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)?

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)? (A)  (B)  (C)  (D) All of these

Tardigrade Admin · Accepted Answer

Longest wavelength is specified by λ=2 L. next by λ=L, then λ=L × (2/3).etc. In general λn=(2 L/n), n=1,2,3, ldots For (a) λ=(2 L/3) For (b) λ=L For (c) λ=2 L. Hence, all are possible.

Q. 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)?

All of these

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.

Q. 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)?

All of these

Longest wavelength is specified by λ=2L. next by λ=L, then λ=L×32​.etc. In general λn​=n2L​,n=1,2,3,… For (a) λ=32L​ For (b) λ=L For (c) λ=2L. Hence, all are possible.

Q. 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)?

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.