Question

A metal plate is exposed to light with wavelength $\lambda$. It is observed that electrons are ejected from the surface of the 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)

• A. ${\lambda }_0={(\frac{1}{\lambda }-\frac{hc}{eEd})}^{-1}$
• B. ${\lambda }_0={(\frac{1}{\lambda }-\frac{eEd}{hc})}^{-1}$
• C. ${\lambda }_0=\lambda -\frac{hc}{eEd}$
• D. ${\lambda }_0=\lambda -\frac{eEd}{hc}$

Answer 1

The correct option is B ${\lambda }_0={(\frac{1}{\lambda }-\frac{eEd}{hc})}^{-1}$

The maximum kinetic energy of the electrons immediately upon ejection is the difference between the energy of the incident photon and the threshold energy.

$K=\frac{hc}{\lambda }-\frac{hc}{{\lambda }_0}$
This kinetic energy of ejected electron is converted to electrostatic potential energy.

$\Delta U=eEd$, as electrons come to rest while moving in the direction of electric field.

Therefore, $K=Eed$
and ${\lambda }_0={(\frac{1}{\lambda }-\frac{eEd}{hc})}^{-1}$