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 varries cyclists between two valuse `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 wavelength is `lambda_(1)`, the particle is nearer the origin than when its value is `lambda_(2)`
D. When the de-broglie wavelength is `lambda_(2)`, the particle is nearer the origin than when its value is `lambda_(1)`

Answer

b,d

Explanation

The de-Broglie wavelength of the particle can be varying cyclically between two values `lambda_(1) and lambda_(2)`, if particle is moving in an elliptical orbit with origin as its one focus. Let `v_(1) ,v_(2)` be the speed of particle at A and B respectively and origin is at focus O. If `lambda_(1), lambda_(2)` are the de-Broglie wavelength associated with particle while moving at A and B respectively, then
`lambda_(1)=h/(mv_(1)) and lambda_(2)=h/(mv_(2))`
`:. (lambda_(1))/(lambda_(2))=(v_(2))/(v_(1)) , Since lambda_(1)gt lambda_(2) :. v_(2)gtv_(1)`
From figure we note that origin O is close to P than A. thus options (b) and (d) are true.