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  4. The de Broglie wavelength λ associated with a proton increases by 25 %, if its momentum is decreased by p0. The initial momentum was

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Q. The de Broglie wavelength $\lambda$ associated with a proton increases by $25 \%$, if its momentum is decreased by $p_{0}$. The initial momentum was

Dual Nature of Radiation and Matter

Solution:

$\frac{\lambda_{2}-\lambda_{1}}{\lambda_{1}}=\frac{25}{100}$
$\frac{\lambda_{2}}{\lambda_{1}}=\frac{5}{4} $
$\Rightarrow \frac{P_{1}}{P_{2}}=\frac{5}{4}$
$P_{2}-P_{1}=-P_{0}$
$\frac{4 P_{1}}{5}-P_{1}=-P_{0}$
$P_{1}=5 P_{0}$