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(A) According to the de-Broglie hypothesis,the wavelength $\lambda$ is related to momentum $p$ by $\lambda = \frac{h}{p}$.For a particle in a box of l

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$\frac{nh}{2L}$

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(A) According to the de-Broglie hypothesis,the wavelength $\lambda$ is related to momentum $p$ by $\lambda = \frac{h}{p}$.For a particle in a box of length $L$ with perfectly elastic collisions,the standing wave condition requires that the length $L$ must be an integer multiple of half-wavelengths: $L = \frac{n\lambda}{2}$,where $n = 1, 2, 3, \dots$.Rearranging for $\lambda$,we get $\lambda = \frac{2L}{n}$.Substituting this into the de-Broglie relation: $p = \frac{h}{\lambda} = \frac{h}{(2L/n)} = \frac{nh}{2L}$.

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