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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.

Solution:

i) Cut-off Voltage (V₀) 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 (ν₀).

Einstein's equation is
Kmax = hν – hν₀
so, eV₀ = hν – hν₀
or V₀ = h/e(ν – ν₀)

Now the variation of stopping potential or cut-off potential (V₀) with incident frequency (ν) is shown in figure. We can calculate the threshold frequency from the point of intersection on the frequency axis and cut-off voltage from the point of intersection on the potential axis.