graduate students in
Leiden, Goudsmit and Uhlenbeck,

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00:03:47,700 --> 00:03:50,340
who proposed the notion
of electron spin.

79
00:03:50,340 --> 00:03:52,980
And from that came the
fourth quantum number,

80
00:03:52,980 --> 00:03:54,900
s, and we're going to
throw that into the mix

81
00:03:54,900 --> 00:03:58,100
even though Sommerfeld didn't
give it to us back in 1916.

82
00:03:58,100 --> 00:04:00,260
But I just want to move
forward with all of them.

83
00:04:00,260 --> 00:04:02,980
And we recognize
that s could take

84
00:04:02,980 --> 00:04:07,660
on two values,
plus or minus 1/2,

85
00:04:07,660 --> 00:04:11,920
or we could call it
spin up or spin down.

86
00:04:11,920 --> 00:04:14,160
And, as you're going
to learn in 802,

87
00:04:14,160 --> 00:04:17,180
the convention in
electromagnetism

88
00:04:17,180 --> 00:04:18,490
is the right-hand rule.

89
00:04:18,490 --> 00:04:21,750
That is to say, the thumb
indicates the vector

90
00:04:21,750 --> 00:04:25,570
and the curl of the fingers
indicate the rotation.

91
00:04:25,570 --> 00:04:28,040
So we would argue that
this is an electron

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00:04:28,040 --> 00:04:31,790
spin from looking top-down
anticlockwise and then

93
00:04:31,790 --> 00:04:33,130
vice versa.

94
00:04:33,130 --> 00:04:35,960
So that's as far as we got.

95
00:04:35,960 --> 00:04:38,410
And so now what
I'd like to do is

96
00:04:38,410 --> 00:04:41,520
to take a look at
the periodic table

97
00:04:41,520 --> 00:04:43,950
and get a sense of
electron filling.

98
00:04:43,950 --> 00:04:48,310
And whether that explains the
trends in the periodic table.

99
00:04:48,310 --> 00:04:51,600
And for that I'm going to go
to table 6-3 in your reading.

100
00:04:51,600 --> 00:04:53,710
And all we're going
to do, basically,

101
00:04:53,710 --> 00:04:57,960
is say, well can we can we
use this idea of n, l and m,

102
00:04:57,960 --> 00:05:01,600
and explain the order of
filling in a periodic table.

103
00:05:01,600 --> 00:05:05,530
So when n equals 1,
l must be equal to 0.

104
00:05:05,530 --> 00:05:08,150
And the m must be equal to 0.

105
00:05:08,150 --> 00:05:10,350
So that means there's
only one orbital.

106
00:05:10,350 --> 00:05:13,800
And, in that orbital, we
can have two electrons.

107
00:05:13,800 --> 00:05:19,760
So we've got the possibility of
two different electrons going

108
00:05:19,760 --> 00:05:22,100
into the 1s orbital.

109
00:05:22,100 --> 00:05:23,830
Then we go, n equals 2.

110
00:05:23,830 --> 00:05:25,610
l can take a value of 0.

111
00:05:25,610 --> 00:05:29,080
Which is the same as
what we had before.

112
00:05:29,080 --> 00:05:32,550
Just one orbital
in that subshell.

113
00:05:32,550 --> 00:05:36,750
Or we can have l equals
1, in which case m can

114
00:05:36,750 --> 00:05:40,660
take three different values;
minus 1, 0, and plus 1.

115
00:05:40,660 --> 00:05:42,400
So there's three orbitals there.

116
00:05:42,400 --> 00:05:44,070
3 plus 1 is 4.

117
00:05:44,070 --> 00:05:45,910
And that gives us
the possibility

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00:05:45,910 --> 00:05:47,680
of putting 8 electrons in.

119
00:05:47,680 --> 00:05:49,110
Because this is n, l, and m.

120
00:05:49,110 --> 00:05:53,230
And then we've got the choice
of s plus or minus 1/2.

121
00:05:53,230 --> 00:05:54,180
And we'll do one more.

122
00:05:54,180 --> 00:05:55,420
We'll go to n equals 3.

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00:05:55,420 --> 00:05:59,430
So at l equals 0,
we just have 1.

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00:05:59,430 --> 00:06:01,500
When l equals 1, we
have the same thing

125
00:06:01,500 --> 00:06:03,770
as we had with the 2p.

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00:06:03,770 --> 00:06:07,690
And then when l equals 2, we
have what's known as the 3d.

127
00:06:07,690 --> 00:06:09,710
Remember the
spectroscopists there.

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00:06:09,710 --> 00:06:11,200
They don't like numbers.

129
00:06:11,200 --> 00:06:14,330
So they use s, p, d, f.

130
00:06:14,330 --> 00:06:15,030
But we're smart.

131
00:06:15,030 --> 00:06:16,680
We can go 0, 1, 2.

132
00:06:16,680 --> 00:06:17,700
It didn't hurt us.

133
00:06:17,700 --> 00:06:20,770
And we go minus 2,
minus 1, 0, 1, 2.

134
00:06:20,770 --> 00:06:21,610
So there's 5.

135
00:06:21,610 --> 00:06:24,080
So 5 plus 3 is 8, and 9.

136
00:06:24,080 --> 00:06:25,880
9 times 2 is 18.

137
00:06:25,880 --> 00:06:27,320
Now let's go to
the periodic table

138
00:06:27,320 --> 00:06:29,030
and see if this reconciles.

139
00:06:29,030 --> 00:06:33,830
So, when we have 1s,
there's hydrogen, helium.

140
00:06:33,830 --> 00:06:37,390
And then the next is n equals 2.

141
00:06:37,390 --> 00:06:39,740
So that should give
us 4 times 2 is 8.

142
00:06:39,740 --> 00:06:44,140
So, 3, 4, 5, 6, 7, 8, 9, 10.

143
00:06:44,140 --> 00:06:46,940
So there's the 8 different
electrons that get us

144
00:06:46,940 --> 00:06:49,000
all the way over to neon.

145
00:06:49,000 --> 00:06:50,760
And now let's go to n equals 3.

146
00:06:50,760 --> 00:06:54,750
So, I have 1, 2,
3, 4, 5, 6, 7, 8.

147
00:06:54,750 --> 00:06:56,300
And then I'm over to 4.

148
00:06:56,300 --> 00:06:57,350
4s.

149
00:06:57,350 --> 00:07:02,450
But look, this is
saying I should have 18.

150
00:07:02,450 --> 00:07:06,610
18 electrons in n equals 3.

151
00:07:06,610 --> 00:07:11,670
So what I'm pointing out here
is that there's a disconnect,

152
00:07:11,670 --> 00:07:15,440
there's a disconnect between
the populating of electrons

153
00:07:15,440 --> 00:07:17,790
just in ascending
quantum number,

154
00:07:17,790 --> 00:07:20,570
and the way the elements are
arranged in the periodic table.

155
00:07:20,570 --> 00:07:23,120
There's some other
factor at work here.

156
00:07:23,120 --> 00:07:26,810
So we want to take a look at
what that could possibly be.

157
00:07:26,810 --> 00:07:39,360
And, so what we need is to
go to a modified energy level

158
00:07:39,360 --> 00:07:40,360
diagram.

159
00:07:40,360 --> 00:07:44,560
A modified energy
level diagram, that

160
00:07:44,560 --> 00:07:49,880
can explain what the
filling sequence is

161
00:07:49,880 --> 00:07:52,300
in the periodic table.

162
00:07:52,300 --> 00:07:55,020
And the modified
energy level diagram

163
00:07:55,020 --> 00:07:59,156
is drawn on the basis
of the Aufbau principle.

164
00:07:59,156 --> 00:08:00,030
The Aufbau principle.

165
00:08:00,030 --> 00:08:03,560
Aufbau, German,
meaning construction.

166
00:08:03,560 --> 00:08:06,130
I think it actually
means out-build.

167
00:08:06,130 --> 00:08:10,720
But, anyways, it generates
the filling sequence.

168
00:08:10,720 --> 00:08:14,540
So, there are three parts
to the Aufbau principle.

169
00:08:14,540 --> 00:08:17,370
And the Aufbau principle
is going to govern,

170
00:08:17,370 --> 00:08:25,770
it's going to govern or direct
the electron filling sequence.

171
00:08:29,980 --> 00:08:31,890
Directs the electron
filling sequence.

172
00:08:31,890 --> 00:08:34,870
So, the first component
of the Aufbau principle

173
00:08:34,870 --> 00:08:37,910
is the Pauli
exclusion principle.

174
00:08:37,910 --> 00:08:43,770
Pauli exclusion principle.

175
00:08:43,770 --> 00:08:47,270
Wolfgang Pauli was an Austrian.

176
00:08:47,270 --> 00:08:51,720
He did his Ph.D under
Sommerfeld in Munich,

177
00:08:51,720 --> 00:08:54,130
and then he post-docced
with Born in Gottingen

178
00:08:54,130 --> 00:08:58,690
and on to Niels Bohr Copenhagen.
These people worked together.

179
00:08:58,690 --> 00:09:01,140
They traveled from
lab to lab, and it

180
00:09:01,140 --> 00:09:03,660
was a very vibrant
conversation going on.

181
00:09:03,660 --> 00:09:06,930
Eventually, he became a
professor physics in Hamburg.

182
00:09:06,930 --> 00:09:10,500
And the Pauli exclusion
principle, simply stated,

183
00:09:10,500 --> 00:09:15,380
is that in any electron
system, each electron

184
00:09:15,380 --> 00:09:19,650
has a unique set of
four quantum numbers.

185
00:09:19,650 --> 00:09:23,390
A unique set of four
quantum numbers.

186
00:09:23,390 --> 00:09:35,870
Any atom set, four
quantum numbers

187
00:09:35,870 --> 00:09:37,370
are unique for each electron.

188
00:09:44,492 --> 00:09:47,220
For each electron.

189
00:09:47,220 --> 00:09:53,530
So you can think of this
as the set of n, l, m and s

190
00:09:53,530 --> 00:09:55,300
as sort of the social
security number,

191
00:09:55,300 --> 00:10:00,730
if you like, for each of
the electrons in the set.

