March 24, 192 1] 



NATURE 



109 



Electrons.^ 



By Sir William Bragg, K.B.E., F.R.S. 



II. 



y^ HEPING in mind the results already de- 

 ■*-^ scribed, we can now appreciate a very 

 remarkable development of electron theory 

 which has been made in the last few years. 

 Spectrum analysis has long been occupied 

 with the extraordinary complications of the light 

 radiation emitted by the various atoms. As a 

 result it appears that the frequencies of the lines 

 in a spectrum often display curious and exact 

 numerical relations, in the form g-enerally involv- 

 ing differences of frequencies of similar lines or 

 groups of lines. For instance, the famous Balmer 

 equation : — • 



Frequency = v = N(i//7j- — ijn^), 



where N = 3-290 x lo^^, gives the frequencies of 

 series of lines in the hydrogen spectrum. When 

 nj is put equal to 2, and ti.y to 3, 4, 5 in succes- 

 sion, the series of values for v represent the fre- 

 quencies of the lines in the visible spectrum. If 



"1 = 3 and n2 = 4, 5, 6, ... , 

 in succession, we have the frequencies of lines 

 in the infra-red (Paschen) ; and if 



Wi=i, "2=2, 3, 4, ... , 

 we have the frequencies recently shown by Lyman 

 to exist in the ultra-violet. 



Now there is nothing in our older conception 

 of the origin of radiation within the atom to give 

 us a clue as to why differences of frequencies should 

 come into these empirical, though most useful, 

 formulae. We have pictured to ourselves vibrat- 

 ing systems, mechanical or electric, and waves 

 arising therefrom. But what connection between 

 masses or electricities gives us in any simple way 

 equations involving the addition or subtraction of 

 frequencies? We are in a blind alley- Let us, 

 therefore, abandon our preconceptions as to the 

 origin of those lines which we find in the light 

 spectrum and suppose that here also they arise 

 in the same fashion as we actually know that they 

 arise in the cases we have considered above. 

 Suppose that the energy of an emission of radia- 

 tion is derived from the energy of an electron. 

 It may be the only way in which radiation ever 

 does arise, but it is not necessary to suppose so 

 much at present. It is enough that we carry into 

 the atom the whole process which in X-rays and 

 the photo-electric effect we have observed to take 

 place in part outside. Suppose that within the 

 atom there are certain positions or conditions in 

 which electrons may be, each postulating a certain 

 energy associated with the electron ; and suppose 

 that sometimes an electron slips from one position 

 to another of lower energy, and that the differ- 

 ence in energies is transformed into wave radia- 

 tion according to the same law as before, i.e. 



' The Twelfth Kelvin Lecture deliverfd before the Inst'tution of Elec- 

 trical Engineers on Tanuary 13. Continned from p. 82. 



NO. 2682, VOL. 107] 



energy transferred = /i x frequency. Let the energy 

 in these states be N^/i2; ^hl2^; Nh/f; etc., and 

 so on. Then all the series yielded by the Balmer 

 formula are accounted for at the same time. 



What may these states be? Why not, as Bohr 

 suggests, so many different orbits in which elec- 

 trons can move round the central positive nucleus 

 in the atom, the nucleus the sure existence of 

 which Rutherford has established ? At one time, if 

 we had presumed the existence of these orbits, we 

 should have been inclined to connect them with 

 the direct emission of radiation, and the fre- 

 quency of that radiation would be the number of 

 revolutions in a second. But now we assume 

 these orbits to persist without radiation, and that 

 radiation arises where the electron steps from 

 one orbit to another; moreover, the frequency of 

 the issuing radiation is determined by the simple 

 rule : Frequency is equal to change of electron 

 energy divided by h. We are not picturing any 

 new process here, or evolving new ideas to fit 

 awkward facts ; we are supposing a process to 

 exist in one place which we already know to exist 

 in another. 



It is a very remarkable fact that the number 

 N is equal to 2n^me*/h^ within small errors of ex- 

 periment. Spectrum measurements show that N 

 is equal to 3-29033 x lo^^ ; and 2irhne^/h^ is equal, 

 taking the most recent determinations of m, e, and 

 h, to 3-289 X 10^^. Imagine an electron revolving 

 in a circle about the positive nucleus of the hydro- 

 gen atom according to the orthodox laws of 

 dynamics with kinetic energy 2ir^me*/n%^ = Nh/n^. 

 Its velocity, v, is 2iTe^/hn; the radius, r, of the 

 circular orbit is found by putting mv^/r = e^/r^, 

 and is equal to n^^/^ir'^ehn. The angular 

 momentum is mvr = nh/2'7r. If the electron 

 changes its orbit from n = n2 to n = n^, where n^^ is 

 greater than n^, its kinetic energy in the new orbit 

 is greater than in the old by ^h{x jn^^-i jn^). 

 But an amount of potential energy has been set 

 free equal to e\\ Ir-i^ — i jr^, and this is equal to 

 twice the change in kinetic energy, as is easily 

 seen by substituting for the r's their values as 

 found above. Consequently, the right amount of 

 energy is available for radiation. We can, there- 

 fore, following Bohr, define the necessary separate 

 states as those of motion in circular orbits in 

 which the angular momentum is an integral mul- 

 tiple of /i/27r. The simplicity of these expressions 

 is very attractive. But the matter is far from 

 ending here. During the last few years Bohr 

 and Sommerfeld have led an inquiry into the pos- 

 sibilities of this theory which has produced very 

 remarkable results. These are due to a slight 

 modification in the original conception. The dif- 

 ferent circular orbits which Bohr first pictured 

 have become groups of orbits fixed by laws which 

 are somewhat arbitrary, but not without founda- 

 tion. A group contains a limited number of orbits 



