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42 



Relation ( 1 ) allows us to determine the frequency of the radiation emitted during 

 a transition, but gives no information as regards the intensity and polarisation 

 of this radiation. Now the mechanism of the radiation process with which the 

 (juantum theory operates is quite unknown and must, on account of the essential 

 discontinuity involved in relation (1), be entirely different from the radiation process 

 in ordinary electrodynamics, which is essentially continuous. Due to this discon- 

 tinuous character, it has been necessary to introduce in the quantum theory the 

 notion of the "a-priori probability of spontaneous transition" between two stationary 

 states of an atomic system, which was used by Einstein') in his explanation of 

 the law of temperature radiation on the basis of the quantum theory. Imagine an 

 atomic system in one of its stationary states, and let us for the present assume that 

 it is uninfluenced by external radiations. Then the S3'^stem must be assumed to possess 

 a tendency within a given time interval to pass spontaneously to one of the other 

 stationary states of the system for which the value of the total energy is smaller; 

 in analogy with the circumstance that on ordinary electrodynamics a vibrating 

 electron will emit radiation and loose energy independent of surrounding radiations. 

 A measure for this a-priori probability of spontaneous transition is given by the 

 quantity A!„, introduced by Einstein, which is defined in such a way that A',(i/ 

 represents the probability that the atom in a stationary state characterised by one 

 dash (') will pass spontaneously within a time interval di to another stationary 

 state which is characterised by two dashes ("). Besides the quantities A, Einstein 

 has introduced other quantities B which are deflned in a corresponding way and 

 which measure the probability that a transition will take place due to the presence 

 of radiation in the surrounding space, in analogy with the circumstance that on 

 ordinary electrodynamics a vibrating electron will emit or absorb energy due to 

 the action of the electric and magnetic forces in the electromagnetic radiation 

 existing in the surrounding space. These probabilities of transition due to the 

 surrounding radiation will, however, be proportional to the density of this radiation ; 

 as a consequence of this, it is easily seen that the value of K„ alone will be the 

 determinative factor for a calculation of the intensity with which the corresponding 

 spectral line will be emitted by the vacuum tube (or flame) in which the radiation 

 is excited. In fact, in the luminescent gas (or vapour) this radiation is excited by 

 impact of electrons, due to which one electron or several electrons are knocked out 

 of the atom, so that the atoms in their different stationary states will not be in 

 temperature equilibrium with the radiation present in the surrounding space; on 

 the contrary, the density of the latter radiation will be comparatively very small, 

 and the quantities B will not play any considerable part in the determination of 

 the intensity of the spectrum. If v is the frequency of the radiation emitted during 

 a certain transition, and a' the number of atoms present in the vacuum tube (or 

 flame) in the initial state, the energy of the radiation of frequency v emitted in 

 unit time will consequently be given by a' x A!„ x h v. 



•) A. Einstein, Phys. Zeitsclir. XVIII, p. Vl\ il917). 



