question_answer

Define the terms (i) 'cut-off voltage' and (ii) 'threshold frequency' in relation to the phenomenon of photoelectric effect. Using Einstein's photoelectric equation 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:

                (i) Cut-off voltage or stopping potential. The minimum negative potential given to the anode of a photocell for which the photoelectric current becomes zero is called cut-off voltage or stopping potential. (ii) Threshold frequency. The minimum value of the frequency of incident radiation below which the photo- electric emission stops is called threshold frequency. According to Einstein's photoelectric equation, the maximum K.E. of a photoelectron is given by \[{{K}_{\max }}=hv-{{W}_{0}}\] If \[{{V}_{0}}\] is the stopping potential, then \[{{K}_{\max }}=e{{V}_{0}}\] \[\therefore \]  \[e{{V}_{0}}=hv-{{W}_{0}}\] or            \[{{V}_{0}}=\left( \frac{h}{e} \right)v-\frac{{{W}_{0}}}{e}\]          ?(1) So the graph of \[{{V}_{0}}\] versus \[v\] is a straight line as shown in Fig. We can read the value of threshold frequency,\[{{v}_{0}}\] from the graph. From equation (1), we can find stopping potential \[{{V}_{0}}\] for any frequency \[\text{v}\].