When the light of frequency `2 v_(0)` (where `v_(0)` is threshold frequency), is incident on a metal plate, the maximum velocity of electrons emitted is `v_(1)`. When the frequency of the incident radiation is increased to `5 v_(0)`, the maximum velocity of electrons emitted from the same plate is `v_(2)`. the ratio of `v_(1)` to `v_(2)` is

Options

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

Answer

A

Explanation

According to the Einstein.s photoelectric equation
`E= W_(0)+1/2 ,mv^2`
when frequency of incident light `2upsilon_0`
`h(2upsilon_(0))+hupsilon_(0) +1/2 mv_(1)^(2) implies hupsilon_(0)=1/2 mv_(1)^(2)" "...(i)`
When frequency of incident light is `5upsilon_0`
`h(5upsilon_0)`
`h(5upsilon_0) = hupsilon_0+1/2 mv_2^2 implies 4upsilon_0 =1/2 mv_2^2 " "...(ii)`
Dividing (i) by (ii) , `1/4 =v_1^2/v_2^2 " or " v_1/v_2=1/2`