At an incident radiation frequency of `v_(1)`, which is greater than the threshold frequency, the stopping potential for a certain metal is `V_(1)`. At frequency `2v_(1)`, the stopping potential is `3V_(1)`. If the stopping potential at frequency `4v_(1)` is `nV_(1)` then n is

Options

A. 2
B. 3
C. 6
D. 7

Answer

D

Explanation

Photoelectric effect, `hv=hv_(0)+eV` (Einstein's equation)
`implies" "V=(h)/( e )(v-v_(0))`
Given, `V_(1)=(h)/(e)(v_(1)-v_(0))" and "3V_(1)=(h)/(e)(2v_(1)-v_(0))`
`implies" "(3V_(1))/(V_(1))=(2v_(1)-v_(0))/(v_(1)-v_(0))impliesv_(1)=2v_(0)`
`:." "V_(1)=(h)/(e)(2v_(0)-v_(0))=(h)/(e)v_(0)`
At frequency `4v_(1),nV_(1)=(h)/(e)(4v_(1)-v_(0))`
`=(h)/(e)(8v_(0)-v_(0))=7xx(h)/(e)v_(0)`
`implies" "nV_(1)=7V_(1)impliesn=7`