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Physics · 2025 · 3 marks
Dual Nature of Radiation and MatterEinstein’s Photoelectric Equation: Energy Quantum of Radiation3 marksApplyshort answer
CBSE 2025 · Region 7 · Set 2 · Q23
(a) Briefly explain Einstein's photoelectric equation. (b) Four metals with their work functions are listed below: K =2 · 3 eV, Na =2 · 75 eV, Mo =4…
(a)
Briefly explain Einstein's photoelectric equation.
(b)
Four metals with their work functions are listed below: $\displaystyle \mathrm{K}=2 \cdot 3 \mathrm{eV}, \mathrm{Na}=2 \cdot 75 \mathrm{eV}, \mathrm{Mo}=4 \cdot 17 \mathrm{eV}$ and $\displaystyle \mathrm{Ni}=5 \cdot 15 \mathrm{eV}$. The radiation of wavelength $\displaystyle 330$ nm from a laser source placed $\displaystyle 1$ m away, falls on these metals. Which of these metals will not show photoelectric emission? What will happen if the laser source is brought closer to a distance of $\displaystyle 50$ cm?
Marking-scheme solution
(a)
$\displaystyle h\nu = \phi_0 + K_{max}$
$\displaystyle h\nu$ = Energy of incident radiation
$\displaystyle \phi_0$ = Work function or minimum energy required to emit an electron from metal surface
$\displaystyle K_{max}$ = maximum kinetic energy of emitted electron
Alternatively:
The energy of incident radiation E ($\displaystyle > \phi_0$) incident on a metal surface, a part of it is used to overcome the work function & remaining energy provides maximum kinetic energy to the electrons.
(b)
$\displaystyle \lambda = 330\,nm$
$\displaystyle E = \dfrac{hc}{\lambda} = \dfrac{6.63\times10^{-34}\times 3\times 10^{8}}{330\times10^{-9}\times1.6\times10^{-19}}$
$\displaystyle = 3.77\,eV$
Mo and Ni will not show photoelectric emission.
No change.
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