PHOTONS AND ELECTRONS 17 



known collectively as "excited states." The values of hc/\i for such a 

 gas are then the energy values of these excited states reckoned from 

 a common zero of energy, viz., the energy of the normal state. If we 

 measure the lines of the absorption spectrum of such a gas, we are at the 

 same time determining the energy values of various states of the atoms 

 all reckoned from this common zero. 



What happens if a photon meets an atom which has already been 

 transferred into an excited state by absorbing a previous photon? Usu- 

 ally this is not a likely occurrence, as an excited atom usually reverts 

 to the normal state within an exceedingly short time, of the order of 10"^ 

 sec. It can, however, be made to occur sufficiently often to be observed, 

 by using a very intense beam of light and a not too rarefied gas. More- 

 over, atoms in excited states — "excited atoms" — can be made relatively 

 abundant in a gas by instigating an electrical discharge in it (a glow or an 

 arc), or even in some cases merely by heating it. It turns out (as can 

 be easily foreseen) that for every excited state there is a new absorption 

 spectrum, with new values of Xi such that the products hc/\i give the 

 energy values of other states reckoned from the energy of that state as 

 zero. The absorption spectrum of a gas full of excited atoms can thus 

 be extremely intricate (as the emission spectrum actually is), and it was 

 on this account that in the previous paragraph I specified a "cool, rarefied, 

 and unexcited gas." 



Reverting to such a gas: in the simplest cases the absorption fines 

 form a converging sequence or "series" in which every line is closer to 

 its neighbor of higher frequency than to its neighbor of lower frequency, 

 and the gap between consecutive lines approaches zero as the frequency 

 rises, so that there is a "convergence frequency" or "limit frequency." 

 The most famous series is a certain series of monatomic hydrogen, of 

 which the frequencies of the various lines are obtained by assigning the 

 values of the integers (from 3 upward) to the symbol n in the equation 



" = '^(1-^) » = 3, 4, 5 • • • (/«) 



where R stands for a certain constant. This series is named after Balmer 

 who discovered the formula (not the series). His formula implies an 

 infinite number of lines, converging upon the limit frequency v^-,^ = R/4. 

 Actually, we observe, of course, a finite number of lines (about 50), each 

 of them fainter than the next lower, and the highest of them merging 

 into a broad haze or "continuum." Only a few other series conform to 

 algebraic expressions as simple as Balmer's, but there are many of which 

 the lines can be fitted by formulas of the same general type, implying 

 an infinite sequence of converging lines of which we observe only the 

 first few dozen (or sometimes only the first few) as discrete lines, while 



