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Q.
If in a photoelectric cell, the wavelength of incident light is changed from $4000 \mathring{A}$ to $3000 \mathring{A}$ then change in stopping potential will be
JIPMERJIPMER 2015Dual Nature of Radiation and Matter
Solution:
The Einstein's equation for photoelectric effect is given $by eV _{0}=\frac{ hc }{\lambda}- W$ 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, $e V_{01}=\frac{h c}{\lambda_{1}}-W \ldots(1)$ and $e V_{02}=\frac{h c}{\lambda_{2}}-W \ldots(2)$
From $(1)$ and $(2), e V_{02}=\frac{h c}{\lambda_{2}}+e V_{01}-\frac{h c}{\lambda_{1}}$
$eV _{02}- eV _{01}=\frac{ h c }{\lambda_{2}}-\frac{ hc }{\lambda_{1}}$
$V _{02}- V _{01}=( h c / e )\left[ 1 / \lambda_{2}- 1 / \lambda_{1}\right]=\frac{6.62 \times 10^{-34} \times 3 \times 10}{1.6 \times 10^{-19}}\left[\frac{1}{ 3 0 0 0 \times 1 0 ^{- 1 0 }}-\right.$
$\left.\frac{1}{4000 \times 10^{-10}}\right]=1.04 V$