ON ABSORPTION SPECTRA OF ORGANIC COMPOUNDS. 299 



different elements. An atom can only absorb energy in terms of its funda- 

 mental unit or quantum, and as its energy quanta are absorbed the electron is 

 progressively shifted from one orbit to another of greater radius. Conversely, 

 the loss of energy by an atom consists in the shift of an electron from one orbit 

 to another of smaller radius, each such shift being accompanied by the loss of 

 the fixed quantity of energy, which may be called the atomic quantum of energy. 

 These atomic quanta are of the order of from 6.5x10-'° to 2x10"" erg. 



The second assumption is that the electron shift occupies a definite period 

 of time which is the same for all atoms. Since 



Quantum of energy „ 



^1 — —- °^ = i! requency 



Time factor 



it follows that an atom becomes endowed with the power of absorbing its energy 

 quantum on exposure to radiant energy of a definite frequency. For the time 

 factor the Planck constant, 6.57x10"-', may be used, and therefore 



' Atomic quantum 



6.57x10- 



= Atomic frequency. 



The characteristic frequencies exhibited by atoms are thus of the order of from 

 1x10'' to 3x10". 



When atoms unite to form a molecule energy is lost in the process, and this 

 energy can only have been given up by the atoms, for there is no other source 

 from which the energy can have been derived. The case of two atoms entering 

 into combination may first be considered. Both atoms lose energy when they 

 combine, and the third assumption may be made that each atom loses the same 

 amount of energy. This assumption is the simplest possible — namely, that each 

 of the two atoms contributes one-half of the total energy lost when the two 

 combine. It must, however, be remembered that each atom can only lose energy 

 in terms of its atomic quantum, and for the sake of argument let the two atoms 

 be characterised by the quanta llxlO'" and 9x10'° respectively. Since the 

 two atoms can only lose their energy quanta, and since each of them loses the 

 same amount of energy, it follows that the smallest amount each can lose is the 

 least common integral multiple of the two atomic quanta. The first atom, 

 therefore, will lose 9 quanta of the size 11 x 10"' erg, whilst the second atom 

 will lose 11 quanta of the size 9x10''° erg. The total amount of energy lost 

 in the combination will be 2x 11x9 xl0-'° = 1.98x lO""* erg. 



Before dealing with this principle of the least common integral multiple in 

 greater detail a very important reservation must be made. The two quanta were 

 assumed of 11x10"'° and 9x10-'°, but if, for example, the first quantum were 

 11.01x10-"'' the least common integral multiple would be 1101x9x10-'°. Indeed, 

 the least common multiple of two numbers can have no possible physical signifi- 

 cance unless the two numbers can be expressed in terms of a common unit 

 (C&mDbell and B.aly, Pfiil. Mag., 41,707 (1921)). The fourth and last assumption 

 may be made, therefore, that the atomic quanta of all atoms are integral 

 multiples of a fundamental unit of energy. It may well be that this funda- 

 mental unit is the atomic quantum characteristic of the hydrogen atom, and 

 there is much in favour of this being the case. 



In the case of the molecule formed by the combination of two atoms having 

 the atomic quanta of 11x10-'° and 9x10'° erg respectively, the loss or gain 

 of energy by this molecule may be considered. This molecule obviously can 

 only lose or gain energy in terms of the atomic quanta characteristic of its 

 atoms, and consequently the minimum amount of energy the molecule can gain 

 or lose as a whole entity will be the minimum amount lost in its formation — that 

 is to say. twice the least common integral multiple of the atomic quanta of its 

 component atoms. This establishes the conception of a molecular quantum of 

 energy, which, however, is not a physical entity in the same sense as an atomic 

 quantum, but is the sum of an integral number of atomic quanta. Just as an 

 atona is endowed with a freouency by virtue of its quantum, so also is a molecule 

 endowed with a molecular frequency established by its riuantum. 



Although the two atoms have entered into combination, they cannot have 

 lost their individuality as absorbers or radiators of energy. They still must 

 possess the power of absorbing or evolving their characteristic quanta of energy. 



