a. Every metal has a definite work function. Why all photoelectrons do not come out with the same energy of incident radiation in monochromatie ? Why there is an energy distribution of photoelectrons?
b. The energy and momentum of an electron are related to the frequency and wave-length of the associated matter wave by the relations,
`E=h upsilon, p=(h)/(lambda)`
But while the value of `lambda` is physically significant, the value of `upsilon` (and therefore the value of the phase speed `upsilon lambda` has no physical significance. Why?

Explanation

a. Work function is minimum amount of energy required for the electron in the topmost level of the conduction band to get out of the metal. All the electrons do not belong to this topmost level. Different electrons are knocked off from the metal from different levels, with different energy for the same incident radiation. Thus the emitted electrons occupy a continuous band of energy levels.
b. The absolute value of energy E (but not momentum, p) of any particle is arbitrary to within an additive constant. Hence absolute value of `.upsilon.` of a metter wave has no direct physical meaning, while `.lambda.` is physically significant. The phase speed `(upsilon lambda)` is physically insignificant, while group speed is physically significant.