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Physics · 2025 · 3 marks
Dual Nature of Radiation and MatterEinstein’s Photoelectric Equation: Energy Quantum of Radiation3 marksUnderstandshort answer
CBSE 2025 · Region 4 · Set 1 · Q27
Explain the following observations using Einstein's photoelectric equation: (a) Photoelectric emission does not occur from a surface when the…
Explain the following observations using Einstein's photoelectric equation :
(a)
Photoelectric emission does not occur from a surface when the frequency of the light incident on it is less than a certain minimum value.
(b)
It is the frequency, and not the intensity of the incident light which affects the maximum kinetic energy of the photoelectrons.
(c)
The cut-off voltage ( $\displaystyle \mathrm{V}_{\mathrm{o}}$ ) versus frequency ( $\displaystyle v$ ) of the incident light curve is a straight line with a slope $\displaystyle \frac{\mathrm{h}}{\mathrm{e}}$.
Marking-scheme solution
(a)
Einstein photoelectric equation:
$\displaystyle h \nu=h \nu_{0}+K_{\max }$
$\displaystyle K_{\max }=h\left(\nu-\nu_{0}\right)$
For $\displaystyle \nu<\nu_{0}$, $\displaystyle K_{\max }$ will be negative.
Hence, photoelectric emission is not possible.
(b)
According to Einstein photoelectric equation:
$\displaystyle K_{\max }=h\left(\nu-\nu_{0}\right)$
Hence $\displaystyle K_{\max } \propto \nu$
It shows $\displaystyle K_{\max }$ depends upon frequency only and does not depend upon intensity.
(c)
$\displaystyle e V_{0}=h \nu-h \nu_{0}$
$\displaystyle V_{0}=\frac{h}{e} \nu-\frac{h}{e} \nu_{0}$
This equation represents the equation of a straight line $\displaystyle (y=m x+c)$ with slope $\displaystyle \frac{h}{e}$.
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