192
00:10:00,730 --> 00:10:04,439
And he eventually gets the
Nobel Prize for this, in 1945.

193
00:10:04,439 --> 00:10:05,980
Virtually everybody
I'm going to talk

194
00:10:05,980 --> 00:10:08,480
about today, with the
exception of Sommerfeld,

195
00:10:08,480 --> 00:10:09,790
gets the Nobel Prize.

196
00:10:09,790 --> 00:10:12,790
Sommerfeld is a very
interesting character, though.

197
00:10:12,790 --> 00:10:17,050
While he himself never won
the Nobel Prize, many, many

198
00:10:17,050 --> 00:10:21,350
of his students and proteges
won Nobel Prizes, to which you

199
00:10:21,350 --> 00:10:23,850
must include that there
was something very, very

200
00:10:23,850 --> 00:10:26,710
special about the quality of
the mentoring that he gave,

201
00:10:26,710 --> 00:10:30,070
that so many of his proteges
went on to win the Nobel Prize.

202
00:10:30,070 --> 00:10:32,670
So this is the first part
of the Aufbau principle.

203
00:10:32,670 --> 00:10:35,750
The second part is
that the electrons fill

204
00:10:35,750 --> 00:10:37,830
from lowest to highest energy.

205
00:10:37,830 --> 00:10:43,820
So electrons fill orbitals.

206
00:10:43,820 --> 00:10:46,280
You can think of the
orbitals as placeholders.

207
00:10:46,280 --> 00:10:47,820
They're really energy concepts.

208
00:10:47,820 --> 00:10:53,710
But we populate orbitals from
lowest to highest energy.

209
00:10:53,710 --> 00:11:00,345
From lowest to highest energy.

210
00:11:00,345 --> 00:11:02,220
Or if I wanted to be a
wise guy, I would say,

211
00:11:02,220 --> 00:11:04,540
I'm going to define
energy in such a way

212
00:11:04,540 --> 00:11:06,855
as I get that as the
filling sequence.

213
00:11:09,700 --> 00:11:11,880
One's got to fit the other.

214
00:11:11,880 --> 00:11:15,210
And the energy is
itself a function

215
00:11:15,210 --> 00:11:18,240
of the four quantum numbers.

216
00:11:18,240 --> 00:11:21,320
So energy, once I
specify n, l, m, and s,

217
00:11:21,320 --> 00:11:26,950
you can give me the
energy and away we go.

218
00:11:26,950 --> 00:11:29,910
And the thing is that
you need to realize

219
00:11:29,910 --> 00:11:34,750
that the energy levels are
actually a function of electron

220
00:11:34,750 --> 00:11:35,690
occupancy.

221
00:11:35,690 --> 00:11:37,440
So you can look
carefully, if you get down

222
00:11:37,440 --> 00:11:39,700
into the d orbitals
and the f orbitals,

223
00:11:39,700 --> 00:11:43,130
as you add one more
electron moving one element

224
00:11:43,130 --> 00:11:44,750
to the right on
the periodic table,

225
00:11:44,750 --> 00:11:49,470
sometimes you see the
population not adding by one,

226
00:11:49,470 --> 00:11:52,020
because the addition
of an electron

227
00:11:52,020 --> 00:11:56,200
changes the relative energies
of the various orbitals.

228
00:11:56,200 --> 00:12:00,930
So let's remember that,
that energy is a function

229
00:12:00,930 --> 00:12:05,130
of electron occupancy.

230
00:12:05,130 --> 00:12:08,520
Energy is a function
of electron occupancy.

231
00:12:08,520 --> 00:12:10,720
And then the third part
of the Aufbau principle

232
00:12:10,720 --> 00:12:13,070
is called Hund's rule.

233
00:12:13,070 --> 00:12:14,440
Hund's rule.

234
00:12:14,440 --> 00:12:18,550
Now, Hund is German for dog, but
this isn't named after a dog.

235
00:12:18,550 --> 00:12:22,590
This is named after Friedrich
Hund, a professor of physics

236
00:12:22,590 --> 00:12:24,200
at Frankfurt.

237
00:12:24,200 --> 00:12:25,590
He taught for many years.

238
00:12:25,590 --> 00:12:30,080
He died at the
tender age of 101.

239
00:12:30,080 --> 00:12:34,430
And he spoke about degeneracy.

240
00:12:34,430 --> 00:12:40,660
Not societal degeneracy,
but degeneracy in an atom.

241
00:12:40,660 --> 00:12:42,570
And this degeneracy
is the condition

242
00:12:42,570 --> 00:12:45,910
where you have a plurality of
orbitals at the same energy

243
00:12:45,910 --> 00:12:46,800
level.

244
00:12:46,800 --> 00:12:52,150
So, in orbitals of
equivalent energy,

245
00:12:52,150 --> 00:12:58,510
in orbitals of
equivalent energy,

246
00:12:58,510 --> 00:13:01,265
we strive for
unpaired electrons.

247
00:13:01,265 --> 00:13:02,140
This is filling, now.

248
00:13:02,140 --> 00:13:04,280
This is how to direct
the filling sequence.

249
00:13:04,280 --> 00:13:14,390
Strive for unpaired electrons.

250
00:13:14,390 --> 00:13:16,820
Let's say unpaired
electron spins.

251
00:13:16,820 --> 00:13:18,640
Let's make it a little clearer.

252
00:13:18,640 --> 00:13:21,420
Unpaired electron spins.

253
00:13:21,420 --> 00:13:24,230
So I'm going to
give you an example,

254
00:13:24,230 --> 00:13:25,460
work through an example.

255
00:13:25,460 --> 00:13:28,180
So, what have we got here?

256
00:13:28,180 --> 00:13:29,540
Here's carbon.

257
00:13:29,540 --> 00:13:32,720
And if you look at any
element on the periodic table,

258
00:13:32,720 --> 00:13:34,150
you'll see this green.

259
00:13:34,150 --> 00:13:36,670
And this is the
electronic configuration.

260
00:13:36,670 --> 00:13:39,620
This tells you what
the sequence looks

261
00:13:39,620 --> 00:13:44,230
like for that particular element
in the neutral form, et cetera,

262
00:13:44,230 --> 00:13:47,520
et cetera, subject to
many, many considerations.

263
00:13:47,520 --> 00:13:49,910
So let's look at carbon.

264
00:13:49,910 --> 00:13:59,350
So if we look at carbon, it
tells us 1 s2, 2 s2, 2 p2.

265
00:13:59,350 --> 00:14:01,400
So what's all this mean?

266
00:14:01,400 --> 00:14:03,150
Well, it's all written
in code for us.

267
00:14:03,150 --> 00:14:06,340
So the first number
here is the n number.

268
00:14:06,340 --> 00:14:08,650
So this means n equals 1.

269
00:14:08,650 --> 00:14:12,030
s is the spectrocopist's
notation,

270
00:14:12,030 --> 00:14:14,740
so this means that l equals 0.

271
00:14:14,740 --> 00:14:20,780
And then the 2 here means
2 electron occupancy.

272
00:14:20,780 --> 00:14:27,650
So the 1s orbital is filled
to the tune of two electrons.

273
00:14:27,650 --> 00:14:29,750
And the 2s orbital
has two electrons,

274
00:14:29,750 --> 00:14:32,620
and the 2p orbital
likewise has two electrons.

275
00:14:32,620 --> 00:14:35,970
So now we want to do is
put these electronics

276
00:14:35,970 --> 00:14:39,270
into their orbitals.

277
00:14:39,270 --> 00:14:42,500
And we can use, there's
a variety of notations.

278
00:14:42,500 --> 00:14:44,600
This is one I'll use today.

279
00:14:44,600 --> 00:14:46,550
This is a box notation.

280
00:14:46,550 --> 00:14:49,180
So this is 1s.

281
00:14:49,180 --> 00:14:51,040
This is 2s.

282
00:14:51,040 --> 00:14:53,210
And then this is 2p.

283
00:14:53,210 --> 00:14:56,850
If you recall, 2p there's
going to be three of them.

284
00:14:56,850 --> 00:15:01,990
If you go back here,
2p has three orbitals

285
00:15:01,990 --> 00:15:05,200
in that sub-shell.

286
00:15:05,200 --> 00:15:07,240
And we said that
this is the one time

287
00:15:07,240 --> 00:15:09,730
that m makes some
sense with respect

288
00:15:09,730 --> 00:15:11,150
to Cartesian coordinates.

289
00:15:11,150 --> 00:15:19,910
m is -1, 0, +1 so we can call
this 2p x, 2p y, and 2p z.

290
00:15:19,910 --> 00:15:21,330
And I don't know which is which.

291
00:15:21,330 --> 00:15:24,659
I don't know what the arbitrary
standards of x, y, and z,

292
00:15:24,659 --> 00:15:26,700
I don't know where the
origin of the universe is,

293
00:15:26,700 --> 00:15:27,908
so I can't tell you all this.

294
00:15:27,908 --> 00:15:30,481
But, arbitrarily, if
I choose one as x,

295
00:15:30,481 --> 00:15:32,980
I know where the other two are
according to right-hand rule.

296
00:15:32,980 --> 00:15:34,420
So let's start filling.

297
00:15:34,420 --> 00:15:40,010
This says 2, so I'll put in
one spin up, and one spin down.

298
00:15:40,010 --> 00:15:41,570
Now it says 2s 2.

299
00:15:41,570 --> 00:15:44,340
One spin up, one spin down.

300
00:15:44,340 --> 00:15:46,490
And now here's where
the Hund rule comes in.

301
00:15:46,490 --> 00:15:50,330
I've got to put two electrons
into these three boxes.

302
00:15:50,330 --> 00:15:53,735
Now, I could be a librarian
and start left to right,

303
00:15:53,735 --> 00:15:55,750
and make them nice and neat.

304
00:15:55,750 --> 00:16:02,360
Or, I could just put
them in wherever I want.

305
00:16:02,360 --> 00:16:06,720
What the Hund rule says is,
strive for unpaired electron

306
00:16:06,720 --> 00:16:07,220
spin.

307
00:16:07,220 --> 00:16:11,390
So for the Hund rule, you'd
put them in both same spin

308
00:16:11,390 --> 00:16:13,284
and in different orbitals.

