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Physics · 2026 · 3 marks
CBSE 2026 · Region 2 · Set 3 · Q28
(a) A particle of charge q and mass m is accelerated through a potential difference V. Deduce an expression for the de Broglie wavelength associated…
(a)
A particle of charge q and mass m is accelerated through a potential difference V. Deduce an expression for the de Broglie wavelength associated with the particle.
(b)
Plot a graph for a particle of charge q and mass m showing variation of de Broglie wavelength $\displaystyle \lambda$ with $\displaystyle \frac{1}{\sqrt{\mathrm{~V}}}$, where V is the potential difference through which the particle is accelerated.
Marking-scheme solution
(a)
Let the charged particle be accelerated by potential difference V: $\displaystyle \dfrac{1}{2} m v^{2}=q V$
$\displaystyle v=\sqrt{\dfrac{2 q V}{m}}$
de Broglie wavelength $\displaystyle \lambda=\dfrac{h}{m v}$
$\displaystyle \lambda=\dfrac{h}{m \sqrt{\dfrac{2 q V}{m}}}$
$\displaystyle \lambda=\dfrac{h}{\sqrt{2 m q V}}$
(b)
$\displaystyle \lambda$ varies linearly with $\displaystyle \dfrac{1}{\sqrt{V}}$: the graph is a straight line through the origin.
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