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  4. Radiations of two photon energies twice and five times the work function of metal are incident successively on the metal surface. The ratio of the maximum velocity of the photoelectrons emitted in the two cases will be

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Q. Radiations of two photon energies twice and five times the work function of metal are incident successively on the metal surface. The ratio of the maximum velocity of the photoelectrons emitted in the two cases will be

ManipalManipal 1980Dual Nature of Radiation and Matter

Solution:

$ E - W_0 = \frac{ 1}{2} mv^2 $
First case, $ 2 W_0 = W_0 = \frac{ 1}{2} mv_1^2 $ ..(i)
Second case, $ 5 W_0 - W_0 = \frac{ 1}{2} mv_2^2 $ ..(ii)
Therefore, from Eqs. (i) and (ii),
$ \frac{ 2 W_0 - W_0 }{ 5 W_0 - W_0 } = \frac{ v_1^2 }{ v_2^2 } $ or $ \frac{ v_1 }{ v_2 } = \frac{ 1}{2} $