Question

A light source of wavelength $\lambda$ illuminates a metal and ejects photo-electrons with $(K.E.{)}_{max}=1eV$
Another light source of wavelength $\frac{\lambda }{3},$ ejects photo-electrons from same metal with $(K.E.{)}_{max}=4eV$
Find the value of reciprocal of work function

Answer 1

$\frac{hc}{\lambda }=1+\varphi$ ...(1)
$3\times \frac{hc}{\lambda }=4+\varphi$ ...(2)
From equation (1) and (2),
$3(1+\varphi )=4+\varphi$
$3+3\varphi =4+\varphi$
$2\varphi =1$
$\varphi =\frac{1}{2}ev.$
$\varphi =0.5ev$
Reciprocal of wave function =$\frac{1}{\varphi }=\frac{2}{1}=2$