First slide

Matter waves (DC Broglie waves)

Question

A moving particle of mass m has a de Broglie wave length $λ$ . Then energy of the particle is

Moderate

A

$h^{2} / 4 m λ^{2}$
B

$\frac{2 h^{2}}{m λ^{2}}$
C

$\frac{m λ^{2}}{2 p^{2}}$
D

$h^{2} / 2 m λ^{2}$

Solution

de Broglie wavelength $λ = \frac{h}{p} \Rightarrow p = \frac{h}{λ}$
$∴$ kinetic energy $= \frac{p^{2}}{2 m} = \frac{{(h / λ)}^{2}}{2 m} = \frac{h^{2}}{2 m λ^{2}}$

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