In 1914 Bragg and Peirce showed that apart from the discon tinuities, the quality ,u/p approximately followed a law of the form The coefficient C assumes a new value at each discontinuity.
Numerous experimental researches have confirmed this result, but the values of the powers of X and of N, though certainly in the neighbourhood of 3, have not yet been accurately established. If we consider the absorption per atom, the preceding law be comes Each time one of the critical values of the frequency is passed through, in the direction of increasing frequency, the coefficient A undergoes a sudden increase. It attains its maximum value when the quantum of the radiation is greater than the energy required to remove one of the K electrons from the absorbing atom. Richtmeyer found for fairly heavy elements the value when X is expressed in centimetres, while Windgardh found Bragg's law gives the variation of the coefficient only be tween the discontinuities, but we can also represent the whole of the curve by a single mathematical formula. We may consider each one of the absorption mechanisms, which come successively into play as the frequency increases, as contributing a term in to the value of A., and write the summation extending over all groups of electrons whose "extraction work" is less than the quantum of the incident radiation. The sum thus increases by one term each time the frequency passes one of the critical values v„. It is evident that It is very instructive to consider the ratio of the values of /.4„, on the two sides of a discontinuity; this is termed the "absorption jump." The K jump has been carefully studied, especially by Allen. According to him, its value for different elements is : Other Writers give, it is true, slightly different figures; for ex ample, for silver, Stoner and Martin give 6.7 and Richt meyer = 6.6. One thing however is certain, the K jump diminishes as the atomic number increases. This shows that the Bragg-Peirce law cannot be rigorously true, at least so far as the factor is concerned; for if it were we should have: and this is contrary to experience.
L. de Broglie and A. H. Kramers have put forward interesting theories to predict the values of the absorption coefficients and jumps and, although we cannot regard their arguments as rigorous, have obtained results which are confirmed at least approximately by experiments.
When a continuous spectrum is analysed by means of crystal diffraction after having passed through an absorbing screen, absorption bands are found beginning abruptly and extending towards the high frequencies. The K band is single, the L band triple whilst the M and N bands exist in still greater numbers.
Bohr's simple scheme predicted one band for each series; Sommerfeld's theory, at least in its original form, predicted only two L bands; we shall not deal with the more complicated theories by means of which attempts have been made to explain the observed phenomena. (See the article on the spectroscopy of X-rays by M. Siegbahn.) Photoelectric Effect.—The absorption of X-rays by the atoms of matter is accounted for by the removal of an electron which leaves the atom with kinetic energy hv =TV., where v is the frequency of the absorbed radiation, and W. is the work required for the removal of the electron. It follows that if hetero geneous radiation falls on a body, each wave-length included in the spectrum of the incident beam will be able to excite all those levels whose "extraction work" is less than its own par ticular quantum. Further, the characteristic rays of the irradiated body will appear as a result of the return to their normal state of the excited atoms and these radiations will act in their turn on the material of the screen to produce in it the same phenomena. We ought therefore, to observe a large series of groups of elec trons, each group of corpuscles having an energy which can be expressed by a relation of the form Imp— W„, in conformity with Einstein's expression.
Experiments have confirmed this point of view entirely ; by irradiating secondary radiators with X-rays and analysing in a magnetic field the streams of electrons produced, actual cor puscular spectra are obtained, an electronic analogy as it were, of the X-ray spectra, which yield information both as to the incident radiations and the levels of the atoms irradiated.