309
00:16:13,284 --> 00:16:14,700
And then when you
get to nitrogen,

310
00:16:14,700 --> 00:16:16,960
nitrogen will have
a third one here.

311
00:16:16,960 --> 00:16:18,430
And when you get
to oxygen you've

312
00:16:18,430 --> 00:16:21,240
got three plus the fourth one's
going to be one of these three

313
00:16:21,240 --> 00:16:21,950
and I don't care.

314
00:16:21,950 --> 00:16:23,879
I mean, some people are
really anal about it,

315
00:16:23,879 --> 00:16:25,670
and they want you to
go from left to right.

316
00:16:25,670 --> 00:16:28,840
As long as you've got two of
them unpaired and one of them

317
00:16:28,840 --> 00:16:32,510
paired for oxygen I'll be happy.

318
00:16:32,510 --> 00:16:35,390
So now we can use
this concept and look

319
00:16:35,390 --> 00:16:38,990
at the energy level diagram
for multi-electron atoms.

320
00:16:38,990 --> 00:16:41,790
And this is taken from the book.

321
00:16:41,790 --> 00:16:46,340
So this is different
from the energy level

322
00:16:46,340 --> 00:16:47,780
diagram for
hydrogen, because you

323
00:16:47,780 --> 00:16:49,710
can see some compression here.

324
00:16:49,710 --> 00:16:53,270
And I want you to know first
of all, all of these values

325
00:16:53,270 --> 00:16:53,870
are negative.

326
00:16:53,870 --> 00:16:56,620
It's true that energy
increases vertically,

327
00:16:56,620 --> 00:16:58,140
but the zero is way up here.

328
00:16:58,140 --> 00:17:00,130
So these are all
negative values.

329
00:17:00,130 --> 00:17:01,390
And I want to zoom in here.

330
00:17:01,390 --> 00:17:05,960
Because the energy difference
between 1s and 2s is large.

331
00:17:05,960 --> 00:17:10,924
And we know in hydrogen it's 3/4
of the total energy difference.

332
00:17:10,924 --> 00:17:13,340
Because there's some compression
in a multi-electron atom.

333
00:17:13,340 --> 00:17:15,320
But nevertheless,
n equals 1 to n

334
00:17:15,320 --> 00:17:17,260
equals 2 is a huge
energy difference.

335
00:17:17,260 --> 00:17:19,180
So let's zoom in on here.

336
00:17:19,180 --> 00:17:20,520
And what do we see?

337
00:17:20,520 --> 00:17:24,300
Well, 2s, 2p, 3s, 3p and look.

338
00:17:24,300 --> 00:17:28,070
4s lies below 3d.

339
00:17:28,070 --> 00:17:29,880
4s lies below 3d.

340
00:17:29,880 --> 00:17:32,720
So that tells us, there's my 3s.

341
00:17:32,720 --> 00:17:34,570
3s 1, 3s 2.

342
00:17:34,570 --> 00:17:40,710
There's 3p x1, 3p
y1, 3p z1, 2, 2, 2.

343
00:17:40,710 --> 00:17:42,020
And now what's next?

344
00:17:42,020 --> 00:17:43,190
It says go to 4s.

345
00:17:43,190 --> 00:17:45,670
So potassium is 4s 1.

346
00:17:45,670 --> 00:17:46,880
Calcium's 4s 2.

347
00:17:46,880 --> 00:17:49,000
And scandium is 3d 1.

348
00:17:49,000 --> 00:17:51,930
So this energy level
diagram is the map.

349
00:17:51,930 --> 00:17:57,770
It tells you how to put
electronics in sequence.

350
00:17:57,770 --> 00:18:03,530
So, this now gives us
the rational basis for e

351
00:18:03,530 --> 00:18:06,220
equals n, l, m and s.

352
00:18:06,220 --> 00:18:06,720
All right.

353
00:18:06,720 --> 00:18:07,470
Well this is nice.

354
00:18:07,470 --> 00:18:09,140
It's been graphical, and so on.

355
00:18:09,140 --> 00:18:11,340
Now I want to go to
the same position.

356
00:18:11,340 --> 00:18:14,160
I want to get back to this, I
want to get back to this point.

357
00:18:14,160 --> 00:18:16,130
But I want to go
by different route.

358
00:18:16,130 --> 00:18:18,300
I want to go by different
route, and for that we're

359
00:18:18,300 --> 00:18:21,810
going to go by wave mechanics.

360
00:18:21,810 --> 00:18:25,340
So, same destination.

361
00:18:25,340 --> 00:18:30,230
Same destination,
via wave mechanics.

362
00:18:30,230 --> 00:18:35,140
Now, you don't have partial
differential equations

363
00:18:35,140 --> 00:18:38,412
as a prerequisite
for 3.091, so I'm not

364
00:18:38,412 --> 00:18:39,620
going to go through the math.

365
00:18:39,620 --> 00:18:42,370
I'm going to give you the
features of the wave mechanics.

366
00:18:42,370 --> 00:18:44,930
So that later on you're going
to spiral around and study this

367
00:18:44,930 --> 00:18:45,720
again.

368
00:18:45,720 --> 00:18:47,550
You'll have seen it before.

369
00:18:47,550 --> 00:18:50,010
And again, there's going
to be people involved,

370
00:18:50,010 --> 00:18:53,300
and they're all giants
in modern physics.

371
00:18:53,300 --> 00:18:56,050
The first one is de Broglie.

372
00:18:56,050 --> 00:19:00,520
The first one is
Louis-Victor de Broglie.

373
00:19:00,520 --> 00:19:03,380
Let's get his name on the board.

374
00:19:07,190 --> 00:19:11,710
Louis-Victor de Broglie, he was
an aristocrat from Normandy,

375
00:19:11,710 --> 00:19:13,380
who had gone to the Sorbonne.

376
00:19:13,380 --> 00:19:14,840
He was studying humanities.

377
00:19:14,840 --> 00:19:17,870
Political science,
literature, and around

378
00:19:17,870 --> 00:19:19,780
about the time of his
senior year he decided

379
00:19:19,780 --> 00:19:22,070
to switch horses
for graduate school

380
00:19:22,070 --> 00:19:25,070
and forget about a career
in the diplomatic corps,

381
00:19:25,070 --> 00:19:27,320
do a Ph.D in physics.

382
00:19:27,320 --> 00:19:29,050
So, he did a Ph.D in physics.

383
00:19:29,050 --> 00:19:35,460
And in 1924 he published this
Ph.D thesis, beautiful piece

384
00:19:35,460 --> 00:19:36,430
of elegant writings.

385
00:19:36,430 --> 00:19:38,880
Less than 30 pages long.

386
00:19:38,880 --> 00:19:44,590
And I'll give you sort of the
summary, the one-liner that

387
00:19:44,590 --> 00:19:47,730
summarizes his Ph.D thesis.

388
00:19:47,730 --> 00:19:49,900
Most of you are going to
have to write a thesis.

389
00:19:49,900 --> 00:19:53,930
The word thesis comes from the
Greek, and it means, sort of,

390
00:19:53,930 --> 00:19:56,070
my position.

391
00:19:56,070 --> 00:19:57,810
My statement.

392
00:19:57,810 --> 00:20:01,030
Before I have a thesis, I have
something that is not a thesis.

393
00:20:01,030 --> 00:20:03,350
It's my trial balloon.

394
00:20:03,350 --> 00:20:06,030
That's a hypo-thesis,
a hypothesis.

395
00:20:06,030 --> 00:20:07,990
Now, the key to
writing a good thesis

396
00:20:07,990 --> 00:20:10,760
is to ask a really
good question.

397
00:20:10,760 --> 00:20:13,090
If you ask a
pedestrian question,

398
00:20:13,090 --> 00:20:15,950
you're probably going to get
some pedestrian answers and ho

399
00:20:15,950 --> 00:20:16,630
hum.

400
00:20:16,630 --> 00:20:18,380
If you ask a really
interesting question,

401
00:20:18,380 --> 00:20:21,790
you give rise to the possibility
of interesting answers.

402
00:20:21,790 --> 00:20:24,410
And what de Broglie did is,
he asked a really interesting

403
00:20:24,410 --> 00:20:25,090
question.

404
00:20:25,090 --> 00:20:28,600
So here's his question: He
says, if a photon, which

405
00:20:28,600 --> 00:20:32,670
has no mass, photon's
just an energy packet.

406
00:20:32,670 --> 00:20:35,810
If a photon which has no mass
can behave as a particle,

407
00:20:35,810 --> 00:20:37,050
and we've seen.

408
00:20:37,050 --> 00:20:40,240
We model ray optics
as particle beams.

409
00:20:40,240 --> 00:20:44,370
And a photon, and Max Planck
said equals h nu got no mass,

410
00:20:44,370 --> 00:20:47,610
but we can think of it in our
little anthropomorphic brains

411
00:20:47,610 --> 00:20:51,110
as, photon photon photon.

412
00:20:51,110 --> 00:20:54,330
So if a photon, which has no
mass, can behave as a particle,

413
00:20:54,330 --> 00:20:58,030
does it follow that an
electron, which has mass,

414
00:20:58,030 --> 00:21:01,060
can behave as a wave?

415
00:21:01,060 --> 00:21:01,847
It's beautiful.

416
00:21:01,847 --> 00:21:02,930
Let's do it one more time.

417
00:21:02,930 --> 00:21:06,030
If a photon, which has no
mass, can behave as a particle,

418
00:21:06,030 --> 00:21:08,705
does it follow that an
electron which has mass,

419
00:21:08,705 --> 00:21:09,580
can behave as a wave?

420
00:21:13,160 --> 00:21:14,530
So he asked the question.

421
00:21:14,530 --> 00:21:15,720
And he answers it.

422
00:21:15,720 --> 00:21:18,410
In less than 30 pages.

423
00:21:18,410 --> 00:21:19,870
So, let's get this on the board.

424
00:21:19,870 --> 00:21:21,630
Because this is beautiful.

425
00:21:21,630 --> 00:21:25,390
It's like, ask not what you
can do for your country.

