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

Periodic Table. Periodic Table. Characteristic X-rays.Characteristic X-rays.

Today

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.