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Physics Question on Dual nature of radiation and matter

Two streams of photons, possessing energies equal to five and ten times the work function of metal are incident on the metal surface successively. The ratio of maximum velocities of the photoelectron emitted, in the two cases respectively, will be

A

1 : 2

B

1:3

C

2 : 3

D

3 : 2

Answer

2 : 3

Explanation

Solution

12mv12=E−ϕ=5ϕ−ϕ=4ϕ\frac{1}{2}mv_1^2=E-ϕ=5ϕ-ϕ=4ϕ

12mv22=E′−ϕ=10ϕ−ϕ=9ϕ\frac{1}{2}mv_2^2=E'-ϕ=10ϕ-ϕ=9ϕ

v1v2=23\frac{v_1}{v_2}=\frac{2}{3}