426
00:21:25,390 --> 00:21:39,010
If a photon, which has no
mass, can behave as a particle,

427
00:21:39,010 --> 00:21:44,240
or can be modeled as a
particle, behave really means,

428
00:21:44,240 --> 00:21:48,120
so that the theoreticians
can model it as a particle,

429
00:21:48,120 --> 00:22:05,750
does it follow that an
electron, which has mass,

430
00:22:05,750 --> 00:22:08,750
can behave as a wave?

431
00:22:08,750 --> 00:22:11,090
See, if you understand
the question then

432
00:22:11,090 --> 00:22:21,020
the impact of the answer, and
the answer is, if it does,

433
00:22:21,020 --> 00:22:23,150
this is what its
wavelength is going to be.

434
00:22:23,150 --> 00:22:26,830
So de Broglie said, the
wavelength of an electron,

435
00:22:26,830 --> 00:22:29,170
if it were to behave
as a wave, would

436
00:22:29,170 --> 00:22:32,350
be given by the ratio
of the Planck constant

437
00:22:32,350 --> 00:22:36,650
to the Newtonian momentum,
which you know from 8.01

438
00:22:36,650 --> 00:22:43,730
is simply h over the product of
electron mass and its velocity.

439
00:22:43,730 --> 00:22:45,784
So that's de Broglie's thesis.

440
00:22:45,784 --> 00:22:47,700
So let's take a look
what we can do with this.

441
00:22:47,700 --> 00:22:54,210
Now, you remember in the
Bohr model, recall Bohr.

442
00:22:54,210 --> 00:22:58,130
Well, Bohr taught us that mvr,
that's the quantum, condition,

443
00:22:58,130 --> 00:23:03,080
mvr equals the ratio
of h over 2 pi times n,

444
00:23:03,080 --> 00:23:06,980
where n takes on
the discrete values.

445
00:23:06,980 --> 00:23:08,400
1, 2, 3, et cetera.

446
00:23:08,400 --> 00:23:11,700
That's the quantum condition.

447
00:23:11,700 --> 00:23:16,010
Now let's take this
idea of de Broglie.

448
00:23:16,010 --> 00:23:20,866
And first of all we have to
put the electron in its orbit.

449
00:23:20,866 --> 00:23:23,540
So we'll put the
electron in its orbit.

450
00:23:23,540 --> 00:23:26,280
And now I'm going to
have it behave as a wave.

451
00:23:26,280 --> 00:23:31,330
So if it behaves as a wave,
I'm going to draw it as a wave.

452
00:23:34,930 --> 00:23:36,330
Now, why did I draw it this way?

453
00:23:36,330 --> 00:23:37,580
There's two kinds of
waves in this world.

454
00:23:37,580 --> 00:23:39,705
There's standing waves and
there's traveling waves.

455
00:23:39,705 --> 00:23:41,780
Now, this orbit's station,
it's in this orbit.

456
00:23:41,780 --> 00:23:44,470
So it better be a standing wave.

457
00:23:44,470 --> 00:23:46,910
I think there's a
cartoon in the book.

458
00:23:46,910 --> 00:23:49,944
There you go, standing wave.

459
00:23:49,944 --> 00:23:51,610
In order for this to
be a standing wave,

460
00:23:51,610 --> 00:23:53,730
there's a geometric
constraint on this.

461
00:23:53,730 --> 00:23:56,720
Listen carefully
geometric constraint.

462
00:23:56,720 --> 00:24:00,540
I'm not saying anything
about quantum mechanics.

463
00:24:00,540 --> 00:24:09,470
Geometric constraint,
the geometric constraint

464
00:24:09,470 --> 00:24:16,407
for a standing wave is what?

465
00:24:16,407 --> 00:24:17,990
You know what this
distance is, right?

466
00:24:17,990 --> 00:24:20,450
I mean, this is not to scale.

467
00:24:20,450 --> 00:24:22,240
This should be
10,000:1, in which case

468
00:24:22,240 --> 00:24:25,030
these ripples are
barely visible.

469
00:24:25,030 --> 00:24:27,245
But here it looks
kind of exaggerated.

470
00:24:27,245 --> 00:24:28,490
This is a hyper wave.

471
00:24:28,490 --> 00:24:32,890
This is emphasis added in proof.

472
00:24:32,890 --> 00:24:36,040
So that means that the
circumference here, 2 pi

473
00:24:36,040 --> 00:24:42,000
r, the circumference must be an
integral number of wavelengths

474
00:24:42,000 --> 00:24:45,540
for a standing wave.

475
00:24:45,540 --> 00:24:49,040
But we know that
from de Broglie,

476
00:24:49,040 --> 00:24:55,200
I can write n lambda
as n h over m v. I've

477
00:24:55,200 --> 00:24:59,720
just put in de Broglie's
definition of the wavelength

478
00:24:59,720 --> 00:25:01,420
of an electron.

479
00:25:01,420 --> 00:25:07,040
And now I can
cross-multiply and I get mvr

480
00:25:07,040 --> 00:25:16,059
equals h over 2 pi times n.

481
00:25:16,059 --> 00:25:17,475
Which is Bohr's
quantum condition.

482
00:25:20,310 --> 00:25:25,110
So we've got validation
of the Bohr model,

483
00:25:25,110 --> 00:25:26,840
so that's a pretty
compelling case

484
00:25:26,840 --> 00:25:29,930
that maybe the electron
really does behave as a wave,

485
00:25:29,930 --> 00:25:32,860
and that explains why we
have the quantum condition

486
00:25:32,860 --> 00:25:33,405
that we do.

487
00:25:37,000 --> 00:25:41,510
So de Broglie, that's
his Ph.D in 1924.

488
00:25:41,510 --> 00:25:44,610
Einstein read the
thesis, loved the thesis.

489
00:25:44,610 --> 00:25:46,580
But we don't care
what Einstein says,

490
00:25:46,580 --> 00:25:48,200
because he's a theoretician.

491
00:25:48,200 --> 00:25:51,110
So one theoretician praising
another theoretician.

492
00:25:51,110 --> 00:25:52,400
That's not how science works.

493
00:25:52,400 --> 00:25:54,190
How does science work?

494
00:25:54,190 --> 00:25:54,860
Data.

495
00:25:54,860 --> 00:25:56,670
We need data.

496
00:25:56,670 --> 00:26:00,830
And the data come in 1927.

497
00:26:00,830 --> 00:26:04,332
1927, at Bell Labs
in New Jersey.

498
00:26:04,332 --> 00:26:09,070
At Bell Labs in New Jersey
come the critical data.

499
00:26:09,070 --> 00:26:11,705
And they were taken by
Davisson and Germer.

500
00:26:15,460 --> 00:26:17,360
Davisson and Germer.

501
00:26:17,360 --> 00:26:19,840
Davisson and Germer
were studying crystals.

502
00:26:19,840 --> 00:26:23,940
They were studying crystals
of various elements,

503
00:26:23,940 --> 00:26:25,825
and in particular
metal crystals.

504
00:26:28,380 --> 00:26:33,790
Metal crystals,
by X-ray analysis.

505
00:26:36,390 --> 00:26:38,380
And in order for
you to appreciate

506
00:26:38,380 --> 00:26:41,162
what I'm going to show you of
Davisson and Germer's work,

507
00:26:41,162 --> 00:26:42,870
I'm going to take you
back to high school

508
00:26:42,870 --> 00:26:45,550
to those thrilling days
with the wave tanks.

509
00:26:45,550 --> 00:26:47,040
Remember the wave tank?

510
00:26:47,040 --> 00:26:50,000
This is the top view, this is
the side view of the wave tank.

511
00:26:50,000 --> 00:26:53,840
And you might have some kind
of a mechanical device here

512
00:26:53,840 --> 00:26:55,060
that has a paddle.

513
00:26:55,060 --> 00:26:56,810
And it starts
vibrating up and down,

514
00:26:56,810 --> 00:26:59,370
and it starts sending
waves into the tank.

515
00:26:59,370 --> 00:27:02,320
So the waves come like
this, from the edge

516
00:27:02,320 --> 00:27:04,370
it looks like this.

517
00:27:04,370 --> 00:27:05,170
Remember that?

518
00:27:05,170 --> 00:27:06,210
Sure you do.

519
00:27:06,210 --> 00:27:07,510
You're toying with me.

520
00:27:07,510 --> 00:27:10,160
Oh, I don't remember
anything, we never did that.

521
00:27:10,160 --> 00:27:12,920
Sure you did.

522
00:27:12,920 --> 00:27:15,170
OK, so you can send waves down.

523
00:27:15,170 --> 00:27:17,820
Now, what we can do is,
we can put a dam here.

524
00:27:17,820 --> 00:27:20,960
I'm going to put a dam.

525
00:27:20,960 --> 00:27:25,840
And depending on, if
this is the wavelength,

526
00:27:25,840 --> 00:27:27,990
this is the wavelength,
it's the distance

527
00:27:27,990 --> 00:27:30,910
between two successive crests.

528
00:27:30,910 --> 00:27:35,560
And, if this spacing
here, the gap

529
00:27:35,560 --> 00:27:39,020
between the wall and
the edge of the dam, d,

530
00:27:39,020 --> 00:27:42,950
if d is greater than
lambda, the waves

531
00:27:42,950 --> 00:27:45,910
just propagate but
for the place where

532
00:27:45,910 --> 00:27:47,450
they're blocked by the dam.

533
00:27:47,450 --> 00:27:49,575
So you get, you
essentially cast a shadow.

534
00:27:53,830 --> 00:27:55,380
You've seen that.

535
00:27:55,380 --> 00:27:59,460
And so I could model
this system as a beam.

536
00:27:59,460 --> 00:28:01,800
This is a beam.

537
00:28:01,800 --> 00:28:03,850
This is a water beam.

538
00:28:03,850 --> 00:28:06,300
This is a water beam shadow.

539
00:28:06,300 --> 00:28:08,750
And this is equivalent
to ray optics.

540
00:28:08,750 --> 00:28:12,930
Straight lines, if something
gets in the way it's opaque.

541
00:28:12,930 --> 00:28:14,140
Blocks transmission.

542
00:28:14,140 --> 00:28:15,420
End of story.

543
00:28:15,420 --> 00:28:17,020
So you've seen all that.

