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  4. When a metallic surface is illuminated with radiation of wavelength λ , the stopping potential is V. If the same surface is illuminated with radiation of wavelength 2 λ, the stopping potential is (V/4) . The threshold wavelength for the metallic surface is :

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Q. When a metallic surface is illuminated with radiation of wavelength $\lambda$ , the stopping potential is V. If the same surface is illuminated with radiation of wavelength $2 \lambda$, the stopping potential is $\frac{V}{4}$ . The threshold wavelength for the metallic surface is :

NEETNEET 2016Dual Nature of Radiation and Matter

Solution:

$eV = \frac{hc}{\lambda} - \frac{hc}{\lambda_0}$ ....(i)
$eV/4 = \frac{hc}{2 \lambda} - \frac{hc}{\lambda_0} $ .....(ii)
From equation (i) and (ii)
$\Rightarrow 4 = \frac{\frac{1}{\lambda} - \frac{1}{\lambda_{0}}}{\frac{1}{2\lambda} - \frac{1}{\lambda_{0}}} $ On solving $ \lambda_{0} = 3 \lambda $