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JEE Main 2023 (11 Apr, Shift 1) · Photoelectric Effect: Einstein's Equation

Photoelectric Effect: Einstein's Equation question from JEE Main 2023 (11 Apr, Shift 1)

Q83JEE Main 2023 · 11 APR · SHIFT 1Medium

Photoelectric Effect: Einstein's Equation

A metallic surface is illuminated with radiation of wavelength $\lambda$ , the stopping potential is $V_0$ . If the same surface is illuminated with radiation of wavelength $2\lambda$ . the stopping potential becomes $\frac{V_0}{4}$ . The threshold wavelength for this metallic surface will be

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Answer: (a)

Einstein: $\frac{hc}{\lambda} = \phi + eV_s$ ; write $A = \frac{hc}{\lambda}$ .
$A - \phi = eV_0$ and $\frac{A}{2} - \phi = \frac{eV_0}{4}$
$A - \phi = 2A - 4\phi \Rightarrow \phi = \frac{A}{3}$
$\lambda_0 = 3\lambda$
So the answer is (a) $3\lambda$ .

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