544
00:28:17,020 --> 00:28:20,890
But you also did this other
experiment, I'm willing to bet.

545
00:28:20,890 --> 00:28:22,665
So let's do the
other experiment.

546
00:28:22,665 --> 00:28:24,040
We're going to do
the same thing.

547
00:28:24,040 --> 00:28:26,520
I'm going to send
waves down here.

548
00:28:26,520 --> 00:28:30,320
Only, this time we're going
to make the dam a little bit

549
00:28:30,320 --> 00:28:31,310
different.

550
00:28:31,310 --> 00:28:35,620
This time we're going to bring
the dam in from the wall.

551
00:28:35,620 --> 00:28:38,470
And we're going to
put a tiny opening.

552
00:28:38,470 --> 00:28:41,540
And I'm going to go
some more into the tank.

553
00:28:41,540 --> 00:28:42,890
And then another tiny opening.

554
00:28:42,890 --> 00:28:43,794
It could be the same.

555
00:28:43,794 --> 00:28:45,835
It's probably best to keep
it the same dimension.

556
00:28:48,700 --> 00:28:59,030
Now, in this case, the spacing,
d, is much less than lambda.

557
00:28:59,030 --> 00:29:00,960
d is much less than lambda.

558
00:29:00,960 --> 00:29:02,590
And what happens in this case?

559
00:29:02,590 --> 00:29:05,430
When d is much less than lambda,
you don't get the shadow.

560
00:29:05,430 --> 00:29:07,780
You don't get something
like this instead, remember.

561
00:29:07,780 --> 00:29:08,760
You've got the rings.

562
00:29:11,840 --> 00:29:15,170
This is called diffraction.

563
00:29:15,170 --> 00:29:16,880
Diffraction.

564
00:29:16,880 --> 00:29:21,620
And there is no way to
explain diffraction modeling

565
00:29:21,620 --> 00:29:23,750
water as a beam.

566
00:29:23,750 --> 00:29:28,500
You must implore the
wave-like behavior of water

567
00:29:28,500 --> 00:29:31,450
in order to explain diffraction.

568
00:29:31,450 --> 00:29:40,010
Explain only by invoking
wave-like properties.

569
00:29:43,250 --> 00:29:47,370
So with wave-like properties, we
get something that makes sense

570
00:29:47,370 --> 00:29:50,160
in terms of the data.

571
00:29:50,160 --> 00:29:52,320
Now, let's do this
same experiment,

572
00:29:52,320 --> 00:29:54,790
let's do this same experiment
on a metal crystal.

573
00:29:54,790 --> 00:29:57,940
So if you go back to
the gas discharge tube.

574
00:29:57,940 --> 00:30:01,120
Remember the gas discharge
tube that we were looking

575
00:30:01,120 --> 00:30:04,020
at for lecture after lecture?

576
00:30:04,020 --> 00:30:08,280
If you take a look and go
through the energetics of it.

577
00:30:08,280 --> 00:30:10,740
If you put one volt
across the plates,

578
00:30:10,740 --> 00:30:13,240
you know the energy is going
to be a product of charge times

579
00:30:13,240 --> 00:30:13,870
voltage.

580
00:30:13,870 --> 00:30:17,210
And that's equal
to 1/2 mv squared.

581
00:30:17,210 --> 00:30:20,250
Which you know from 801
is p squared over 2m.

582
00:30:20,250 --> 00:30:23,670
And p is equal to h over lambda.

583
00:30:23,670 --> 00:30:26,580
Pretty soon you can come
up with the wavelength.

584
00:30:26,580 --> 00:30:29,240
And that will give you the
wavelength of the electron.

585
00:30:29,240 --> 00:30:31,410
This is a ballistic
electron now.

586
00:30:31,410 --> 00:30:32,640
See what I'm doing?

587
00:30:32,640 --> 00:30:35,860
See, once I said
that this indicates

588
00:30:35,860 --> 00:30:37,980
that the electronic
in stationary orbit

589
00:30:37,980 --> 00:30:41,450
can be modeled as a wave
of a certain wavelength, so

590
00:30:41,450 --> 00:30:43,750
now the free electron.

591
00:30:43,750 --> 00:30:46,680
It's got m, it's got v,
there's Planck constant.

592
00:30:46,680 --> 00:30:49,130
I can go ahead and
compute its wavelength.

593
00:30:49,130 --> 00:30:52,630
I can compute the
wavelength of a baseball.

594
00:30:52,630 --> 00:30:54,130
So, you go through it.

595
00:30:54,130 --> 00:30:58,970
And you get a value
of about 12 Angstroms.

596
00:30:58,970 --> 00:30:59,850
12 Angstroms.

597
00:30:59,850 --> 00:31:05,080
Now, if I want to see whether
there's wave-like properties,

598
00:31:05,080 --> 00:31:07,850
I need to have a condition
that gives me diffraction.

599
00:31:07,850 --> 00:31:09,670
So I'm going to have
to find something

600
00:31:09,670 --> 00:31:13,160
that gives me a dam
with an opening that's

601
00:31:13,160 --> 00:31:15,840
less than 12 Angstroms.

602
00:31:15,840 --> 00:31:19,960
If I'm going to use 1 volt.

603
00:31:19,960 --> 00:31:21,170
So what can I do?

604
00:31:21,170 --> 00:31:24,190
Well, turns out you're going
to learn this in greater detail

605
00:31:24,190 --> 00:31:27,200
later, but if this is
a crystal of nickel.

606
00:31:27,200 --> 00:31:30,890
Crystal of nickel, the atoms
are arranged in regular arrays.

607
00:31:30,890 --> 00:31:34,550
And this is what the face of
nickel looks like, 4 atoms each

608
00:31:34,550 --> 00:31:35,410
at the corner.

609
00:31:35,410 --> 00:31:37,190
And one in the
center of that face.

610
00:31:37,190 --> 00:31:41,040
This distance is 3.53 Angstroms.

611
00:31:41,040 --> 00:31:42,490
Perfect.

612
00:31:42,490 --> 00:31:43,170
Perfect.

613
00:31:43,170 --> 00:31:49,230
So what Davisson and Germer
did is, they irradiated this.

614
00:31:49,230 --> 00:31:54,590
They irradiated this first with
X-rays on the order of lambda,

615
00:31:54,590 --> 00:31:58,090
on the order of,
say, 10 Angstroms.

616
00:31:58,090 --> 00:31:59,960
And what did they get?

617
00:31:59,960 --> 00:32:01,230
This is the output.

618
00:32:01,230 --> 00:32:02,130
This is the output.

619
00:32:02,130 --> 00:32:05,620
You get a diffraction pattern.

620
00:32:05,620 --> 00:32:07,940
It's a set of rings,
concentric rings.

621
00:32:07,940 --> 00:32:13,090
So this is the
X-ray diffraction.

622
00:32:13,090 --> 00:32:17,520
This is the X-ray
diffractogram, if you like.

623
00:32:17,520 --> 00:32:20,140
And then, what did they do next?

624
00:32:20,140 --> 00:32:25,325
They irradiate the same
crystal with an electron beam.

625
00:32:27,990 --> 00:32:32,930
lambda of the electron
beam, 10 Angstroms.

626
00:32:32,930 --> 00:32:35,230
And what did they get?

627
00:32:35,230 --> 00:32:36,220
Are you ready?

628
00:32:36,220 --> 00:32:36,910
Drum roll.

629
00:32:40,140 --> 00:32:44,140
Now, there is no way
that you can get a ring

630
00:32:44,140 --> 00:32:49,670
pattern from a beam of electrons
acting as a particle beam.

631
00:32:49,670 --> 00:32:53,550
The only explanation for
this is that the electrons

632
00:32:53,550 --> 00:32:58,020
were behaving as
waves of this value

633
00:32:58,020 --> 00:33:01,260
to give us the same spacing
as we got with X-rays.

634
00:33:01,260 --> 00:33:04,430
And you're comfortable
if I say that X-rays

635
00:33:04,430 --> 00:33:07,050
are a type of light.

636
00:33:07,050 --> 00:33:09,680
So, therefore, it's got
wave-like properties.

637
00:33:09,680 --> 00:33:11,280
And it's got
particle-like properties.

638
00:33:11,280 --> 00:33:12,700
Well, now I've
just made the point

639
00:33:12,700 --> 00:33:16,820
that this is the
electron diffractogram.

640
00:33:16,820 --> 00:33:21,710
So this is evidence of
electron diffraction.

641
00:33:21,710 --> 00:33:23,210
And this shook the world.

642
00:33:23,210 --> 00:33:24,680
Because now it's real.

643
00:33:24,680 --> 00:33:27,190
There's no way you can
get this otherwise.

644
00:33:27,190 --> 00:33:31,970
This is electron diffraction.

645
00:33:31,970 --> 00:33:33,720
This was 1927.

646
00:33:33,720 --> 00:33:37,110
1929, de Broglie
gets the Nobel Prize.

647
00:33:37,110 --> 00:33:42,540
1937, Davisson gets
the Nobel Prize.

648
00:33:42,540 --> 00:33:47,710
So this means the wave-particle
duality is complete.

649
00:33:47,710 --> 00:33:52,130
It applies not only to light,
but it applies to matter.

650
00:33:52,130 --> 00:33:57,200
So, wave-particle
duality, they call it.

651
00:33:57,200 --> 00:33:59,665
Wave-particle
duality is complete.

652
00:34:02,770 --> 00:34:05,640
Matter can act as waves.

653
00:34:05,640 --> 00:34:08,710
Electromagnetic radiation
can act as particles.

654
00:34:08,710 --> 00:34:12,230
So, sometimes people refer to
de Broglie's accomplishment

655
00:34:12,230 --> 00:34:15,370
as matter waves.

656
00:34:15,370 --> 00:34:15,974
Matter waves.

657
00:34:18,810 --> 00:34:23,530
And what do you call the
behavior of billiard balls

658
00:34:23,530 --> 00:34:24,700
banging around and so on?

659
00:34:24,700 --> 00:34:26,500
We call that mechanics.

660
00:34:26,500 --> 00:34:28,850
So now we're going
to use what might

661
00:34:28,850 --> 00:34:32,930
seem as an oxymoron,
contradiction, wave mechanics.

