When a given photosensitive material is irradiated with light of frequency `nu`, and maximum speed of the emitted photoelectrons equals `v_(max)`. The square of `v_(max)`is observed to very with `v`, as per the graph shown in fig. Obtain expression for (i) Planck's constant and (ii) the work function of the given photosensitive material, in terms of the parameter `l`, `n` and the mass `m` of the electrons.

Explanation

(a) By Einstein.s photoelectric equation we have
`K_(max)=1/2mv_(max)^2=hv-phi_0`
or `v_(max)^2=((2h)/m)v-(2phi_0)/m`
Slope of the graph `=(2h)/m=l/n`
(b) The intercept on `v_(max)^2` axis is `(2phi_0)/m=l`
Therefore , work function `phi_0=(ml)/2`
(c) Threshold frequency is the intercept on v axis i.e.