First slide

Wave nature of matter

Question

Which of the following is not a possible de-Broglie's wavelength of a particle, which moves inside a cubical box of side length L, without losing any energy (elastically colliding with walls of cube)?

Moderate

A
B
C
D

All of these

Solution

Using concept of stationary waves, we can say at rigid walls Node formation takes place.
$L = \frac{λ}{2}, λ, \frac{3 λ}{2}, 2 λ . . ., \frac{n λ}{2} w h e r e n = 1, 2, 3 . . .$
Longest wavelength is specified by $λ = 2 L . next by λ = L$
then $λ = L \times \frac{2}{3} . etc$
$In general λ_{n} = \frac{2 L}{n}, n = 1, 2, 3, \dots$
For(a) $λ = \frac{2 L}{3}$
For (b) $λ = L$
For (c) ) $λ = 2 L .$ Hence, all are possible.

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