& X-ray absorption, emission, Moseleyhttp://hyperphysics.phy-astr.gsu.edu

Haken H and Wolf H C: Atomic and quantum physics

(Springer)***

Eisberg R and Resnick R; Quantum physics of atoms,

molecules, solids, nuclei and particles (2nd ed) Wiley**

Softley T P; Atomic spectra (Oxford)**

White H E; Introduction to Atomic Spectra (McGraw-Hill)**

Woodgate G K; Elementary atomic structure (Oxford)**

Herzberg G; Atomic spectra and atomic structure (Dover

Reprint)*

Energy level (Grotrian) diagramsAs predicted by Bohr As predicted by QM

1s

2s

3s

3p

2p

3d

1s

2s

3s

3p

2p

3d

From WhiteFrom Bransden and Joachain

SE prediction of radialSE prediction of radial functions (left) and radial distribution functions (right)

Comparison of the old (orbital) quantum theory and the SE

Stern-Gerlach experiment

Total a.m (j) and the vector diagram The H Balmer alpha (Hα, n=3 – 2) transition

Dirac theory suggestions energy of transitions marked * (d & e) and + (f & g) should have the same energy. Measurement (and QED) show they do not. This is referred to as the Lamb shift. Thus, there are 7 components to the Hα (Balmer alpha) line.

For a D-term (L=2) there are 10 states= Σ(2j+1) = 2Σ(2L+1)

H 3d 2D5/2

H 3d 2D3/2

mj = +5/2 shown

mj = -1/2 shown

l = 2

J = l + s

j = 2 + ½ = 5/2

(2j + 1) = 6

states

mj = 5/2

3/2

1/2

l = 2

J = l + s

j = 2 – ½ = 3/2

(2j + 1) = 4

states

mj = 3/2

1/2

2s 2S1/2 2p 2P1/2

2p 2P3/2

BohrEnergy level diagram for Sodium

Sodium‘D’-line589 nm

n=5

n=4

n=3

n=1

n=2

Comparison of the quantum-mechanical with the semi-classical of the neutral sodium atom. Three of the lowest possible states (3s, 3p, 3d) for the single valence electron are shown. Note the size of the core of closed (n=1 and 2) shells.

The neutral Sodium atom (Z = 11)Ground state 1s22s22p63s 2S1/2

Energy level diagram for Sodium showing fine structure and the emission lines

Quantum defect δ() for the Alkali metals

eV 2

22*l,n

)(δn

16.13

)(δn

1hcR

n

1hcRE

Effective principal quantum number n*

for the Alkali metals ground states

Sodium ‘D’-lines2P1/2 – 2S1/22P3/2 – 2S1/2

n=2

3

4

5

6

X-ray production and emission

Bombard an anode with an energetic electron beam to produce x-rays. The emission spectrum is beam energy dependent

A spectrum consists of a smooth bremsstrahlung component and characteristic lines.

K-level refers to n = 1L-level n = 2M-level n = 3 etc

K refers to n = 2-1K n = 2-1etc

L refers to n = 3-2L n=4-2etc

refers to a Δn =1 transitionΔn =2 transition

etc

Characteristic x-rays

ON

M

L

K

P

Kα Kβ Kγ

Lα Lβ Lγ

Mα Mβ Mγ

n=1

2

3

4

65

The spin-orbit interaction results in significant level splitting (or fine structure) in high atomic number atoms

Platinum (Z=78), notice the K- etc are split the vertical energy scale is in keV

Selection rulesΔ = ±1Δj = 0, ±1

Moseley’s Law Moseley diagram plots ZhcR

E ,n vs.

2

2n

nn

sZhcRE

Apparatus for studying x-ray absorption

Mas

s ab

sorp

tio

n c

oef

. m