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  4. 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)?

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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)?Physics Question Image

Dual Nature of Radiation and Matter

Solution:

Longest wavelength is specified by $\lambda=2 L$.
next by $\lambda=L$, then $\lambda=L \times \frac{2}{3}$.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.