W.N. Catford/P.H. Regan 1AMQ

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Characteristic X-rays and Selection Rules.

Characteristic X-rays: are emitted by atoms when electrons make transitions between inner shells (note a vacancy must be created before this can happen).

An incident photon, electron or alpha-particle can knock out an e- from the atom. Electrons at higher excitation energies cascade down to fill the vacancy. A vacancy in the K shell can be filled with an e- from the L shell (a K transition) or the M shell (K) etc.

n=4, N n=3, M n=2, L

n=1, K

K series

L series

M series

K

K series

L

L series

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The Auger Effect

X-Ray Auger electron

If we have a vacancy in an inner shell then it is filled as shown here by an electron from a higher shell.

The movement of charge from one shell to another createsan electromagnetic field.It is this which generates the photon.There is an alternative, namely that the field interacts directlywith another electron in an even higher shell and ejects it from

the atom.This process is called the Auger Effect.

E(X-ray) = E(K) – E(L)

E(Auger) = E(K) –E(L) –E(M) in example shown.

Note:- After an X-ray we have 1 vacancy and after the Auger process we have two vacancies

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The Auger Effect

It is obvious that following the creation of a vacancy in an inner shell there is competition between X-ray emission and the Auger effect when the vacancy is filled by the transition

of an electron from a higher shell.

We introduce a quantity called the fluorescence yieldto take account of this.

Fluorescence Yield

K = No.of X-rays emitted

No.of vacancies

A similar quantity can be defined for each shell, indeed for each subshell

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X-ray tubes and spectra

Henry J.G.Moseley(1887-1915

Schematic of an X-ray tube.Electrons are generatedFrom a heated filament F

And are accelerated towards theMetal target T.The slit S acts as aCollimator. The electrons generate

X-rays when they hit the target.

Continuous spectrum is due to bremsstrahlung or braking radiation

Sharp lines are due to discrete X-ray lines.TheyFollow an electron being

Knocked out of an inner shell

Note:-No sharp lines for Tungsten because energy is

too low

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The Effects of Screening

Shown here is a schematic of a Na(Z = 11) atom. It has 11 protonsIn the nucleus and, in a neutral atom it has 11 electrons

arranged in shells around the nucleus.The outermost electron” feels” forces from the nucleus and from

the other 10 electrons.In essence it feels a force roughly equivalent to (11 – 10) +ve

Charges i.e.It is just as if it was in the H atom.

What about the electron in the 2s orbit?

The second picture Shows the forces there

And we see that the screening is only by

the two inner electrons.The effect of the other 8 electrons averages out

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We can calculate the K

energy for each element approximately. Consider an L-shell electron, about to fill a K-shell vacancy.

K

L+Ze

Approximately, the L electron orbits an “effective” charge of +(Z-1)e. To allow for penetrating orbits, say +(Z-b)e, where we expect b to be approximately equal to 1.

We can use Bohr theory, for an electron orbiting a charge +(Z-b)e, to estimate the X-ray energies.

2/172

222

f

))(105( )(75.0

2

1

1

1)( and ,

12 between transition

)( chargenuclear effective

sbZxbZcR

bZcRhE

nn

ebZ

H

H

i

Moseley’s Law

This compares to experiment to within 0.5% witha value for the intercept, b of very close to 1.

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1,0j and 1 l are observed to occur.

Fine Structure of X-ray SpectraThe subshells are split in energy by the spin-orbit interaction, into (+1/2) and ( -1/2) levels. Note that not all the energetically allowed transitions are observed. The notation LI, LII, LIII etc. is used for the split inner levels.

Only transitions which obey the selection rules

The selection rules are related to the underlying physics of (a) the spatial properties (symmetry) of the charge oscillations that produce transitions and (b) the angular momentum (spin) carried away by the photon itself (at least 1).

W.N. Catford/P.H. Regan 1AMQ

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