662
00:34:32,930 --> 00:34:36,120
Wave mechanics.

663
00:34:36,120 --> 00:34:38,680
That means matter
behaving as a wave.

664
00:34:38,680 --> 00:34:40,480
But still behaving as a matter.

665
00:34:40,480 --> 00:34:42,200
So this is the dynamic.

666
00:34:42,200 --> 00:34:48,170
So that's pretty
good for de Broglie.

667
00:34:48,170 --> 00:34:49,650
So let's go to number two.

668
00:34:49,650 --> 00:34:51,649
I said there were going
to be three people here.

669
00:34:51,649 --> 00:34:54,270
Number two is Werner Heisenberg.

670
00:34:54,270 --> 00:34:55,020
Werner Heisenberg.

671
00:34:58,820 --> 00:35:01,640
Heisenberg studied with Pauli.

672
00:35:04,260 --> 00:35:06,960
Sommerfeld.

673
00:35:06,960 --> 00:35:10,290
Did his Ph.D in Munich in 1923.

674
00:35:10,290 --> 00:35:14,750
Got his Ph.D with
Sommerfeld at the age of 22.

675
00:35:14,750 --> 00:35:17,765
And then he decided to
take a postdoc with Bohr.

676
00:35:17,765 --> 00:35:19,890
And he was working with
Bohr for a couple of years,

677
00:35:19,890 --> 00:35:22,020
he was feeling a
little bit burned-out.

678
00:35:22,020 --> 00:35:24,820
And decided to take
three weeks off.

679
00:35:24,820 --> 00:35:28,590
Went up to a deserted island
off the coast of Norway.

680
00:35:28,590 --> 00:35:31,450
Came back three weeks later with
the mathematical formulation

681
00:35:31,450 --> 00:35:33,700
of quantum mechanics.

682
00:35:33,700 --> 00:35:36,950
I'm not kidding you, that's
what he did in his time

683
00:35:36,950 --> 00:35:39,330
off, to kind of unwind.

684
00:35:39,330 --> 00:35:44,650
And so one of the things that
he used as a critical piece

685
00:35:44,650 --> 00:35:49,350
of this derivation is that
the position and velocity

686
00:35:49,350 --> 00:35:53,000
of an electron cannot
be fully specified.

687
00:35:53,000 --> 00:35:56,470
They cannot be fully specified
below certain limits.

688
00:35:56,470 --> 00:35:59,590
There's a threshold
below which we can't go.

689
00:35:59,590 --> 00:36:01,500
This is sort of
like, if I asked you

690
00:36:01,500 --> 00:36:04,960
to time a 100-meter
sprint, which typically

691
00:36:04,960 --> 00:36:06,670
takes less than 10 seconds.

692
00:36:06,670 --> 00:36:09,680
But I give you a clock, and
the nearest unit on the clock

693
00:36:09,680 --> 00:36:10,910
is the minute.

694
00:36:10,910 --> 00:36:13,740
So you wouldn't be
able to distinguish.

695
00:36:13,740 --> 00:36:16,020
So, he says-- and
the reason for this

696
00:36:16,020 --> 00:36:18,580
is, it's a consequence
of quantization.

697
00:36:18,580 --> 00:36:20,340
Light itself is quantized.

698
00:36:20,340 --> 00:36:24,770
So, at some point you're asking
for a continuous splitting

699
00:36:24,770 --> 00:36:27,400
and splitting and splitting into
finer and finer time segments.

700
00:36:27,400 --> 00:36:28,400
And you can't get there.

701
00:36:28,400 --> 00:36:30,650
So we already knew
this from Planck.

702
00:36:30,650 --> 00:36:35,580
And so one of the ways that
he expressed the inability

703
00:36:35,580 --> 00:36:41,360
to go below a certain threshold
is the uncertainty principle.

704
00:36:41,360 --> 00:36:43,220
The uncertainty principle.

705
00:36:43,220 --> 00:36:44,820
And that's
unfortunate that, see,

706
00:36:44,820 --> 00:36:46,580
it was originally
published in German.

707
00:36:46,580 --> 00:36:51,170
And the idea really is the
indeterminacy principle.

708
00:36:51,170 --> 00:36:53,220
But, English says uncertainty.

709
00:36:53,220 --> 00:36:57,350
So it's a limit to
determination, but there it is.

710
00:36:57,350 --> 00:36:59,410
And so one expression
of this is,

711
00:36:59,410 --> 00:37:01,310
the product of the velocity.

712
00:37:01,310 --> 00:37:03,284
Only, he wrote it in
terms of momentum.

713
00:37:03,284 --> 00:37:04,700
So the mass isn't
going to change.

714
00:37:04,700 --> 00:37:08,460
So, think of this as the
uncertainty and the velocity.

715
00:37:08,460 --> 00:37:10,350
And the uncertainty
in the position.

716
00:37:10,350 --> 00:37:13,290
So this is the
x-coordinate of particle.

717
00:37:13,290 --> 00:37:15,780
You can break its
trajectory into three

718
00:37:15,780 --> 00:37:16,910
orthogonal components.

719
00:37:16,910 --> 00:37:19,030
So the uncertainty
in the x direction

720
00:37:19,030 --> 00:37:23,290
of the momentum times the
uncertainty in the position

721
00:37:23,290 --> 00:37:27,550
is greater than or equal to
the Planck constant divided

722
00:37:27,550 --> 00:37:28,940
by 2 pi.

723
00:37:28,940 --> 00:37:30,800
The Planck constant
divided by 2 pi.

724
00:37:33,725 --> 00:37:35,800
And so what this
means is that we're

725
00:37:35,800 --> 00:37:41,635
going to see a transition in
models from individual atoms.

726
00:37:44,160 --> 00:37:47,810
If we want to describe what
happens with individual atoms,

727
00:37:47,810 --> 00:37:50,330
we need what is known as
a deterministic model.

728
00:37:50,330 --> 00:37:51,790
Sort of, Newtonian mechanics.

729
00:37:51,790 --> 00:37:54,025
You tell me the initial
position and velocity.

730
00:37:54,025 --> 00:37:56,570
You tell me the forces, and I
can predict where it's going

731
00:37:56,570 --> 00:37:57,695
and where it's going to be.

732
00:37:57,695 --> 00:38:01,460
So that's deterministic models.

733
00:38:01,460 --> 00:38:06,730
So, deterministic models
describing individual atoms

734
00:38:06,730 --> 00:38:13,790
are going to give rise
to probabilistic models.

735
00:38:17,150 --> 00:38:19,390
Probabilistic models.

736
00:38:19,390 --> 00:38:21,110
And probabilistic
models obviously

737
00:38:21,110 --> 00:38:22,970
can't be talking about
individual atoms.

738
00:38:22,970 --> 00:38:25,760
Must be talking about
ensembles of atoms.

739
00:38:28,360 --> 00:38:30,560
So I can't say where any
individual atom will be,

740
00:38:30,560 --> 00:38:33,240
because I don't have
the ability to do so.

741
00:38:33,240 --> 00:38:36,280
But I can tell you, if you
give me a large number of them,

742
00:38:36,280 --> 00:38:39,440
I'll tell you roughly
what the expected outcome

743
00:38:39,440 --> 00:38:40,680
could be in terms of energy.

744
00:38:40,680 --> 00:38:43,670
And ultimately predict
the spectrum, and so on.

745
00:38:43,670 --> 00:38:45,280
So instead of chicken
and egg we have

746
00:38:45,280 --> 00:38:47,810
now chickenality and egg-ness.

747
00:38:47,810 --> 00:38:51,060
Everything is just sort of
getting a little bit murky.

748
00:38:51,060 --> 00:38:51,890
Little bit murky.

749
00:38:51,890 --> 00:38:53,770
You can do a
calculation on this.

750
00:38:53,770 --> 00:38:56,490
You can do a calculation on
this, a very simple take.

751
00:38:56,490 --> 00:39:00,110
Take the Bohr model and take
the ground state electron

752
00:39:00,110 --> 00:39:03,127
in hydrogen. n equals
1 in atomic hydrogen.

753
00:39:03,127 --> 00:39:04,960
And you know this is
about half an Angstrom.

754
00:39:04,960 --> 00:39:08,180
So the distance across
here is 1 Angstrom.

755
00:39:08,180 --> 00:39:12,610
So make 1 Angstrom
your uncertainty,

756
00:39:12,610 --> 00:39:19,040
and you'll find that the
uncertainty in the momentum

757
00:39:19,040 --> 00:39:21,100
is on the order of 15%.

758
00:39:24,005 --> 00:39:25,880
But what this is saying
is, when you get down

759
00:39:25,880 --> 00:39:29,200
to atomic dimensions, you
can't just shine light on it

760
00:39:29,200 --> 00:39:30,734
and reveal what's going on.

761
00:39:30,734 --> 00:39:32,650
Because you're going to
disturb the very thing

762
00:39:32,650 --> 00:39:34,240
you're trying to measure.

763
00:39:34,240 --> 00:39:36,870
Some people say
that, every time you

764
00:39:36,870 --> 00:39:38,750
try to work at the
atomic level, it's

765
00:39:38,750 --> 00:39:40,510
as though you're trying
to take a picture

766
00:39:40,510 --> 00:39:43,185
with the sun at your back and
your shadow is in the picture.

767
00:39:43,185 --> 00:39:48,445
So you can't get there without
disturbing the very thing.

768
00:39:48,445 --> 00:39:49,820
Another way to
think about it is,

769
00:39:49,820 --> 00:39:51,847
the photons that are
capable of this resolution

770
00:39:51,847 --> 00:39:53,680
are going to have such
high energies they'll

771
00:39:53,680 --> 00:39:56,070
knock the very thing
you're trying to measure.

772
00:39:56,070 --> 00:39:56,570
All right.

773
00:39:56,570 --> 00:40:00,680
He gets Nobel Prize in 1932.

774
00:40:00,680 --> 00:40:04,140
And then the third one
is Erwin Schroedinger.

775
00:40:04,140 --> 00:40:05,130
Let's get him up here.

776
00:40:09,110 --> 00:40:11,810
Erwin Schroedinger.

