When the light of frequency `2v_0` (where `v_0` is threshold frequency), is incident on a metal plate, then the maximum velocity of electrons emitted is `v_1.` When the frequency of the incident radiation is increased to `5v_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

From Einstein’s equation of Photoelectric effect,
`1/2mv_1^2=2hv_0-hv_0 " or " 1/2 mv_1^2 =hv_0" "...(i)`
`1/2mv_2^2=5hv_0-hv_0 " or " 1/2 mv_2^2 =4hv_0" "...(ii)`
By eq, (i) `div` (ii)
`v_1/v_2 =sqrt(1/4) =1/2`