Question

In a photoelectric cell, the wavelength of incident light is changed from $4000\stackrel{o}{A}$ to $3000\stackrel{o}{A}$. The change in stopping potential will be :

• A. 0.14 V
• B. 0.24 V
• C. 0.35 V
• D. 1.04 V

Answer 1

The correct option is D 1.04 V

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

Here, $e{V}_{01}=\frac{hc}{{\lambda }_1}-W....\left(1\right)$ and $e{V}_{02}=\frac{hc}{{\lambda }_2}-W....\left(2\right)$

From (1) and (2), $e{V}_{02}=\frac{hc}{{\lambda }_2}+e{V}_{01}-\frac{hc}{{\lambda }_1}$

$e{V}_{02}-e{V}_{01}=\frac{hc}{{\lambda }_2}-\frac{hc}{{\lambda }_1}$

$V_{02}-V_{01}=\left(hc/e\right)[1/{\lambda }_2-1/{\lambda }_1]=\frac{6.62\times {10}^{-34}\times 3\times 10}{1.6\times {10}^{-19}}[\frac{1}{3000\times {10}^{-10}}-\frac{1}{4000\times {10}^{-10}}]=1.04V$