777
00:40:11,810 --> 00:40:14,640
Also an Austrian,
University of Zurich.

778
00:40:14,640 --> 00:40:16,480
He too was burned out.

779
00:40:16,480 --> 00:40:18,320
They get burned out, these guys.

780
00:40:18,320 --> 00:40:22,940
So at Christmastime,
1925, took a vacation.

781
00:40:22,940 --> 00:40:26,100
At Villa Herwig, in Aurora.

782
00:40:26,100 --> 00:40:31,580
And comes back two weeks
later with the wave mechanics

783
00:40:31,580 --> 00:40:35,150
formulation, of
quantum mechanics.

784
00:40:35,150 --> 00:40:37,940
See, sometimes going
away on a vacation.

785
00:40:37,940 --> 00:40:41,720
So he took de Broglie's notion
of the electron as a wave

786
00:40:41,720 --> 00:40:44,770
and wrote equations to
model wave-like behavior.

787
00:40:44,770 --> 00:40:48,535
So, let's look at
how to get there.

788
00:40:48,535 --> 00:40:51,850
And here's what he did.

789
00:40:51,850 --> 00:40:54,630
So, you know, for
example, that we could

790
00:40:54,630 --> 00:40:56,820
start with a violin string.

791
00:40:56,820 --> 00:40:58,660
And it has a
geometric constraint.

792
00:40:58,660 --> 00:41:00,560
It must be fixed at both ends.

793
00:41:00,560 --> 00:41:02,750
And if I pluck
that string, it can

794
00:41:02,750 --> 00:41:07,485
vibrate as long as it conforms
to the geometric constraint

795
00:41:07,485 --> 00:41:08,600
of a standing wave.

796
00:41:08,600 --> 00:41:11,210
So here's one possibility.

797
00:41:11,210 --> 00:41:13,160
Wherein we would
call this n equals 1.

798
00:41:13,160 --> 00:41:17,410
I have simply the
entire string vibrating

799
00:41:17,410 --> 00:41:18,930
in the matter that's shown.

800
00:41:18,930 --> 00:41:20,600
But here's a second possibility.

801
00:41:20,600 --> 00:41:23,030
I could have it vibrating
as is shown here,

802
00:41:23,030 --> 00:41:24,880
n equals 2 with a
node in the middle

803
00:41:24,880 --> 00:41:26,530
where that node
doesn't move at all.

804
00:41:26,530 --> 00:41:30,620
The string is stationary
at its mid-point.

805
00:41:30,620 --> 00:41:33,460
And what's the
characteristic here?

806
00:41:33,460 --> 00:41:36,160
This is operating at
a certain frequency.

807
00:41:36,160 --> 00:41:39,650
Let's say it's middle C.
And this is the overtone.

808
00:41:39,650 --> 00:41:41,400
This is the first harmonic.

809
00:41:41,400 --> 00:41:43,530
And it's going to
be an octave higher,

810
00:41:43,530 --> 00:41:47,050
because it's as though we
have two strings, each fixed.

811
00:41:47,050 --> 00:41:49,830
See, from a physics
standpoint I could literally

812
00:41:49,830 --> 00:41:53,100
cut this string in half and
fix it there, and this is now n

813
00:41:53,100 --> 00:41:55,380
equals 1 for the half-length.

814
00:41:55,380 --> 00:41:58,140
So it's going to have the
same pitch as the half-length.

815
00:41:58,140 --> 00:42:00,425
Which means that this
is an octave higher,

816
00:42:00,425 --> 00:42:02,990
and this is going to be two
octaves higher, and so on.

817
00:42:02,990 --> 00:42:04,520
And all of these conform.

818
00:42:04,520 --> 00:42:08,110
So you get a plurality
of solutions.

819
00:42:08,110 --> 00:42:10,890
You get a plurality
of solutions.

820
00:42:10,890 --> 00:42:13,780
And the solutions look
something like this.

821
00:42:13,780 --> 00:42:20,700
They'll eventually teach you
the string as a simple harmonic

822
00:42:20,700 --> 00:42:22,700
oscillator.

823
00:42:22,700 --> 00:42:27,960
Simple harmonic oscillator.

824
00:42:27,960 --> 00:42:31,540
And it has equations
that look like this.

825
00:42:31,540 --> 00:42:33,165
If you want to
plot its position,

826
00:42:33,165 --> 00:42:38,250
this is x going from 0 to l.

827
00:42:38,250 --> 00:42:40,650
And this is the y-coordinate.

828
00:42:40,650 --> 00:42:44,060
So you can, for example,
write something like this.

829
00:42:44,060 --> 00:42:48,380
So, the function
will look like this.

830
00:42:48,380 --> 00:42:52,320
Some pre-multiplier
times cosine of kx

831
00:42:52,320 --> 00:42:57,190
plus another pre-multiplier
b times the sine of kx.

832
00:42:57,190 --> 00:43:01,620
And the geometry will
dictate that the value of k

833
00:43:01,620 --> 00:43:03,720
is n pi over l.

834
00:43:03,720 --> 00:43:06,020
So, pi over l is the geometry.

835
00:43:06,020 --> 00:43:10,430
And n takes multiple values.

836
00:43:10,430 --> 00:43:13,940
Just as you see here, there's
not a unique solution.

837
00:43:13,940 --> 00:43:15,470
So listen carefully.

838
00:43:15,470 --> 00:43:19,690
Wave equation,
plurality of solutions.

839
00:43:19,690 --> 00:43:22,330
But subject to some constraints.

840
00:43:22,330 --> 00:43:23,670
Subject to some constraints.

841
00:43:23,670 --> 00:43:27,250
So what Schroedinger did
is, he wrote a wave equation

842
00:43:27,250 --> 00:43:33,720
to describe the motion
of electron in its orbit.

843
00:43:33,720 --> 00:43:35,210
And guess what he gets?

844
00:43:35,210 --> 00:43:37,860
He gets a plurality
of solutions.

845
00:43:37,860 --> 00:43:40,670
And when you look at the
plurality of solutions,

846
00:43:40,670 --> 00:43:42,870
the plurality of
solutions ultimately

847
00:43:42,870 --> 00:43:50,970
map into what we know as the
distinct values of n, l, m

848
00:43:50,970 --> 00:43:52,180
and s.

849
00:43:52,180 --> 00:43:54,030
See, this is the
one-dimensional.

850
00:43:54,030 --> 00:43:57,990
So this is giving us
n numbers. n equals 1,

851
00:43:57,990 --> 00:44:00,210
this is now n equals 2.

852
00:44:00,210 --> 00:44:02,020
So I'm getting
quantum numbers here.

853
00:44:02,020 --> 00:44:04,130
Now, if I did this
in three dimensions,

854
00:44:04,130 --> 00:44:06,040
I'd have a plurality
of quantum numbers.

855
00:44:06,040 --> 00:44:10,480
And Schroedinger gets us all
the way to n, l, m and s.

856
00:44:10,480 --> 00:44:13,010
And so here's what
it looks like.

857
00:44:13,010 --> 00:44:15,320
This is the equation,
it's a wave equation,

858
00:44:15,320 --> 00:44:18,480
so there's a double
derivative in space.

859
00:44:18,480 --> 00:44:19,700
There's a forcing function.

860
00:44:19,700 --> 00:44:23,070
And this is i, square root of
minus 1 in a time base here.

861
00:44:23,070 --> 00:44:26,610
So it's a harmonic
kind of equation.

862
00:44:26,610 --> 00:44:29,249
Psi is the wave function,
it's an abstract concept

863
00:44:29,249 --> 00:44:31,040
but we'll show you how
to make sense of it.

864
00:44:31,040 --> 00:44:33,940
And these are the
various solutions,

865
00:44:33,940 --> 00:44:35,480
the plurality of solutions.

866
00:44:35,480 --> 00:44:39,930
And we can now map those into
what we know as 1s, 2s, 2px,

867
00:44:39,930 --> 00:44:42,720
2py, 2pz, et cetera, et cetera.

868
00:44:42,720 --> 00:44:45,090
And you see this number a sub 0.

869
00:44:45,090 --> 00:44:46,660
That's our Bohr radius.

870
00:44:46,660 --> 00:44:48,710
Comes right out
of the equations.

871
00:44:48,710 --> 00:44:51,890
0.529 Angstroms.

872
00:44:51,890 --> 00:44:54,910
So, this is quite good.

873
00:44:54,910 --> 00:44:58,770
But, as I said, the psi
is the wave function.

874
00:44:58,770 --> 00:45:00,620
Or psi, however you
want to call this.

875
00:45:00,620 --> 00:45:03,090
This is called
the wave function.

876
00:45:03,090 --> 00:45:04,530
Wave function.

877
00:45:04,530 --> 00:45:07,005
And we have plurality
of solutions.

878
00:45:10,542 --> 00:45:11,750
We call these Eigenfunctions.

879
00:45:14,400 --> 00:45:15,840
Eigenfunctions.

880
00:45:15,840 --> 00:45:19,860
And the closest we can
get to something physical

881
00:45:19,860 --> 00:45:24,110
is the product of psi and
its complex conjugate.

882
00:45:24,110 --> 00:45:27,240
And that is related
to the probability

883
00:45:27,240 --> 00:45:29,560
of finding the electron.

884
00:45:29,560 --> 00:45:33,222
Probability of
finding the electron.

885
00:45:33,222 --> 00:45:36,180
Which, in essence, gives the
boundaries of the orbitals.

886
00:45:36,180 --> 00:45:39,030
So now I'm going to put, we're
going to get a Cartesian shape.

887
00:45:39,030 --> 00:45:40,480
I told you, 1s, 2s.

888
00:45:40,480 --> 00:45:41,530
What do they look like?

889
00:45:41,530 --> 00:45:42,900
Here's what they look like.

890
00:45:42,900 --> 00:45:46,696
So these are the square of
the wave function plotted.

891
00:45:46,696 --> 00:45:48,570
So this is in a radial
distribution function.

892
00:45:48,570 --> 00:45:51,220
It's only in one direction,
out from the radius.

893
00:45:51,220 --> 00:45:53,590
Now, if you whip
this around in 3-D,

894
00:45:53,590 --> 00:45:55,680
you'll generate the surface.

