Transcript Precursors to Modern Physics

Spin and Atomic Physics
1.
2.
3.
Today
HW 8, problem 7.38
Quiz 11.6
Topics in this chapter:




The spin and the Stern-Gerlach experiment.
Fermion, Boson and the Pauli exclusion
principle.
Multi-electron atoms and the Periodic Table.
Characteristic X-rays.
HW problem 7.38
Since it is an attractive central force
and the angular momentum is given:
L  l  l  1
 1.00 1033 kg  m/s  l  l  11.055 1034 J  s
 l 9
 ml  0, 1, 2,..., 9
 Lz  ml  0, 1 , 2 ,..., 9
The Stern-Gerlach experiment in the history of QM
The Balmer series
Empirical
410 nm 434 nm 486 nm
1
1 1 
formula in 1885:   1.097 107 m1  4  n2  , n  3,4,5,...


656 nm
1885
Electron discovered in
by J.J. Thomson in 1897
1897
Rutherford discovered
nucleus in 1909
1909
1913
Niels Bohr’s Hydrogen
model in 1913
The de Broglie wave (1924):
h p
p k E 
Stern-Gerlach experiment,
electron spin in 1922
1922
The Schrödinger Equation (1926):

2
2m
 2Ψ  x,t 
x 2
 U  x  Ψ  x,t   i
Ψ  x,t 
t
1924
1926
The Stern-Gerlach experiment

F =  μ  B

Interesting to read:
http://scitation.aip.org/journals/doc/PHTOAD-ft/vol_56/iss_12/53_1.shtml
The Stern-Gerlach experiment

F =  μ  B

B z
ˆz
F = z
z
Classical
F=
Quantum
B
e
Lz z ˆz Lz  ml
2me
z
F=
Bz
e
ˆz
ml
2me
z
observed
WOW !
The Stern-Gerlach experiment
Bz
e
ˆz
ml
2me
z
Quantum
F=
But:
Lz  ml , ml  0, 1, 2,..., l
n  1, 2,3,...
From:
l  0,1, 2,3,...,n  1
ml  0,1,2,3,...,l
When ground
state:
n  1, l  0, ml  0
But this was
observed:
WOW !!!
What is this?
F=
Bz
e
ˆz = 0
ml
2me
z
Spin, an intrinsic property
Spin: an intrinsic magnetic dipole moment of particles like electron, proton and photons.
This dipole moment is related to an intrinsic angular momentum. The symbol is S, which
is like L the orbital angular momentum. The corresponding quantum number is s.
L  l  l  1
S  s  s  1
Lz  ml
Sz  ms
ms  s, s  1,...,s 1,s
The spin magnetic dipole moment is
μs  g
q
S
2m
electron
μs  
e
S
me
F=
Bz
e
ˆz
ms
2me
z
Spin is an intrinsic property of a particle like mass and charge.
Example 8.1
Fermions and Bosons
Spin is an intrinsic property of a particle like mass and charge.
Fermions
(half-integral spin)
Particle
Electron, eProton, p
Neutron, n
Neutrino, ν
Omega, Ω-
s
Bosons
(integral spin)
Particle
s
½
½
½
½
½
Pion, π 0
Alpha
Photon, γ
Deuteron, d
Graviton
0
0
1
1
2
The building blocks for our Universe
Spin is an intrinsic property of a particle like mass and charge.
The Pauli exclusion principle
The Pauli exclusion principle (1924):
No two indistinguishable fermions may occupy the same
individual particle state.
This principle applies only to fermions in In an atom, or an
isolated system like a molecule.
This principle does not apply to bosons.
Review questions
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What is the spin of a particle in CM and in QM?
Give one example in each the Pauli exclusion
principle is applied.
Preview for the next class (11/11)

Text to be read:


8.4 and 8.5
Questions:
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
Why we have H2 as hydrogen molecules while Ne as neon
molecules?
What is the energy ordering of electron states in an atom
with Z = 30? Can you fill the electrons for the element Zn if
asked for?
Homework 12, due by 11/13
Problems 8.28, 8.31 on page 339.
Read section 8.2 and 8.3 one more time and see if
you can answer questions in problem 8.7 on page
338.