(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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(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: $p = \frac{h}{\lambda} = \frac{h}{(2L/n)} = \frac{nh}{2L}$.

Class 12 Physics Dual Nature of Radiation and matter Matter Waves and de Broglie Wavelength

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$A$ particle is moving along the $x-$axis back and forth in a box of length $L$. Assuming the de-Broglie hypothesis is applicable for the particle,and it is moving with a constant speed in the box making perfectly elastic collisions with the walls. The possible value of the momentum of the particle is (Note: $h$ is Planck's constant,$n$ is the principal quantum number).

A
$\frac{nh}{2L}$
B
$\frac{nh}{L}$
C
$\frac{nh}{4L}$
D
$\frac{2nh}{3L}$

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Dual Nature of Radiation and matter

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Matter Waves and de Broglie Wavelength

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$A$ particle is dropped from a height $H$. The de Broglie wavelength of the particle depends on height as

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An electron of mass $m$ with an initial velocity $\vec{V} = V_0 \hat{i} \,(V_0 > 0)$ enters an electric field $\vec{E} = -E_0 \hat{i} \,(E_0 = \text{constant} > 0)$ at $t = 0$. If $\lambda_0$ is its de-Broglie wavelength initially,then its de-Broglie wavelength at time $t$ is:

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The de Broglie wavelengths of an electron $(e)$,proton $(p)$,neutron $(n)$,and $\alpha$-particle are $\lambda_e, \lambda_p, \lambda_n$,and $\lambda_\alpha$ respectively. All have the same kinetic energy of $1 \ MeV$. Which of the following represents the correct increasing order of their wavelengths?

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Find the de-Broglie wavelength of an electron with kinetic energy of $ 120 eV $. (in $pm$)

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An electron of mass $m$ with an initial velocity $\vec{V} = V_0 \hat{i} \,(V_0 > 0)$ enters an electric field $\vec{E} = -E_0 \hat{i} \,(E_0 = \text{constant} > 0)$ at $t = 0$. If $\lambda_0$ is its de-Broglie wavelength initially,then its de-Broglie wavelength at time $t$ is:

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