Radiation 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 photo electrons emitted in the two cases will be

A
1 :2
B
2 :1
C
1 :4
D
4 :1

Solution:

Here we have
$2 W_{0} - W_{0} = \frac{1}{2} {mv}_{1}^{2}$
and $5 W_{0} - W_{0} = \frac{1}{2} {mv}_{2}^{2}$
Dividing eq .(1) by eq . (2) we get
$\frac{2 W_{0} - W_{0}}{5 W_{0} - W_{0}} = \frac{v_{1}^{2}}{v_{2}^{2}} or \frac{v_{1}}{v_{2}} = \frac{1}{2}$

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