Question

State Einstein's photoelectric equation. Explain 'two' characteristics on the basis of this equation.

Answer 1

Einstein's photoelectric equation is $h\nu =\varphi +E_k$

where $h$ is Planck's constant, $\nu$ is frequency of electro magnetic radiation, $h\nu$$\to$ energy of photon incident on metal surface, $\varphi$ is the work function and $E_k$ is the maximum kinetic energy of the photoelectrons.

Characteristic of photo electric effect:

(a) From the above equation, we find that for photoejection $h\nu \ne \varphi$ i.e., $h{\nu }_{min}=h{\nu }_0$ must be equal to $\varphi$. Hence Photoelectric effect is observed only if $h\nu \ne h{\nu }_0$ or $v\ne {\nu }_0$. This shows the existence of a thershold frequency ${\nu }_0$ for which photo-electrons are just liberated from a metal surface with with $(KE=0).$ Since metals differs in electronic configuration the work function $h{\nu }_0$ and therefore, frequency ${\nu }_0$ are different and characteristic of different metals.

(b) From equation $\frac{1}{2}m{v}_{max}^2=h\nu -\varphi =h(\nu -{\nu }_0)$. This shows that the maximum KE increases linearly with the frequency $\nu$ of the incident photon $(\nu \ne {\nu }_0)$ and does not depend on the time rate at which photons are incident on a metal surface.