Which of the following is possible de-Broglie's wavelengths of a particle, which moves inside a cubi

Question

Which of the following is possible de-Broglie's wavelengths of a particle, which moves inside a cubical box of side length $L$, without losing any energy (elastically colliding with walls of cube)?

Professor PC Thomas Classes · Answer

(d): Longest wavelength is specified by $\lambda=2 L$, next by $\lambda=L$, then $\lambda=L 	imes \frac{2}{3}$, etc..., In general $\lambda_n=\frac{2 L}{n}, n=1,2,3 \ldots$ For (a) $\lambda=\frac{2 L}{3}$, For (b) $\lambda=L$ For (c) $\lambda=2 L$. Hence, all are possible.