Einstein's photoelectric equation is Ek = hv -W for a single photon ejecting a single electron.
(i) Explanation of frequency law: When frequency of incident photon (v), increases, the kinetic energy of emitted electron increases. Intensity has no effect on kinetic energy of photoelectrons.
(ii) Explanation of intensity law: When intensity of incident light increases, the number of incident photons increases, as one photon ejects one electron; the increase in intensity will increase the number of ejected electrons. In other words, photocurrent will increase with increase of intensity. Frequency has no effect on photocurrent.
(iii) Explanation of no time lag law: When the energy of incident photon is greater than work function, the photoelectron is immediately ejected. Thus there is no time lag between incidence of light and emission of photoelectrons.