Question

Define the terms (i) 'cut-off voltage' and (ii) 'threshold frequency' in relation to the phenomenon of photoelectric effect.
Using Einstein's photoelectric equations show how the cut-off voltage and threshold frequency for a given photosensitive material can be determined with the help of a suitable plot/graph.

Answer 1

i) Cut-off Voltage $\left(V_0\right)$ is the minimum negative anode voltage for which the photo-current of the circuit reduces to zero.

ii) For a given material, the minimum frequency of the incident frequency below which no emissions of photo-electrons occur, is called threshold frequency $\left({\nu }_0\right)$.

Einstein's equation is $K_{max}=h\nu -h{\nu }_0$

so, $e{V}_0=h\nu -h{\nu }_0$ or $V_0=\frac{h}{e}(\nu -{\nu }_0)$

Now the variation of stopping potential or cut-off potential $\left(V_0\right)$ with incident frequency $\left(\nu \right)$ is shown in figure.

We can calculate the threshold frequency from point of intersection on frequency axis and cut-off voltage from point of intersection on potential axis.