What two main observations in photoelectricity led Einstein to suggest the photon theory for the interaction of light with the free electrons in metal? Obtain an expression for threshold frequency for photoelectric emission in terms of the work function of the metal.

Solution

The two main observations are:

(i) The maximum kinetic energy of emitted photoelectron is independent of intensity of light.

(ii) For each photoelectron, there must be a threshold frequency of incident light below which no emission takes place.

For a metal of work function ɸ, the kinetic energy of photoelectron emitted due to falling of photon of frequency v is,
$\frac{1}{2} {mv}^{2}_{\max} = hv - ϕ = hv - {hv}_{0}$

where $v_{0}$ is the threshold frequency.

For photoelectric emission,

$v_{\max} = 0$

$∴$ $hv = {hv}_{0} = ϕ$

or $v_{0} = \frac{ϕ}{h} .$
gives us the relationship between threshold frequency and work function of the metal.

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Wave Optics

What two main observations in photoelectricity led Einstein to suggest the photon theory for the interaction of light with the free electrons in metal? Obtain an expression for threshold frequency for photoelectric emission in terms of the work function of the metal.

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