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 elliptical orbit with origin as its focus.
C. When the de Broglie wavelength is `lamda_(1)`, the particle is nearer the origin than when its value is `lamda_(2)`.
D. Both (a) and (c )

Answer 1

Correct Answer - B
(b) : The de Broglie wavelength of the particle can be varying cyclically betweenb two values `lamda_(1) and lamda_(2)`, if particle is moving in an elliptical orbit with origin as its one focus. Refer figure.
Let `v_(1),v_(2)` be the speed of particle at A and B jrespectively and origin is at focus O. If `lamda_(1),lamda_(2)` are the de Broglie wavelength associated with particle while moving at A and B respectively.
Then, `lamda_(1)=(h)/(mv_(1)) and lamda_(2)=(h)/(mv_(2)):.(lamda_(1))/(lamda_(2))=(v_(2))/(v_(1))`
Since `lamda_(1)gtlamda_(2):.v_(2)gtv_(1)`
From figure we note that origin O is close to B than A. Thus option (b) is true.