w.n. catford/p.h. regan 1amq 83 characteristic x-rays and selection rules. characteristic x-rays:...
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W.N. Catford/P.H. Regan 1AMQ
1
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
W.N. Catford/P.H. Regan 1AMQ
2
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
W.N. Catford/P.H. Regan 1AMQ
3
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
W.N. Catford/P.H. Regan 1AMQ
4
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
W.N. Catford/P.H. Regan 1AMQ
5
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
W.N. Catford/P.H. Regan 1AMQ
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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.
W.N. Catford/P.H. Regan 1AMQ
7
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).