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The photoelectric effect

Experimental facts Heinrich Hertz found out experimentally that, electrons were ejected from metallic surface when light is incident on it. The variation of current versus potential difference, V is given by,

There is a stopping potential $V_o$ for which no current flows. As V increases current soon reaches a saturation value. For a different intensity of light, the saturation value of current charges but the stopping potential remains same as long as the wavelength of incident light is kept fixed.

The features of photoelectric effect were not fully explained by classic using Planck’s quantum theory. According to Einstein, when it hits a photo metal, a photon is completely absorbed by an electron. The kineüc energy of the ejected electron will be $KE=h\nu-W_o$ .

where $W_o$ is the work done needed to overcome the attractive binding forces and also collisions With other atoms as it comes out. KE is maximum when W is minimum, say  $W_o$

$$KE_{max}=h\nu-W_o$$

The minimum amount of work done needed to pull out the most loosely bounded electron and assuming no collisions on the way out is called the work function,

$W_o$ In terms of the stopping potential $V_o$,

$$eV_o=h\nu-W_o$$

The existence of a minimum frequency is obvious because $h\nu\geq W_o$

        $$V_{min}=\frac{W_o}h$$

Whether an electron is ejected from the metal or not does not depend on the intensity or the number of photons per unit volume but on the frequency, v. So, the electron current does not depend on the frequency but on the intensity. Current depends on the number electrons ejected and this depends on the intensity. If the incident frequency v is less than $V_{min}$ no matter how high the intensity, no photon can eject on electron because $hV_{min}$ is the minimum energy required. As one photon is absorbed by an electron, there is also no time lag. Thus, Einstein’s theory of photoelectric effect explains all the observed phenomena which could not be reconciled with classical wave theory.