Question

When a certain metallic surface is illuminated with mono-chromatic light of wave length $\lambda$, the stopping potential for photo electric current is $6V_0$. When the same surface is illuminated with light of wave length $2\lambda$, the stopping potential is $2V_0$. The threshold wavelength of this surface for photoelectric effect is :

• A. $6\lambda$
• B. $4\lambda /3$
• C. $4\lambda$
• D. $8\lambda$

Answer 1

The correct option is C $4\lambda$

$K_{max}=\frac{hc}{\lambda }-\frac{hc}{{\lambda }_0}$ or $e{V}_0=\frac{hc}{\lambda }-\frac{hc}{{\lambda }_0}$
$\frac{hc}{\lambda }-\frac{hc}{{\lambda }_0}=6e{V}_0...\left(i\right)$
$\frac{hc}{2\lambda }-\frac{hc}{{\lambda }_0}=2e{V}_0...\left(iii\right)$
Dividing (i) and (ii), we get
$\frac{hc}{\lambda }-\frac{hc}{{\lambda }_0}=\frac{3hc}{2\lambda }-\frac{3hc}{{\lambda }_0}$ or $\frac{3}{2\lambda }-\frac{1}{\lambda }=\frac{3}{{\lambda }_0}-\frac{1}{{\lambda }_0}$
or $\frac{1}{2\lambda }=\frac{2}{{\lambda }_0}$ or ${\lambda }_0=4\lambda$