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 particles varies cyclically between two values `lambda_(1), lambda_(2) with lambda_(1)gtlambda_(2)`. Which of the following statements are true?

Options

A. The particle could be moving in a circular orbit with origin as centre.
B. The particle could be moving in an elliptic orbit with origin as its focus.
C. When the de Broglie wave length is `lamda_1` , the particle is nearer the origin than when its value is `lamda_2`.
D. When the de Broglie wave length is `lamda_2` , the particle is nearer the origin than when its value is `lamda_1`.

Answer

B, D

Explanation

In circular orbit, speed remain constant and hence different wavelengths are not possible. So, it must be an elliptical orbit. Option (b) is correct.
Since angular momentum (L = mvr) of the particle remains constant and hence , when the distance of the particle from the orgin decreases then its speed increase. Increases in speed means decreases in wavelength `(lamda-h//mv)` . Hence option (d) is also correct.
The correct options are (b) and (d).