Question

A light of wavelength $\lambda =320nm$ is incident on a metal surface of threshold frequency ${\lambda }_0=496nm$ which is connected to a photocurrent circuit. What is the minimum potential $V_0$ required to stop the photocurrent?

Answer 1

Energy of a light wave of wavelength $\lambda$ (in $nm$) is given by:

$E=\frac{1240}{\lambda \left(nm\right)}$ in $eV$

There hold wavelength of metal $\left({\lambda }_0\right)=496nm$

So, work function $W_o=\frac{1240}{{\lambda }_0}=\frac{1240}{496}=2.5eV$

and, energy of incident light

$E=\frac{1240}{\lambda }=\frac{1240}{320}=3.88eV$

From Einstein's phoroelectric equation

$KE=E-W_o$

$=3.88-2.5$

$\Rightarrow KE=1.38eV$

Now, value of $KE$ is numerically equal to stopping potential $\left(v_0\right)$

Thus , $v_o-1.38V$