A particle moves in a closed orbit around the origin, due to a forc...

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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 values \( \lambda_{1}, \lambda_{2} \) with \( \lambda_{1}\lambda_{2} \). Which of the following statement 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 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 \( \lambda_{1} \)
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