Question

A particle moves in a closed orbit around the origin, due to a force which is directed towards the origin. The de Broglie wavelength to the particle varies cyclically between two values $\lambda_{1}$ and $\lambda_{2}$ with $\lambda_{1} > \lambda_{2}$. Which of the following statements is true?

• A. The particle could be moving in a circular orbit with origin as centre.
• B. The particle could be moving in an elliptical orbit with origin as its focus.
• C. When the de Broglie wavelength is $\lambda_{1}$, the particle is nearer the origin than when its value is $\lambda_{2}$.
• D. Both (1) and (2)

Answer 1

Answer: (B)

The particle could be moving in an elliptical orbit with origin as its focus.

Answer 2

: The de Broglie wavelength of the particle can be varying cyclically between two values $\lambda_{1}$and$\lambda_{2}$ if particle is moving in an elliptical orbit with origin as its one focus

Refer figure

Let $v_{1}$,$v_{2}$ be the speed of particle at A and B respectively and origin is at focus O. if $\lambda_{1}$,$\lambda_{2}$ are the de Broglie wavelength associated with particle while moving a A and B respectively

Then

$\lambda_{1} = \frac{h}{mv_{1}}and\lambda_{2} = \frac{h}{mv_{2}}\therefore\frac{\lambda_{1}}{\lambda_{2}} = \frac{v_{2}}{v_{1}}$

Since $\lambda_{1} > \lambda_{2}\therefore v_{2} > v_{1}$

From figure we note that origin O is close To B than A. thus option (2) is true