Threshold frequency for a certain metal is `v_0`. When light of frequency `2v_0` is incident on it, the maximum velocity of photoelectrons is `4xx10^8 cm s^-1`. If frequency of incident radiation is increased to `5v_0`, then the maximum velocity of photoelectrons, in cm `s^-1`, will be

Options

A. `(4)/(5)xx10^8`
B. `2xx10^8`
C. `8xx10^8`
D. `20xx10^8`

Answer

C

Explanation

Einstein's equation for photoelectric effect is
`hv-hv_0=(1)/(2)mv_max^2`
when `v=2v_0`,`v_(max)=4xx10^8cms^-1`
`2hv_0-hv_0=((1)/(2))m(4xx10^8)^2`
`hv_0=(1)/(2)m(4xx10^8)^2` When `v=5v_0`,`v_(max)=v'`
`h(5v_0)-hv_0=(1)/(2)mv^2`
Dividing Eq. (ii) by Eq. (i), we get
`v'=8xx10^8cms^-1`