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A particle moves in a closed orbit aroun...

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 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)`

Text Solution

AI Generated Solution

To solve the problem, we need to analyze the motion of a particle moving in a closed orbit around the origin under the influence of a force directed towards the origin. We also need to understand the implications of the varying de Broglie wavelength of the particle. ### Step-by-Step Solution: 1. **Understanding the Force**: The problem states that the force acting on the particle is directed towards the origin. This indicates that the force is a centripetal force, which is necessary for circular or elliptical motion. 2. **Centripetal Force in Circular Motion**: In a circular orbit, the centripetal force is given by the equation: \[ ...
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