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& 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