The energy associated with an incident photon (E) must equal the sum of its kinetic energy and the work function (W0) of the radiation, according to the rule of conservation of energy.
E = W0 + K.E
⇒ W0 = E – K.E
Energy of incident photon (E)=$ \frac{hc}{\lambda}$
Where,
c denotes the velocity of the radiation
h is Planck’s constant
λ is the wavelength of the radiation
Substituting these values in the expression for E:
$E=\frac{(6.626\times 10^{-34}Js)(3\times 10^{8}ms^{-1})}{(256.7\times 10^{-9}m)}=7.744\times 10^{-19}\, J$
$=\frac{7.744\times 10^{-19}}{1.602\times 10^{-19}}eV$
$ E=4.83\,$
The potential that is applied to the silver is transformed into the kinetic energy (K.E) of the photoelectron.
Hence,
K.E = 0.35 V
K.E = 0.35 eV
Therefore, Work function, W0 = E – K.E
= 4.83 eV – 0.35 eV
= 4.48 eV