#### A particle moves in a closed orbit around the origin, due to a force which is directed towards the origin. The de-BrOglie wavelength of the particle varies cyclically between two values $\lambda_{1},\lambda_{2}$ with  $\lambda_{1}>\lambda_{2}$  Which of the following statements are true? (a) The particle could be moving in a circular orbit with the origin as the centre (b) The particle could be moving in an elliptic orbit with its 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) When the de-Broglie wavelength is $\lambda_{2}$ the particle is nearer the origin than when its value is $\lambda_{1}$

The answer is the option (b,d)

A particle moving in an elliptic orbit with Origin as the centre can have its de-Broglie wavelength varying between $\lambda_{1}$ and $\lambda_{2}$ cyclically. When the de-Broglie wavelength is lower, the particle is closer to the origin.

$\lambda_{1}=\frac{h}{mv_{1}}\; and \; \lambda_{2}=\frac{h}{mv_{2}}\\ As,\lambda_{1}>\lambda_{2}\\ v_{2}>v_{1}$

The particle will have a higher velocity closer to focus.