Transcript 30secChem

Newton invented Classical Mechanics to
explain how the Planets orbit the Sun
Is it the Earth orbiting the Sun or…
…or is it an electron orbiting a nucleus?
Quantum Mechanics
the great intellectual advance of the
20th Century
was invented to explain how
electrons orbit the atomic nucleus
J H Van Vleck
The Quantum Mechanical equation for
angular momentum
JxJy – JyJx = iJz
explains the electron motion
Angular momentum is quantised
….with quantum number j
j =
0, 1, 2, 3, 4, …
j
0
1
2
Each j has 2j+1 quantised components
m=
+j ... 0 ... - j
For j=1 there are 3
m = 1
0
-1
j
2j+1
0
1
j
2j+1
0
1
1
3
j
2j+1
0
1
2
1
3
5
Replace the numbers by sets of boxes
2j+1
1
3
5
Replace the numbers by sets of boxes
2j+1
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1
3
5
Replace the numbers by sets of boxes
2j+1
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3
1
5
Replace the numbers by sets of boxes
2j+1
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3
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Double up - because electrons pair up
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Push the boxes together
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Rearrange
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rearrange again
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and again
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add two to the second row
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and to the third row
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and six to the third
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rearrange again
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and again
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And what have we got?
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The Periodic Table!
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When light is absorbed
the elegant Dirac relation
[J2,[J2,T] = [J2,(J2T – TJ2)] = J4T – 2J2TJ2 + TJ4
governs the process
For J=2 there are 5 quantised orientations from +2 to -2
2
1
0
-1
-2
Note that JXJY does not = JYJX
JxJy – JyJx = iJz
Note that these are operators, not
numbers
Numbers commute i.e.
2x3–3x2 =0