Question

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?
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 `lambda_(1)` the particle is nearer the origin that when its value is `lambda_(2)`
D. When the de Broglie wavelength is `lambda_(2)` the particle is nearer the origin that when its value is `lambda_(1)`

Answer 1

Correct Answer - B::D
Angular momentum `(mvr)` of a particle is conserved, when it moves in an elliptical orbit.As `r` changes for elliptical orbit,`mv` also changes and so does `lambda(=h//mv)`
When particle is nearer to the origin,`r` is less,`mv` is more and hence `lambda` is less.
`lambda_(1)=h/(mv_(1))` and `lambda_(2)=h/(mv_(2))`
`therefore lambda_(1)/lambda_(2)=v_(2)/v_(1)`,since `lambda_(1) gt lambda_(2) therefore v_(2) gt v_(1)`