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Physics · 2025 · 2 marks
Dual Nature of Radiation and MatterEinstein’s Photoelectric Equation: Energy Quantum of Radiation2 marksApplyvery short answer
CBSE 2025 · Region 2 · Set 2 · Q20
Radiations of two frequencies are incident on a metal surface of work function 2.0 eV one by one. The energies of their photons are 2.5 eV and 4.5 eV…
Radiations of two frequencies are incident on a metal surface of work function $\displaystyle 2.0$ eV one by one. The energies of their photons are $\displaystyle 2.5$ eV and $\displaystyle 4.5$ eV respectively. Find the ratio of the maximum speed of the electrons emitted in the two cases.
Marking-scheme solution
$\displaystyle h \nu=\phi_{0}+K_{\max }$
For radiation having photons of energy $\displaystyle 2.5$ eV:
$\displaystyle 2.5 \mathrm{~eV}=2 \mathrm{~eV}+\frac{1}{2} m v_{1}^{2}$
$\displaystyle 0.5 \mathrm{~eV}=\frac{1}{2} m v_{1}^{2}$ .............(i)
For radiation having photons of energy $\displaystyle 4.5$ eV:
$\displaystyle 4.5 \mathrm{~eV}=2 \mathrm{~eV}+\frac{1}{2} m v_{2}^{2}$
$\displaystyle 2.5 \mathrm{~eV}=\frac{1}{2} m v_{2}^{2}$ ............(ii)
Dividing eq. (i) by (ii):
$\displaystyle \frac{v_{1}}{v_{2}}=\frac{1}{\sqrt{5}}$
OR
$\displaystyle \frac{v_{2}}{v_{1}}=\sqrt{5}$
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