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 $λ_1$ and $λ_2$ with $λ_1>λ_2$. Which of the following statements is true?

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

The de Broglie wavelength of the particle can be varying cyclically between two values $λ_1$ and $λ_2$, if particle is moving in an elliptical orbit with origin as its one focus.

Let $v_1 , v_2$ be the speed of particle at A and B respectively and origin is at focus O. If $λ_1,λ_2$ are the de Broglie wavelengths associated with particle while moving at A and B respectively.

Then

$λ_1=\frac{h}{mv_1}$ and $λ_2=\frac{h}{mv_2}$

$∴\frac{λ_1}{λ_2}=\frac{v_2}{v_1}$

Since $λ_1>λ_2$

$∴v_2>v_1$

Thus, option (2) is true.