895
00:45:55,680 --> 00:45:57,737
But already you
can see, here's 1s,

896
00:45:57,737 --> 00:45:59,320
and it peaks at about
1/2 an Angstrom.

897
00:45:59,320 --> 00:46:03,240
And here's 2s, and it peaks
at 4 times the Bohr radius.

898
00:46:03,240 --> 00:46:07,020
And psi squared
3s about 9 times.

899
00:46:07,020 --> 00:46:08,750
This is from your book.

900
00:46:08,750 --> 00:46:09,830
So it's a maximum.

901
00:46:09,830 --> 00:46:11,040
But there's some uncertainty.

902
00:46:11,040 --> 00:46:16,040
See, it's not a simple line
fixed at 0.529 Angstroms.

903
00:46:16,040 --> 00:46:17,490
This is another way of plotting.

904
00:46:17,490 --> 00:46:19,120
So these are spherical.

905
00:46:19,120 --> 00:46:22,190
What we were calling circular
now becomes namely spherical.

906
00:46:22,190 --> 00:46:25,400
And there's this node here.

907
00:46:25,400 --> 00:46:27,500
This is the p orbitals.

908
00:46:27,500 --> 00:46:29,960
They're dumbbell-shaped.

909
00:46:29,960 --> 00:46:31,400
With two lobes.

910
00:46:31,400 --> 00:46:33,210
And if you have a
single electron,

911
00:46:33,210 --> 00:46:34,520
it doesn't reside in one lobe.

912
00:46:34,520 --> 00:46:36,755
It can jump from one
side to the other.

913
00:46:36,755 --> 00:46:39,380
You might say, well, how does it
get from one lobe to the other

914
00:46:39,380 --> 00:46:43,875
when halfway between,
there's a nodal plane.

915
00:46:43,875 --> 00:46:46,900
It has zero probability.

916
00:46:46,900 --> 00:46:50,660
Well, it's behaving as a wave.

917
00:46:50,660 --> 00:46:53,630
Behaves as a particle, you
can't get through a wall

918
00:46:53,630 --> 00:46:55,320
that says zero permission.

919
00:46:55,320 --> 00:46:58,000
That's how, you can transfer
energy from here to here

920
00:46:58,000 --> 00:47:02,010
and have that node's
perfectly stationary.

921
00:47:02,010 --> 00:47:03,140
Anybody skip rope?

922
00:47:03,140 --> 00:47:05,919
You know how this works.

923
00:47:05,919 --> 00:47:07,710
Now, this is where I
quarrel with the book.

924
00:47:07,710 --> 00:47:09,560
This is another drawing.

925
00:47:09,560 --> 00:47:11,706
But I'm uncomfortable
with the fact

926
00:47:11,706 --> 00:47:13,080
that they chose
different colors.

927
00:47:13,080 --> 00:47:15,190
Because I think to the
first time learner,

928
00:47:15,190 --> 00:47:17,830
you might be tempted to think,
well, one electron lives here

929
00:47:17,830 --> 00:47:19,250
and the other
electron lives here.

930
00:47:19,250 --> 00:47:21,660
No, the electron,
if there's only one,

931
00:47:21,660 --> 00:47:23,020
it can go from one to the other.

932
00:47:23,020 --> 00:47:25,186
If there are two, they can
go from one to the other.

933
00:47:25,186 --> 00:47:28,020
And, see, they do this
all the way through.

934
00:47:28,020 --> 00:47:31,645
So please don't start
rationalizing in your mind that

935
00:47:31,645 --> 00:47:34,490
one electron goes in the yellow
and the other electron goes

936
00:47:34,490 --> 00:47:37,440
in the grey.

937
00:47:37,440 --> 00:47:38,080
There's the d.

938
00:47:38,080 --> 00:47:38,871
Aren't they pretty?

939
00:47:43,300 --> 00:47:47,700
If you find the f
orbitals, that's wild.

940
00:47:47,700 --> 00:47:50,660
So I think this is probably
a good place to stop.

941
00:47:50,660 --> 00:47:52,119
We've got a few minutes here.

942
00:47:52,119 --> 00:47:53,910
If you want to read
more about uncertainty,

943
00:47:53,910 --> 00:47:56,350
this is a very nice
book by David Peat that

944
00:47:56,350 --> 00:47:59,930
goes into the meanings,
including this indeterminacy,

945
00:47:59,930 --> 00:48:01,210
and so on.

946
00:48:01,210 --> 00:48:04,050
Good book here on hydrogen.

947
00:48:04,050 --> 00:48:05,200
Please, I don't want noise.

948
00:48:05,200 --> 00:48:07,170
We've got, still,
a few more minutes.

949
00:48:07,170 --> 00:48:10,170
Still got a few more minutes.

950
00:48:10,170 --> 00:48:12,000
This book here talks
about hydrogen.

951
00:48:12,000 --> 00:48:13,500
Goes right back to Democritus.

952
00:48:13,500 --> 00:48:19,980
One chapter is a beautiful
thing on the use of hydrogen

953
00:48:19,980 --> 00:48:22,400
as a potential fuel.

954
00:48:22,400 --> 00:48:23,670
All the Bohr and whatnot.

955
00:48:23,670 --> 00:48:27,120
This is a play that won the
Tony Award in the year 2000.

956
00:48:27,120 --> 00:48:29,040
Written by Michael Frayn.

957
00:48:29,040 --> 00:48:34,350
And it's about the fact that
Niels Bohr was the mentor

958
00:48:34,350 --> 00:48:36,140
to Werner Heisenberg.

959
00:48:36,140 --> 00:48:41,500
And now it's 1941, the
Nazis have invaded Denmark.

960
00:48:41,500 --> 00:48:45,530
And Bohr is essentially
waiting to get out

961
00:48:45,530 --> 00:48:52,560
of Denmark before the war
overtakes the rest of Europe.

962
00:48:52,560 --> 00:48:55,970
Meanwhile, Heisenberg is now
the head of the Nazi equivalent

963
00:48:55,970 --> 00:48:57,550
of the Manhattan Project.

964
00:48:57,550 --> 00:49:00,770
And he goes to Copenhagen
to visit his old mentor.

965
00:49:00,770 --> 00:49:01,942
That's a fact.

966
00:49:01,942 --> 00:49:02,650
They have dinner.

967
00:49:02,650 --> 00:49:03,800
That's a fact.

968
00:49:03,800 --> 00:49:04,730
They go for a walk.

969
00:49:04,730 --> 00:49:05,780
That's a fact.

970
00:49:05,780 --> 00:49:08,090
They never speak to each
other after that night.

971
00:49:08,090 --> 00:49:09,490
That's a fact.

972
00:49:09,490 --> 00:49:12,290
So the question is,
what went on that night.

973
00:49:12,290 --> 00:49:15,680
And that's what Michael Frayn
uses as the dramatic point

974
00:49:15,680 --> 00:49:16,720
of departure.

975
00:49:16,720 --> 00:49:21,450
So, did Heisenberg go to
Bohr to get Bohr's opinion

976
00:49:21,450 --> 00:49:23,250
about nuclear weaponry?

977
00:49:23,250 --> 00:49:25,280
Did he try to find out
whether the Allies were

978
00:49:25,280 --> 00:49:26,590
working on a bomb?

979
00:49:26,590 --> 00:49:29,870
Did he go to say, look, we
should on both sides not

980
00:49:29,870 --> 00:49:32,620
develop nuclear weaponry?

981
00:49:32,620 --> 00:49:34,530
What went on in
that conversation?

982
00:49:34,530 --> 00:49:37,610
And so you see
Bohr at the center.

983
00:49:37,610 --> 00:49:40,560
There's Heisenberg
who's the one electron.

984
00:49:40,560 --> 00:49:42,860
And there's Margaret,
who is Bohr's wife, who

985
00:49:42,860 --> 00:49:44,100
was the observer.

986
00:49:44,100 --> 00:49:47,940
And so there's the play
between the uncertainty

987
00:49:47,940 --> 00:49:50,835
in quantum mechanics and the
uncertainty in human relations.

988
00:49:50,835 --> 00:49:53,090
It's a really nice play.

989
00:49:53,090 --> 00:49:55,790
Here's a rendition of it.

990
00:49:55,790 --> 00:49:59,680
This is Stephen Rea playing
Bohr, Francesca Annis playing

991
00:49:59,680 --> 00:50:04,230
Margaret Bohr, and playing
Werner Heisenberg is, do you

992
00:50:04,230 --> 00:50:12,260
recognize him,
it's Daniel Craig.

993
00:50:12,260 --> 00:50:16,080
This is a book that came out not
too long ago about Heisenberg.

994
00:50:16,080 --> 00:50:18,100
A lot of controversy about him.

995
00:50:18,100 --> 00:50:21,480
Some people accused him
of being a collaborator.

996
00:50:21,480 --> 00:50:24,330
Other people say that he
was absolutely brilliant

997
00:50:24,330 --> 00:50:27,450
in the right amount
of foot-dragging.

998
00:50:27,450 --> 00:50:29,720
He did not want to give
Hitler nuclear weapons.

999
00:50:29,720 --> 00:50:32,670
If he'd been a total
disaster he would

1000
00:50:32,670 --> 00:50:35,230
have been replaced
by somebody who

1001
00:50:35,230 --> 00:50:37,100
might have been more zealous.

1002
00:50:37,100 --> 00:50:39,610
And if he went too fast,
he might have figured out

1003
00:50:39,610 --> 00:50:41,430
how to make nuclear weapons.

1004
00:50:41,430 --> 00:50:45,690
So, very interesting
book about him.

1005
00:50:45,690 --> 00:50:47,140
And here's a nice photo.

1006
00:50:47,140 --> 00:50:47,937
This is Bohr.

1007
00:50:47,937 --> 00:50:49,020
This is Werner Heisenberg.

1008
00:50:49,020 --> 00:50:50,960
And this is Wolfgang Pauli.

1009
00:50:50,960 --> 00:50:53,430
Undoubtedly talking
about what goes

1010
00:50:53,430 --> 00:50:56,260
on when you pluck that string.

1011
00:50:56,260 --> 00:50:57,693
So we'll see you on Wednesday.