630 Bnj.L SYSTEM TECIIXICAL JOURNAL 



Now each of these equations defines a value of r; we have 

 r= e", Rli for the normal state 



r = Ae-/Rh for the second stationary stale (4) 



r = 9e- Rli for the third stationary state; and so on. 



Eacli of these \aliies of r represents the distance at which the electron 

 must stand from the nucleus, that the atom may have the energy- 

 \alue of the corrcsi)onding stationary state. If we say that the 

 electron nia\- stand still at and only at the distances gi\en by 



r = e- Rh, -ie'/Rh, 9e'/Rli (5) 



we thus define an alom-model interpreting the Stationary States. It 

 is scarcely an atom-model to be recommended, and I certainly am 

 not taking the responsibilitN' of recommending it. Nevertheless 

 the reader had best beware of picking out the obvious objections to 

 it, and condemning it because of them. For if he objects that I have 

 gi\en no reason wh>- the electron should stand still at all, nor why 

 it should stand still in these and onl\- in these positions, nor why it 

 should cause radiation of a peculiar and well-defined frequency when 

 it passes from one of these positions to another — if he makes the.se 

 objections, I can retort that the atom-model favored by Bohr him- 

 sL'lf suffers from e\cry one of these deficiencies. In fact, the onl\- 

 defects peculiar to this "atom-model of the stationary electron" appear 

 tojje two. The first is, that the distances specified by (5) do not ha\"e 

 distinctive features such as I shall presently show for the orbits specified 

 for the "atom-model of the revolving electron"; and this defect, as I 

 ha\e tried to emphasize, is a grave one. The second is, that an atom 

 in which the charges are stationary is not ipso facto magnetic, whereas 

 an atom with revolving electrons is.' 



Following Bohr, and practically all the other physicists of toda>-, 

 we now assume that the electron re\ohes planetwise around the nu- 

 cleus describing a dosed orbit and radiating none of its energy as it re- 

 volves. A planet re\nj\is in an elliptical orbit; this elliptical orbit 

 may be a circle, or it may not i)e: but for the present paragraph we 

 will think of the circles onl\ . l.el us suppose, then, that the electron 

 may rexolve in a circle about the nucleus, without radiating its 

 energy and spiralling into the nucleus. Designate the radius of the 

 circle by ;•. With the electron revolving in a circle of radius r, the 

 energy of the atom is —e^l2r'. This value is obtained by adding 

 together the potential energy of the atom, which is —e"lr just as it 



' Ifanyrcaflerranalxilish these defects, a imilt it ude of chemists will lnnlad to hear 

 from him. Chemists want atom-models with stationary electrons. 



