Question: Q. 7. Plot a graph showing the variation of stopping potential with the frequency of incident radiation for two different photosensitive materials having work functions $W_{1}$ and $W_{2}\left(W_{1}>W_{2}\right)$. On what factors do the (i) slope and (ii) intercept of the lines depend?
[OD Comptt. I, II, III 2013]
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Solution:
Ans. (i) Slope is determined by $\frac{h}{e}$ (or slope is independent of the metal used).
(ii) Work function of the metal.
[CBSE Marking Scheme 2013]
Detailed Answer :
(i)
where,
$$ \begin{aligned} \mathrm{e} V_{0} & =h v-h v_{0} \ V_{0} & =\text { stopping potential } \ v_{0} & =\text { cutoff frequency } \ V_{0} & =\frac{h}{e}\left(v-v_{0}\right) \end{aligned} $$
Comparing this with straight line equation,
$$ \begin{aligned} y & =m x+c \ m & =\frac{h}{e} \end{aligned} $$
Slope,
Hence, slopes of both lines are same (independen of type of material).
(ii) Intercept of the line depends upon the cut off frequency. It is different for both materials. It is higher for the metal for which work function is higher. Hence, in graph intercept for $W_{1}$ is higher than $W_{2}$.
