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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 λ1, λ2 with λ1> λ2 Which of the following statements are true?

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 statements are true?
(a) The particle could be moving in a circular orbit with the origin as the centre
(b) The particle could be moving in an elliptic orbit with its 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}

Answers (1)

The answer is the option (b,d)

A particle moving in an elliptic orbit with Origin as the centre can have its de-Broglie wavelength varying between \lambda_{1} and \lambda_{2} cyclically. When the de-Broglie wavelength is lower, the particle is closer to the origin.

\lambda_{1}=\frac{h}{mv_{1}}\; and \; \lambda_{2}=\frac{h}{mv_{2}}\\ As,\lambda_{1}>\lambda_{2}\\ v_{2}>v_{1}

The particle will have a higher velocity closer to focus.

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infoexpert24

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