W.N. Catford/P.H. Regan 1AMQ 83 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 K series LL L series

W.N. Catford/P.H. Regan 1AMQ 84 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 creates an electromagnetic field.It is this which generates the photon. There is an alternative, namely that the field interacts directly with 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 85 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 yield to 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 86 X-ray tubes and spectra Henry J.G.Moseley( Schematic of an X-ray tube. Electrons are generated From a heated filament F And are accelerated towards the Metal target T.The slit S acts as a Collimator. 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.They Follow 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 87 The Effects of Screening Shown here is a schematic of a Na(Z = 11) atom. It has 11 protons In 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 88 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/ f ))(105( )( )( and, 12 between transition )( chargenuclear effective            sbZxbZcR bZ hE nn ebZ H H i Moseley’s Law This compares to experiment to within 0.5% with a value for the intercept, b of very close to 1.

W.N. Catford/P.H. Regan 1AMQ 89 are observed to occur. Fine Structure of X-ray Spectra The 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 L I, L II, L III 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 90

W.N. Catford/P.H. Regan 1AMQ 91