A particle moves in a closed orbit around the origin due to a force which directed towards the origin.The de-broglie wavelength of the particle vaies cyclically between two values ${ \lambda }_{ 1 }\& { \lambda }_{ 2 }\quad ({ \lambda }_{ 1 }>{ \lambda }_{ 2 })$ . Which of the following statement(s) are true ?

1)- at ${ \lambda }_{ 1 }$ it is closest to origin .

2)- at ${ \lambda }_{ 2 }$ it is closest to origin .

3)- the kinetic energy of the particle is inversely proportional to the wavelength .

4)- Particle moves in Circular orbits .

5)-Particle moves in Elliptical orbits.

6)-the angular momentum of the Particle is inversely proportional to the wavelength .

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## Comments

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TopNewest@Shashwat Shukla @Raghav Vaidyanathan @Ronak Agarwal @Nishant Rai Do help me please !

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Clearly particle is revolving in a elliptical orbit since the de broglie wavelength is changing between two values.

When wavelength is more means velocity is less hence particle is at farther position ( conserve angular momentum because of central force)

Kinetic energy is inversely proportional to square of wavelength.

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exactly. was thinking the same way.

Original question is from NCERT Exemplar.

Chapter 11 . QNo 13.

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Sorry But I don't able to digest , that It is moving in elliptical orbit . Can you please Explain how It can prooved ?

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Oh sorry sorry we can't say it is an elliptical orbit, I assumed it to be a central force following inverse square law. But it is not.

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Also one more point angular momentum is constant, hence it can't be proportional to anything.

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Magnet Falling in a Copper Tube... beautiful problem. It took some time to analyse the situation.

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@Ronak Agarwal @Nishant Rai please do reply , I'm waiting

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This is the original problem:

This problem is perfect and doesn't leave room for the ambiguity that Ronak mentioned.

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@Nishu sharma @Ronak Agarwal

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