Spin and Atomic Spin and Atomic Physics Physics 1. 1. HW 8, problem 7.38 HW 8, problem 7.38 2. 2. Quiz 11.6 Quiz 11.6 3. 3. Topics in this chapter: Topics in this chapter: The spin and the Stern- The spin and the Stern- Gerlach experiment. Gerlach experiment. Fermion, Boson and the Pauli Fermion, Boson and the Pauli exclusion principle. exclusion principle. Multi-electron atoms and the Multi-electron atoms and the Periodic Table. Periodic Table. Characteristic X-rays. Characteristic X-rays. Today
Transcript
Spin and Atomic Spin and Atomic PhysicsPhysics
1.1. HW 8, problem 7.38 HW 8, problem 7.38
2.2. Quiz 11.6Quiz 11.6
3.3. Topics in this chapter:Topics in this chapter: The spin and the Stern-Gerlach The spin and the Stern-Gerlach
experiment.experiment. Fermion, Boson and the Pauli Fermion, Boson and the Pauli
exclusion principle.exclusion principle. Multi-electron atoms and the Multi-electron atoms and the
HW problem 7.38HW problem 7.38Since it is an attractive central force and the angular momentum is given:
1L l l
33 341 00 10 kg m/s 1 1 055 10 J s. l l .
9l
0 1 2 9lm , , ,...,
0 1 2 9z lL m , , ,...,
The Stern-Gerlach experiment in the The Stern-Gerlach experiment in the history of QMhistory of QM
The Schrödinger Equation
(1926):
Electron discovered in by J.J. Thomson in 1897Rutherford discovered nucleus in 1909
Niels Bohr’s Hydrogen model in 1913
The Balmer series
410 nm
434 nm
486 nm
656 nm
7 12
1 1 11 097 10 m 3 4 5
4. , n , , ,...
n
Empirical formula in 1885:
The de Broglie wave (1924):h p p k E
22
2
Ψ ΨΨ
2
x,t x,tU x x,t i
m x t
1885
1897
1909
1913
19241926
1922
Stern-Gerlach experiment, electron spin in 1922
The Stern-Gerlach experimentThe Stern-Gerlach experiment
Interesting to read: http://scitation.aip.org/journals/doc/PHTOAD-ft/vol_56/iss_12/53_1.shtml
F = μ B
The Stern-Gerlach experimentThe Stern-Gerlach experiment
F = μ B
F = zzz
Bˆ
z
Classical
Quantum
F = z2
zz
e
BeˆL
m z
F = z
2z
le
Beˆm
m z
z lL m
WOW !observed
The Stern-Gerlach experimentThe Stern-Gerlach experiment
Quantum
F = z2
zl
e
Beˆm
m z
0 1 2z l lL m , m , , ,..., l But:
When ground state:
From:
0 1 2 3lm , , , ,..., l
0 1 2 3 1l , , , ,...,n
1 2 3n , , ,...
1 0 0ln , l , m F = z = 02
zl
e
Beˆm
m z
But this was observed:
WOW !!! What is this?
Spin, an intrinsic propertySpin, an intrinsic propertySpin: 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.
The spin magnetic dipole moment is
Spin is an intrinsic property of a particle like mass and charge.
Example 8.1
z lL m 1 1z s sS m m s, s ,...,s ,s
1L l l 1S s s
sμ S2
qgm
electro
nsμ S
e
e
m
F = z
2z
se
Beˆm
m z
Fermions and BosonsFermions and BosonsSpin is an intrinsic property of a particle like mass and charge.
Fermions Bosons(half-integral spin) (integral spin)Particle s Particle sElectron, e- ½ Pion, π 0 0Proton, p ½ Alpha 0Neutron, n ½ Photon, γ 1Neutrino, ν ½ Deuteron, d 1Omega, Ω- ½ Graviton 2
The building blocks for our The building blocks for our UniverseUniverse
Spin is an intrinsic property of a particle like mass and charge.
The Pauli exclusion principleThe 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 questionsReview questions
What is the spin of a particle in CM What is the spin of a particle in CM and in QM? and in QM?
Give one example in each the Pauli Give one example in each the Pauli exclusion principle is applied.exclusion principle is applied.
Preview for the next class Preview for the next class (11/11)(11/11)
Text to be read:Text to be read: 8.4 and 8.58.4 and 8.5
Questions:Questions: Why we have HWhy we have H22 as hydrogen molecules while as hydrogen molecules while
Ne as neon molecules?Ne as neon molecules? What is the energy ordering of electron states What is the energy ordering of electron states
in an atom with Z = 30? Can you fill the in an atom with Z = 30? Can you fill the electrons for the element Zn if asked for? electrons for the element Zn if asked for?
Homework 12, due by 11/13Homework 12, due by 11/13
Problems 8.28, 8.31 on page 339. Problems 8.28, 8.31 on page 339.
Read section 8.2 and 8.3 one more Read section 8.2 and 8.3 one more time and see if you can answer time and see if you can answer questions in problem 8.7 on page 338.questions in problem 8.7 on page 338.
