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JEE Main 2021 (25 Jul, Shift 2) · Photoelectric Effect: Einstein's Equation

Photoelectric Effect: Einstein's Equation question from JEE Main 2021 (25 Jul, Shift 2)

Q109JEE Main 2021 · 25 JUL · SHIFT 2Medium

Photoelectric Effect: Einstein's Equation

When radiation of wavelength $\lambda$ is incident on a metallic surface, the stopping potential of ejected photoelectrons is 4.8 V. If the same surface is illuminated by radiation of double the previous wavelength, then the stopping potential becomes 1.6 V. The threshold wavelength of the metal is:

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Answer: (b)

$A - \phi = 4.8\text{ eV}$ and $\frac{A}{2} - \phi = 1.6\text{ eV}$ , with $A = \frac{hc}{\lambda}$
Subtract: $\frac{A}{2} = 3.2 \Rightarrow A = 6.4\text{ eV},\ \phi = 1.6\text{ eV}$
$\lambda_0 = \frac{hc}{\phi} = \frac{6.4}{1.6}\lambda = 4\lambda$
So the answer is (b) $4\lambda$ .

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