For given metal plate threshold frequency is `V_(0)`. When radiation of `2V_(0)` is incident on metal surface ,maximum velocity of photoelectron emitted is `V_(1)` when frequency of incident radiation is charged to `5V_(0)` ,maximum velocity of photoelectron emitted is `v_(2)`.Ration of `v_(1)` and `v_(2)` is .....

Options

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

Answer

B

Explanation

From Einstein equation
`(1)/(2)mv_(1)^(2)=h(2v_(0))-hv_(0)`
`therefore (1)/(2)mv_(1)^(2)=hv_(0)`…..(1)
and `(1)/(2)mv_(1)^(2)=h(5v_(0))-hv_(0)`
`(1)/(2)mv_(2)^(2)=4hv_(0)`……..(2)
`therefore` Taking ratio of (1) and (2) ,
`((v_(1)^(2))/(v_(2)^(2)))=(1)/(4)`
`therefore (V_(1))/(v_(2))=sqrt((1)/(4))=(1)/(2)`
`therefore` Ratio of `v_(1)` and `v_(2)` is 1:2