Structure in the secondary hydrogen spectrum—Part V

Abstract

In a previous paper entitled “Structure in the Secondary Hydrogen Spectrum,” Part IV, it was shown that there were a number of bands associated with Fulcher’s bands. It now appears that these and other related bands form a set of band systems whose null lines are connected by a Rydberg-Ritz formula. This formula has the normal value of the Rydberg constant, as is the case with the formula found by Fowler to connect the heads of some of the helium bands. This discovery makes it possible to apportion the effects observed as between electron jumps and vibration jumps, a matter which had to be left open in the previous paper (p. 740). The present paper deals only with the Q branches which are the most strongly developed and have been investigated most fully. A preliminary account of some of the results has been published a letter to ‘Nature,’ but the numbering of the vibrational states of the H α bands proposed therein has since been abandoned. It will be shown that all the lines of Fulcher’s red bands arise as a result of transitions in which the total quantum number (electron jump) changes from 3 to 2 and the vibrational quantum number is unchanged. In the part of the band denoted by A in “Structure,” Part IV, the vibrational state has the lowest possible quantum number both before and after the transition. I shall indicate this state of affairs by the symbol 0 → 0. The corresponding vibrational states in the parts denoted by B, C, D, E and F are, both initially and finally, 1, 2, 3, 4 and 5, and I shall denote these transitions by 1 →1, 2 → 2 , 3 → 3 , 4 → 4 and 5 → 5 respectively. The different lines in part A all have the same electron jump (3 → 2) and the same vibration state (0 → 0) but have different rotational jumps either of the molecule as a whole or of the emitting electron or of both. This statement will be equally true if the letter A is replaced by any of the letters B, C, D, E or F, except that the vibrational jump 0 0 is replaced by 1 → 1, 2 → 2, etc. In the present paper I shall confine my attention to the Q branches so that all the rotational transitions here dealt with are of the type m + ½ → m + ½ , m = 1, 2, 3, 4, 5, etc. (see Part IV, p. 749). Fulcher’s green bands also have the same electron jumps (3 → 2), but in these bands the vibrational quantum number is higher by unity in the initial than in the final states. Thus for the various green bands denoted by the letters A, B, C, D, E and F the vibrational transitions are 1 → 0, 2 → 1, 3 → 2, 4 → 3, 5 → 4 and 6 → 5 respectively. In addition to these, bands with the same electron jump (3 → 2) can be found in the infra-red with the vibrational jumps 0 → 1, 1 → 2, 2 → 3, 3 → 4 and 4 → 5 and others on the side of the green towards the violet which correspond to the vibration jumps 2 → 0, 3 → 1, 4 → 2, 5 → 3 and 6 → 4, and a few lines which may correspond to the vibration jumps 3 → 0 and 5 → 2. All these lines have the electron jump 3 → 2 and are the band analogue of the single line H α in the line spectrum of the hydrogen atom. For this reason it is convenient to refer to this system of bands as the H α bands.