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 particle varies cyclically between two value `lambda_(1),lambda_(2)` with `lambda_(1)gtlambda_(2)`.Which of the following statement 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 elliptical 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 values is `lambda_(1)`

Answer

B, D

Explanation

From `lambda=(h)/(mv)`,we can say that for given particle ,`lambda` would change only when v changes .Here `lambda_(1)gtlambda_(2)` is given .Hence `v_(1)ltv_(2)`.
`implies` Path of motion of a particle can not be circular because in tghat case `vecFbotvecv` and so v=constant.
`implies` Given particle must be moving in an elliptical orbit where its angular momentum gets conserved .Hence mvr=constant
`impliesmvprop(1)/(p)implies(1)/(lambda)prop(1)/(r)`
`(because lambda=(h)/(mv)impliesmvprop(1)/(lambda))implieslambdaprop r`
`implies lambda prop r prop (1)/(v)` (`because` vr=constant)
`implies (lambda_(2))/(lambda_(1))=(r_(2))/(r_(1))implies` If `r_(2)ltr_(1)` then `lambda_(2) lt lambda_(1)implieslambda_(1)gtlambda_(2)`
`implies` When de-Broglie wavelength of a particle equal to `lambda_(2)` (which is smaller then `lambda_(1)`),it distance from the origin would be `r_(2)ltr_(1)` which means that it would be closer to origin
`implies`Options (B) and (D) are correct.