The maximum velocity of electrons emitted from a metal surface is v. What would be the maximum velocity if the frequency of incident lightis increased by a factor of 4?

Options

A. 2v
B. more than 2v
C. less than 2v
D. between v and 1.5 v

Answer

B

Explanation

Since there is photoemission, `v gt` threshold frequency `(v_(0))` and the maximum velocity of the emitted photoelectrons is given by using
`hv=hv_(0)+1/2 mv_(m)^(2)`
`v=sqrt((2h(v-v_(0)))/(m)) " " ( :'v=v_(m)"given")` ...(1)
When v is increased to 4v, then maximum velocity
`v'=sqrt((2h(4v-v_(0)))/(m))=sqrt((8h(v-(v_(0))/(4)))/(m))`
`v'=2sqrt((2h(v-(v_(0))/(4)))/(m))` ...(2)
`:.` from (1) and (2), `v' gt 2v`.