In photoelectric effect, stopping potential for a light of frequency `n_(1)` is `V_(1)`. If light is replaced by another having a frequency `n_(2)` then its stopping potential will be

Options

A. `V_(1)-h/e (n_(2)-n_(1))`
B. `V_(1)+h/e (n_(2)+n_(1))`
C. `V_(1)+h/e (n_(2)-2n_(1))`
D. `V_(1)+h/e (n_(2)-n_(1))`

Answer

D

Explanation

`hv=W_(0)+1/2 mv^(2)=W_(0)+eV_(0)`
`:.W_(0)=hv-eV_(0)`
Thus, `W_(0)=hv_(1)-eV_(1)` and `W_(0)=hv_(2)-eV_(2)`
(For the same metal, work function `W_(0)` is the same.)
`:.hv_(1)-eV_(1)=hv_(2)-eV_(2)`
`:.eV_(2)=h(v_(2)-v_(1))+eV_(1)`
`:.V_(2)=(h(v_(2)-v_(1)))/(e)+V_(1)`
or `V_(2)=(h(n_(2)-n_(1)))/(e)+V_(1)" "` (Using `n_(1)` and `n_(2)` for `v_(1)` and `v_(2)` .)