Two radiations containing photons of energy twice and five times the work function of a metal are incident successively on the metal surface. The ratio of the maximum velocities of the emitted electrons in the two cases will be

Options

A. `1:3`
B. `1:4`
C. `1:2`
D. `1:1`

Answer

C

Explanation

`2phi_(0)=phi_(0)+(1)/(2)mv_(1)^(2)`
Then `phi_(0)=(1)/(2) mv_(1)^(2)`
Also `5phi_(0)=phi_(0)+(1)/(2) mv_(2)^(2)`
`:. 4phi_(0)=(1)/(2) mv_(2)^(2)`
so `(v_(1)^(2))/(v_(2)^(2))=(phi_(0))/(4phi_(0))=(1)/(4) rArr (V_(1))/(v_(2))=(1)/(2)`