When light incident on a metal has energy less than the work function of the metal, then no electron is emiited from the surface of the metal. Mathematically justify this statement.

Explanation

Einstein's photoelectric equation
`(1)/(2) mv_("max")^(2) = hf - W_(0)` [`W_(0)` = work function]
If `hf lt W_(0)`, the maximum kinetic energy of electron `((1)/(2) mv_("max")^(2))` is negative and so `v_("max")^(2)` is negative. But the magnitude of the square of a physical quantity cannnot be negative. Hence photoelectrons are not emitted for the surface of the metal.