The energy which is lost by the atom in one of these jumps is turned into a light-wave. What sort of light-wave it is to become is determined by the theory of quanta. A light-wave is a periodic process, and if its frequency is , its period is a of a second. The generalized quantum-principle shows that, if the period of a wave is , the energy of the wave multiplied by must be or an exact multiple of ; in fact, so far as observation goes, it appears to be always . Since is a of a second (when is the frequency), it follows that the energy of the wave is . Also, by the principle of the conservation of energy, the energy of the wave is equal to the energy that the atom has lost. This shows that, if e is the kinetic energy of the electron in the smallest orbit, the wave caused by a transition from the second orbit to the first will have a frequency given by the equation For a transition from the third orbit to the first, [Pg 69] For a transition from the third orbit to the second, and so on. Comparing these results with the empirical results set forth in Chapter IV, we see that they will agree if Rydberg’s constant is equal to divided by and the velocity of light. (We have to divide by the velocity of light, because in this chapter we have been speaking of frequencies, while in Chapter IV we were speaking of wave-numbers.) Now is easily calculated since we know the charge on a hydrogen nucleus and on an electron, the mass of an electron, and the radius of the minimum orbit; also and the velocity of light are known. It is found that the calculated value of Rydberg’s constant, from these data, agrees closely with the observed value; this was, from the first, a powerful argument in favour of Bohr’s theory. For different kinds of light, the frequency is different; in the visible parts of the spectrum, it determines the colour, being smallest for red and greatest for violet. By measuring the frequencies of the different lines in the hydrogen spectrum, and multiplying each by , we find out how much energy the above loses in the different [Pg 70] transitions from orbit to orbit that are possible. The terms in the spectrum are proportional to the energies in the different possible orbits, and the frequencies of the lines are proportional to the loss of energy in passing from one orbit to another. We can calculate what the different possible orbits should be from the fact that their energies must differ by an amount , where is the frequency of some line in the hydrogen spectrum. We can also calculate the possible orbits from the fact that the mass of the electron multiplied by the circumference of an orbit multiplied by the velocity in that orbit must be an exact multiple of . These two methods lead to the same result, and thus confirm our theory.