The threshold frequency of a metal is `f_0`. When the light of frequency `2f_0` is incident on the metal plate, the maximum velocity of electrons emitted is `v_1`. When the frequency of the incident radiation is increased to `5f_0`, the maximum velocity of electrons emitted is `v_2`. Find the ratio of `v_1 and v_2`.

Options

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

Answer

B

Explanation

We have expression for maximum kinetic energy of photon as
`(1)/(2) mv_(max)^(2) = hv - W = hv - hv_(0)`
In cae I :
`(1)/(2) mv_(1)^(2) = h. 2v_(0) - hv_(0) = hv_(0)` ….. (i)
In case II :
`(1)/(2) mv_(2)^(2) = h . 5 v_(0) - hv_(0) = 4 hv_(0)` ...... (ii)
From (i) & (ii) `(v_(1)^(2))/(v_(2)^(2)) = (1)/(4)` or `(v_(1))/(v_(2)) = (1)/(2)`