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 orbit with origin as its focus
C. When the de-Broglie wavelength is `lamda_(1),` the particle is nearer the origin that when its value is `lamda_(2)`
D. When the de-Broglie wavelength is `lamda_(2),` the particle is nearer the origin than when its value if `lamda_(1)`

Explanation

The de-Broglie wavelength of the particle can be varying cyclically between two values `lamda_(1) and lamda_(2),` if particle is moving in an elliptical orbit with origin as its one focus.
Consider the figure given below

Let `v_(1),v_(2)` be the speed of particle at A and B respectively and origin is at focous O. If `lamda_(1),lamda_(2)` are the de-Broglie waveiengths associated with particle while moving at A and B respectively. Then,
`" "lamda_(1)=h/(mv_(1))`
and `" "lamda_(2)=h/(mv_(2))`
`therefore" "(lamda_(1))/(lamda_(2))=(v_(2))/(v_(1))`
since `" "lamda_(1)gtlamda_(2)`
`therefore" "v_(2)gtv_(1)`
By law of conservation of angular momentum, the particle moves faster when it is closer to focous.
From figure, we note that origin O is closed top P than A.