A photosenstive metallic surface has work function `hv_(0)`. If photons of energy `3hv_(0)` falls on this surface. The electrons come out with a maximum velocity of `5xx10^(6)m//s`. When the photon energy is increased to `9hv_(0)`. The maximum velocity of photoelectrons will be:

Options

A. `10^(7)m//s`
B. `8xx10^(5)m//s`
C. `10^(9)m//s`
D. `10^(8)m//s`

Answer

a

Explanation

As `E=phi_(0)+1/2mv^(2) :. 3hv_(0)=hv_(0)+1/2mv^(2)`
or `2hv_(0)=1/2mv^(2)`......(i)
and `9hv_(0)=hv_(0)+1/2mv^(2)`
or `8hv_(0)=1/2mv'^(2)`.........(ii)
Dividing (i) and (ii)
`1/4=(v^(2))/(v'^(2)) or v'^(2)=4v^(2) or v'=2v`
`v'=2xx5xx10^(6)m//s=10xx10^(6)m//s=10^(7) m//s`