Einstein’s photoelectric equation :

hv = Φ + \(\cfrac12\)mv²_max....(1)

where h ≡ Planck’s constant, v ≡ frequency of the electromagnetic radiation, hv ≡ energy of the photon incident on a metal surface, Φ ≡ photo-electric work function, i.e., the minimum energy of light quantum required to liberate an electron from the metal surface, v and –  \(\cfrac12\)mv²_max ≡ the maximum speed and maximum kinetic energy of the photoelectrons at the time of emission. Φ = hv₀, where v₀ is the threshold frequency for the metal.

Explanation of the characteristics of photoelectric effect:

(1) From the above equation we find that for photoejection, hv ≥ Φ. That is, hv_min = hv₀ must be equal to Φ. Hence, photoelectric effect is observed only if hv ≥ hv₀ , i.e., v ≥ v .

This shows the existence of a threshold frequency v₀ for which photoelectrons are just liberated from a metal surface (with zero kinetic energy). Since different metals differ in electronic configuration, the work function hv and, therefore, frequency v are different and characteristic of different metals.

(2) In this particle model of light,’ intensity of incident radiation’ stands for the number of photons incident on a metal 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, the time rate of photoejection and hence photoelectric current increases linearly with the intensity of the incident radiation (v ≥ v₀).

(3) From Eq. (1), \(\cfrac12\)mv²_max , = hv – Φ= h(v – v ) This shows that the maximum kinetic energy in-creases linearly with the frequency v of the incident photon (v ≥ v₀) and does not depend on the time rate at which photons are incident on a metal surface.

(4) As the incident energy is concentrated in the form of a photon, and not spread over a wavefront, it is expected that an electron is emitted from the metal surface as soon as a photon (v ≥ v₀) is absorbed. This is in agreement with the experimental observation.

[Note : The frequency v that appears in the formula E = hv is the frequency of the oscillating electric field / magnetic field in the electromagnetic wave. ]