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 λ₁, λ₂ with λ₁ > λ₂. Which of the following statement are true?

The de Broglie wavelength of the particle varies cyclically between two values λ₁, λ_2.

This means, the particle is moving in an ellipse with origin as one of its foci.

Let v₁ and v₂ be the velocities when the de Broglie wavelengths are λ₁, λ₂ respectively.

We know the de Broglie wavelength of a particle is given by,

So, λ α v^-1

λ₁ > λ₂

Hence, v₂ > v₁

The velocity is maximum when it is closest to the focus.