When a metallic surface is illuminated with radiation of wavelength… | MHT CET 2026 (19 May, Shift 2)

Q11MHT CET 2026 · 19 MAY · SHIFT 2Medium

Photoelectric Effect: Einstein's Equation

When a metallic surface is illuminated with radiation of wavelength $\lambda$ , the stopping potential is $V$ . If the surface is now illuminated with a radiation of wavelength $4\lambda$ , the stopping potential $\left(\frac{V}{8}\right)$ . The threshold wavelength for the surface is

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Answer: (d)

$\frac{hc}{\lambda} - \phi = eV$ and $\frac{hc}{4\lambda} - \phi = \frac{eV}{8}$
Multiply the second by 8: $\frac{2hc}{\lambda} - 8\phi = eV$
Equate: $\frac{hc}{\lambda} - \phi = \frac{2hc}{\lambda} - 8\phi \Rightarrow 7\phi = \frac{hc}{\lambda}$
$\lambda_0 = \frac{hc}{\phi} = 7\lambda$ . So the answer is (d) $7\lambda$ .

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