PHOTONS AND ELECTRONS 13 



is found to vary thus from metal to metal. There are also many addi- 

 tional verifications of the assumptions (a), (h), and (d); but to analyze 

 them all would lead us much too far afield.^ 



It is obvious that if Ai has been determined once for all and A 2 has 

 been determined for a given metal by experiments with light of known 

 wave-lengths, the maximum kinetic energy of the electrons ejected 

 from that metal by light of unknown constitution will give us the photon 

 energy and hence the wave-length of the light if this is monochromatic 

 (or that of the shortest-wave constituent of the light, if it is a mixture of 

 various wave-lengths). A very similar method is used to ascertain the 

 photon energies of X-rays and gamma rays, especially when this is too 

 small to produce a measurable diffraction pattern with any available grat- 

 ing or other diffraction apparatus. We shall consider it later. 



UNITS OF WAVE-LENGTH, WAVE NUMBER, FREQUENCY, AND PHOTON 



ENERGY 



a. The ultimate unit of wave-length is, of course, the centimeter, but 

 various submultiples of this universal unit are of customary use in various 

 parts of the spectrum. These comprise: 



The "micron" (symbol p) equal to 10"'* cm., sometimes employed in 

 the extreme infra-red. 



The "millimicron" (symbol irifx, formerly jxtx) equal to 10"'^ cm., 

 occasionally employed in the infra-red, the visible, and the ultra-violet, 

 but not so common as the unit next mentioned. 



The " Angstrom" (symbol A or A) equal to 10~^ cm., usually employed 

 in the near infra-red, the visible, and the ultra-violet. 



The "X-unit" (symbol X) equal to 10~^^ cm., employed in the X-ray 

 and gamma-ray regions. 



h. "Wave number" is by definition the reciprocal of wave-length. 

 When a wave number is to be calculated from a wave-length, the latter 

 is generally expressed in centimeters, so that the customary unit of wave 

 number is the reciprocal centimeter (symbol cm."^). This is also the case 

 when the values of "terms" (page 22) are expressed in wave numbers. 



c. "Frequency" is by definition the product of wave number by c, 

 the speed of light in vacuo. The first factor is commonly expressed in 



* It was formerly thought that Wi of equation {10) is negHgibly small, but quantvmi 

 mechanics has taught us differently. Actually, the distribution in energy of the free 

 electrons inside of a metal does not have a perfectly sharp upper limit Wi except at 

 the absolute zero of temperature. At temperatures higher than 0°K., there are some 

 free electrons having energies greater than Wi, and consequently some photoelectrons 

 escaping with energies greater than the value of E^^^ which would be observed at 

 zero; the distribution in energy of these electrons agrees so well with that predicted 

 from the quantum-mechanical theory, as to afford extra proof of the fundamental 

 ideas. 



