dual-nature-of-radiation-and-matter Question 22
Question: Q. 5. (i) Draw a plot showing the variation of photoelectric current with collector potential for different frequencies but same intensity of incident radiations.
(ii) Use Einstein’s photoelectric equation to explain the observations from this graph.
(iii) What change will you observe if intensity of incident radiation is changed but the frequency remains the same?
U] [Foreign I, III 2017]
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Solution:
Ans. (i)
(ii) According to Einstein’s photoelectric equation $\mathrm{K}{\max }=h \nu-\phi{0}$
If $V_{0}$ is stopping potential then
$$ e V_{0}=h v-\phi_{0} $$
Thus, for different values of frequency $(v)$ there
(iii)
[CBSE Marking Scheme 2017]
Detailed Answer :
(ii) Einstein equation for photoelectric effect
$$ \text { K.E. }=h v-\phi_{0} $$
where, $h v=$ energy of one photon
$\phi_{0}=$ work function of a metal which is a constant for a particular metal.
K.E. $=$ kinetic energy of an emitted electron $=e V_{0}$; where, $V_{0}=$ stopping potential
Hence,
$$ e V_{0}=h v-\phi_{0} $$
From the above equation, it is clear that for different frequencies there will be different values of stopping potential as work function is constant. (iii) Intensity of incident radiation means the number of photons incident per unit time which is directly proportional to the number of emitted electrons from the metal.
So with change of intensity, number of emitted electrons and hence current varies.
$$ e V_{0}=h v-\phi_{0} $$
As we can see from above equation if frequency remains same, stopping potential does not change as stopping potential depends upon frequency and not upon number of photons.
