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

Answer

C

Explanation

From Einstein equation
`2 hv_(0) = h v_(0) + (1)/(2) mv_(1)^(2)`
`2h v_(0) = m v_(1)^(2)` …….(1)
If frequency is increased to `5 v_(0)` then
`5h v_(0) = h v_(0) + (1)/(2) m v_(2)^(2)`
`4 h v_(0) = (1)/(2) m v_(2)^(2) rArr 8 h v_(0) = m v_(2)^(2)` ..........(2)
From Eqs. (1) and (2)
`(2h v_(0))/(8 h v_(0)) = (m v_(1)^(2))/(m v_(2)^(2)) rArr (v_(1))/(v_(2)) = (1)/(2)`