in which is the change of the electron, that of the nucleus, the radius of the orbit, the orbital frequency, and the mass of the electron. This is merely the assumption that the electron rotates in a circular orbit which is governed by the laws which are known, from the work on the scattering of the [Pg 212] alpha particles, to hold inside as well as outside the atom. The radical element in it is that it permits the negative electron to maintain this orbit or to persist in this so-called “stationary state” without radiating energy even though this appears to conflict with ordinary electromagnetic theory. But, on the other hand, the facts of magnetism[155] and of optics, in addition to the successes of the Bohr theory which are to be detailed, appear at present to lend experimental justification to such an assumption. Bohr’s second assumption is that radiation takes place only when an electron jumps from one to another of these orbits. If represents the energy of the electron in one orbit and that in any other orbit, then it is clear from considerations of energy alone that when the electron passes from the one orbit to the other the amount of energy radiated must be ; further, this radiated energy obviously must have some frequency , and, in view of the experimental work presented in the next chapter, Bohr placed it proportional to , and wrote: being the so-called Planck constant to be discussed later. It is to be emphasized that this assumption gives no physical picture of the way in which the radiation takes place. It merely states the energy relations which must be satisfied when it occurs. The red hydrogen line is, according to Bohr, due to a jump from orbit 3 to orbit 2 (Fig. 26), the blue line to a jump from 4 [Pg 213] to 2, to a jump from 5 to 2, etc.; while the Lyman ultra-violet lines correspond to a series of similar jumps into the inmost orbit 1 (see Fig. 26). Bohr’s third assumption is that the various possible circular orbits are determined by assigning to each orbit a kinetic energy such that in which is a whole number, the orbital frequency, and is again Planck’s constant. This value of is assigned so as to make the series of frequencies agree with that actually observed, namely, that represented by the Balmer series of hydrogen. It is to be noticed that, if circular electronic orbits exist at all, no one of these assumptions is arbitrary. Each of them is merely the statement of the existing experimental situation. It is not surprising, therefore, that they predict the sequence of frequencies found in the hydrogen series. They have been purposely made to do so. But they have not been made with any reference whatever to the exact numerical values of these frequencies.