When a certain metallic surface is illuminated with monochromatic light of wavelength `lamda`, the stopping potential for photoelectric current is `3V_0` and when the same surface is illuminated with light of wavelength `2lamda`, the stopping potential is `V_0`. The threshold wavelength of this surface for photoelectric effect is

Options

A. `4lambda//3`
B. `4lambda`
C. `6lambda`
D. `8lambda`

Answer

b

Explanation

Case (i), `e3V_(0)=(hc)/lambda-phi_(0)............(i)`
Case (ii), `eV_(0)=(hc)/(2lambda)-phi_(0)...........(ii)`
From (i) and (ii) we get,
`(3hc)/(2lambda)-3phi_(0)=(hc)/lambda-phi_(0)`
or `(3hlambda)/(2lambda)-(hc)/lambda=3phi_(0)-phi_(0)`
or `(hc)/(2lambda)=2phi_(0) or phi_(0)=(hc)/(4lambda)`
`:.` Threshold wavelength
`lambda_(0)=(hc)/(phi_(0))=(hc)/(hc)xx4lambda=4lambda`