A metal plate is exposed to light with wavelength `lambda`. It is observed that electrons are ejected from the surface of the metal plate. When a retarding uniform electric field E is imposed, no electron can move away from the plate farther than a certain distance d. Then the threshold wavelength `lambda_(0)` for the material of plate is ( e is the electronic charge, h is Planck's constant and c is the speed of light)

Options

A. `lambda_(0)=(1/lambda-(hc)/(eEd))^(-1)`
B. `lambda_(0)=(1/lambda-(eEd)/(hc))^(-1)`
C. `lambda_(0)=lambda_(0)-(hc)/(eEd)`
D. `lambda_(0)=lambda_(0)-(eEd)/(hc)`

Answer

B

Explanation

The maximum kinetic energy of the electrons immediately upon ejection is the difference between the energy of the incident photon and the threshold energy.`K=(hc)/lambda-(hc)/lambda_(0)`,This kinetic energy of ejected electron is converted to electrostatic potential energy,`DU=eEd`, as electrons come to rest while moving in the direction of electic field. Therefore,`K=Eed` and `1_(0)=(1/lambda-(eEd)/(hc))^(-1)`