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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TopNewestThis is the original problem:

This problem is perfect and doesn't leave room for the ambiguity that Ronak mentioned. – Raghav Vaidyanathan · 2 years ago

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@Nishu sharma @Ronak Agarwal – Raghav Vaidyanathan · 2 years ago

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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. – Ronak Agarwal · 2 years ago

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@Ronak Agarwal @Nishant Rai please do reply , I'm waiting – Nishu Sharma · 2 years ago

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– Nishu Sharma · 2 years ago

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

– Ronak Agarwal · 2 years ago

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.Log in to reply

Also one more point angular momentum is constant, hence it can't be proportional to anything. – Ronak Agarwal · 2 years ago

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– Nishu Sharma · 2 years ago

Sorry But I have answer as Elliptical orbit's .. This was the main problem of mine ... I can't conclude anything .. that's why i posted here...Log in to reply

– Ronak Agarwal · 2 years ago

This simply means the question is incorrect they forgot to mention it as inverse square force. Have you tried the problem Magnet in a copper tube. Also I have corrected the link.Log in to reply

Magnet Falling in a Copper Tube... beautiful problem. It took some time to analyse the situation. – Nishant Rai · 2 years ago

i triedLog in to reply

– Nishu Sharma · 2 years ago

ohh but yes it is not neccessery ..... So would you tell , what are you thinking now ? I'am really want to solve this , I tried my best , but fails . Please help me to get rid out from thisLog in to reply

Original question is from NCERT Exemplar.

Chapter 11 . QNo 13. – Nishant Rai · 2 years ago

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@Shashwat Shukla @Raghav Vaidyanathan @Ronak Agarwal @Nishant Rai Do help me please ! – Nishu Sharma · 2 years ago

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