Question

When a centimeter thick surface is illuminated with light of wavelength $\lambda$, the stopping potential is V. When the same surface is illuminated by light of wavelength $2\lambda$, the stopping potential is V/3. Threshold wavelength for the metallic surface is:

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

Answer 1

The correct option is B $4\lambda$

The Einstein's equation for photoelectric effect is given by , $e{V}_0=\frac{hc}{\lambda }-\frac{hc}{{\lambda }_0}$ where $e=$ charge of electron, $h=$ Planck's constant, $V_0=$ stopping potential , $c=$ velocity of light, $\lambda =$ wavelength of incident light and ${\lambda }_0=$ threshold wavelength.

When $V_0=V\Rightarrow eV=\frac{hc}{\lambda }-\frac{hc}{{\lambda }_0}..\left(1\right)$

and when $V_0=V/3\Rightarrow e\left(V/3\right)=\frac{hc}{2\lambda }-\frac{hc}{{\lambda }_0}...\left(2\right)$

From (1) and (2), $\frac{hc}{3\lambda }-\frac{hc}{3{\lambda }_0}=\frac{hc}{2\lambda }-\frac{hc}{{\lambda }_0}$

or $\frac{2}{3{\lambda }_0}=\frac{1}{6\lambda }$

or ${\lambda }_0=4\lambda$