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Physics · 2026 · 2 marks
CBSE 2026 · Region 2 · Set 1 · Q18
Find ratio (λ_a / λ_p ) of the de Broglie wavelength λ_a and λ_p associated respectively with an alpha particle and a proton, (i) if they are moving…
Find ratio $\displaystyle \left(\lambda_{\mathrm{a}} / \lambda_{\mathrm{p}}\right)$ of the de Broglie wavelength $\displaystyle \lambda_{\mathrm{a}}$ and $\displaystyle \lambda_{\mathrm{p}}$ associated respectively with an alpha particle and a proton,
(i)
if they are moving with the same kinetic energy.
(ii)
just after they are accelerated through the same potential difference.
Marking-scheme solution
(i)
$\displaystyle \lambda=\dfrac{h}{\sqrt{2 mK}}$
$\displaystyle \dfrac{\lambda_{a}}{\lambda_{p}}=\sqrt{\dfrac{m_{p}}{m_{a}}}=\sqrt{\dfrac{m}{4m}}$
$\displaystyle =\dfrac{1}{2}$
(ii)
$\displaystyle \lambda=\dfrac{h}{\sqrt{2 mqV}}$
$\displaystyle \dfrac{\lambda_{a}}{\lambda_{p}}=\sqrt{\dfrac{m_{p} q_{p}}{m_{a} q_{a}}}=\sqrt{\dfrac{m}{4m} \cdot \dfrac{e}{2e}}$
$\displaystyle =\dfrac{1}{2 \sqrt{2}}$
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