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JEE Main 2021 (26 Feb, Shift 2) · Photoelectric Effect: Einstein's Equation

Photoelectric Effect: Einstein's Equation question from JEE Main 2021 (26 Feb, Shift 2)

Q103JEE Main 2021 · 26 FEB · SHIFT 2Easy

Photoelectric Effect: Einstein's Equation

Two streams of photons, possessing energies equal to twice and ten times the work function of metal are incident on the metal surface successively. The value of ratio of maximum velocities of the photoelectrons emitted in the two respective cases is x: y. The value of x is ___________.

Numerical answer type. Work it out, then open the answer.

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Answer: 1

$\frac{1}{2}mv_{max}^2 = E - \phi$ , so $v_{max} \propto \sqrt{E - \phi}$ .
$K_1 = 2\phi - \phi = \phi$ , $K_2 = 10\phi - \phi = 9\phi$
$\frac{v_1}{v_2} = \sqrt{\frac{1}{9}} = \frac{1}{3}$ , so $x:y = 1:3$
So $x = 1$ .

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