Radiation two photons having energies twice and five times the work function of a metal are incident successively on the metal surface. The ratio of the maximum velocity of photoelectrons emitted in the two cases will be

Options

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

Answer

B

Explanation

`E-W_(0)=(1)/(2)mv^(2)`
Case I `2W_(0)-W_(0)=(1)/(2)mv_(1)^(2)` . . (i)
Case II `5W_(0)-W_(0)=(1)/(2)mv_(2)^(2)` . .. (ii)
Therefore, from Eqs. (i) and (ii) we get
`(1W_(0)-W_(0))/(5W_(0)-W_(0))=(v_(1)^(2))/(v_(2)^(2)) or (v_(1))/(v_(2))=(1)/(2)`.