A photosensitive metallic surface has work function , `h v_(0)`. If photons of enegy ` 2hv_(0)` fall on this surface , the electrons come out with a maximum velocity of `4 xx 10^(6) m//s`. When the velocity of photoelectrons will be

Options

A. ` 2 xx 10^(6) m//s`
B. ` 2 xx 10^(7) m//s`
C. ` 8 xx 10^(5) m//s`
D. ` 8 xx 10^(6) m//s`

Answer

D

Explanation

Einstein's photoelectric equation can be written as
`(1)/(2) mv^(2) = hv - phi`
`rArr (1)/(2) m xx ( 4 xx 10^(6))^(2) = 2hv_(0) - hv_(0)` …..(i)
and `(1)/(2) m xx v^(2) = 5hv_(0) - hv_(0)` …..(ii)
Dividing Eq. (ii) by (i) , we get `(v^(2))/((4 xx 10^(6))^(2)) = ( 4hv_(0))/(hv_(0))`
`rArr v^(2) = 4 xx 16 xx 10^(12) rArr v^(2) = 64 xx 10^(12)`
`rArr = v xx 10^(6) m//s`