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Photoelectric Effect: Einstein's Equation question from NEET 2018

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Photoelectric Effect: Einstein's Equation

When the light of frequency 2 $v_0$ (where $v_0$ is threshold frequency), is incident on a metal plate, the maximum velocity of electrons emitted is v1. When the frequency of the incident radiation is increased to 5 $v_0$ , the maximum velocity of electrons emitted from the same plate is v2. The ratio of v1 to v2 is

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Answer: (a)

$\frac{1}{2}mv^2 = h\nu - h\nu_0$
At $2\nu_0$ : $K_1 = h\nu_0$ ; at $5\nu_0$ : $K_2 = 4h\nu_0$
$\frac{v_1}{v_2} = \sqrt{\frac{1}{4}} = \frac{1}{2}$
So the answer is (a) 1 : 2.

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