Einstein's photoelectric equation: `hv=phi +1/2mv_(max)^2 ...(1)`
where `hv-=` Planck's constant, hv `equiv`energy of the photon, i. e., electromagnetic wavepacket of frequency v, incident on a metal surface, `phi equiv` photoelectric work function, ie, the minimum energy of quantum required to liberate an electron from the metal surface, `v_(max)` and `1/2mv_(max)^(2)equiv` the maximum speed and maximum kinetic energy of the photoelectron.`phi =hv_(0)` ,where `v_(0)` is the threshold frequency for the metal.
Explanation : (1) From the above equation we find that for photoejection, `h le phi `. That is- `hv_(min)`, must be equal to d. Hence, photoelectric effect will be observed only if `hv ge hv_(0)` or v ge `v_(0)`. This shows the existence of a threshold frequency v, for which photoelectrons will be just liberated, i.e., with zero kinetic energy from a metal surface. Since different metals differ structurally, the work function hv, and, therefore, frequency v. are different and characteristic of different metals.
(2) In this particle view of light, 'intensity of radiation' stands for the number of incident photons per unit surface area per unit time. As the number of photons incident on a metal per unit surface area per unit time increases, there is a greater likelihood of a photon being absorbed by any electron, Therefore, photoejection and hence photoelectric current increases linearly with the intensity of radiation (v ` ge V _ 0 ` ).
(3) From Eq. (1), `1/2mv_(max)^(2)`=h(v-v_(0))`. This shows that the maximum kinetic energy increases linearly with the frequency v of the incident photon `(v ge v_(0))` and does not depend on the rate at which photons are incident on a metal surface.
