the Quantum Theory

The Compton Effect.

When ordinary light or X-radiation falls on a body there are in general, in addition to a possible photo electric emission, if the wave-length is short enough, two further observable consequences : (i) part of the incident beam is scattered by the body, i.e., a radiation, the character of which is identical with or very closely similar to the incident radiation proceeds from the irradiated material, and (2) the atoms of the material may be excited to emit a radiation characteristic of the material (Barkla's characteristic or fluorescent radiation). While the classical theory requires that the scattered radiation (I) should he exactly similar to, i.e., should have the same frequency and in other respects should be a i eplica of the incident radiation, the light-quantum hypothesis of Einstein leads us to expect the scattered radiation to have a slightly lower frequency (longer wave-length) than the incident radiation. This was first deduced and observed by the American physicist, A. H. Compton, and is named after him the Compton effect. We regard the light quantum or photon, as it is sometimes called, as a sort of cor puscle possessing the energy lip or h/T, where v and r are respec tively the frequency of the vibration associated with the corpuscle and the corresponding period. We further suppose the corpuscle to have the momentum h/X, where X is the wave-length of the light. Since Xv = C, the momentum will also be equal to The application of the principles of conservation of energy and mo mentum leads to a simple solution of the problem of the collision between a photon or corpuscle and an electron as explained in the article COMPTON EFFECT. Indeed, in the simple case where the electron is supposed to be at rest before the collision, it is obvious, without entering into mathematical details, that the effect of the collision will be to reduce the energy of the photon, since the electron must acquire some energy. Therefore by will he less than by and consequently V will be less than v.

Theory of Spectra.

Regularities in the spectrum of hydrogen were discovered as early as 1885 by Balmer and much further progress of this kind was made subsequently by Rydberg, Ritz and others. The first to calculate wave-lengths successfully from an assumed dynamical model of the emitting atom appears to have been J. W. Nicholson, whose work is published in a valuable series of papers on the spectra of nebulae and the solar corona in 1911 and 1912. He ascribed certain nebular and coronal spectral lines, which could not at that time be associated with known terrestrial elements, and which did not apparently exhibit the types of regu larity of series spectra, to hypothetical elements nebulium and protofluorine, the atoms of which he supposed to have a like that suggested by Rutherford to explain the laws of the scat tering of a particles by matter. (See ATOM.) He applied mathe matical methods very similar to those employed by Clerk-Maxwell in his study of the motion of the rings of Saturn, and from the dynamical properties of these atoms of hypothetical elements he calculated the wave-lengths of a very large number of coronal and nebular lines by identifying the frequencies of the radiation emitted by them with those of the small vibrations of the electrons perpendicular to and also in the plane of the circle on which they were situated.

The difference between the calculated and observed wave-lengths was probably in no case as great as 4 Angstrom units and at least one of these lines, X =4,353 A.U., supposed to be emitted by nebu lium, was calculated by Nicholson before it was actually observed as one of the lines in the spectrum of the great nebula in Orion. In the earlier papers only ratios of frequencies were calculated— there being no means of fixing the angular velocity of the electrons in the atomic ring. One frequency was therefore assumed to be

identical with that of a suitable observed line, the others being then calculated from the ratios. In 1912, however, Nicholson published the discovery that the angular momentum of the atom has to be an integral multiple of h/27r in order to give the frequencies of the observed lines. Although we have been forced to give up the view that the coronal and nebular lines which Nicholson investigated are due to a type of atom not found on the earth, his work neverthe less represents the first successful application of the quantum theory to spectra, and the relations he discovered between Planck's constant and angular momentum of the atom furnished an im portant part of the foundation for the great work of Niels Bohr which followed, and which must be regarded as the most consider able of the contributions to the modern theory of spectra and atomic structure. The earliest of Bohr's papers involving the quantum theory appeared in 1913 and contains two basic princi ples. (See ATOM.) (I) The first of these, which we shall term Bohr's postulate, connects (we might say identifies) the spectral terms (see SPEC TROSCOPY) with the energy levels or the energies of the emitting atom in its different stationary states. The frequencies (or wave numbers) of all the lines of series spectra can be expressed as dif (2) The second basic principle is the connection discovered by Nicholson between angular momentum and Planck's constant. Bohr employed this relation to fix the stationary states of the sort of atom he contemplated. In this early form of the quantum theory he considered the simplest atoms of the Rutherford type, consisting of a positively charged nucleus of relatively small dimensions and large mass M, with a charge equal to Ze, where Z is a positive integer and e is the elemen tary unit of charge, 4-774X e.s.u., and a single planetary electron with a mass m and the same numerical charge e. The simplest kind of motion of such a system is that in which the nucleus and electron (A and B in fig. 4) travel in circular orbits, the radii of which we shall lepresent by R and r respectively, with the atomic centre of gravity as their common centre. In V and v are the respective velocities of nucleus and electron, and if T represents the total kinetic energy of the system, we get the following equations from the principles of conservation of energy and momentum and the inverse square law of force: the equation (34) will give wave numbers.

A hydrogen atom was supposed by Bohr to be of the type de scribed, with the integer Z (the atomic number) equal to unity. A helium atom he supposed to have a doubly charged nucleus, Z=2, and in its neutral state two electrons, so that the atomic model just described, with Z= 2 represents an ionized helium atom, Z=3 represents an ionized lithium atom and so on. Putting Z= i and n= 2 in equation (34), we have Balmer's formula. The value of R calculated by (35a) is in entire accord with the ob servational value. By substituting the known values of m,h,e and C in (35a) and taking the approximate value unity for e we find R to lie between 109,000 and i i 0,000 Spectroscopic data furnished the value 109,677.6 in the case of hydrogen.

The deduction of equation (34) was one of Bohr's greatest triumphs. It rendered a complete account of Balmer's formula and predicted other spectral series of hydrogen. Four of these are now known observationally, namely, the Lyman series, n= I, te= 3, 4, • • Balmer series, n=2, fl'=3, 4, 5, • • • Paschen series, n=3, 5, 6, . . .

Brackett series, n=4, =5, 7, . .

In the case of the (singly) ionized helium atom (34) becomes