Modern physics

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 .

#Mechanics

Easy Math Editor

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Comments

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

Nishu sharma - 6 years, 1 month ago

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 - 6 years, 1 month ago

exactly. was thinking the same way.

Original question is from NCERT Exemplar.

Chapter 11 . QNo 13.

Nishant Rai - 6 years, 1 month ago

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

Nishu sharma - 6 years, 1 month 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.

Ronak Agarwal - 6 years, 1 month ago

@Ronak Agarwal – 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 this

Nishu sharma - 6 years, 1 month ago

@Ronak Agarwal – There is nothing to think further, all my other statement are correct also we can't say which kind of orbit it is.

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

Ronak Agarwal - 6 years, 1 month ago

@Ronak Agarwal – 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...

Nishu sharma - 6 years, 1 month ago

@Nishu Sharma – 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.

Ronak Agarwal - 6 years, 1 month ago

@Ronak Agarwal – i tried Magnet Falling in a Copper Tube... beautiful problem. It took some time to analyse the situation.

Nishant Rai - 6 years, 1 month ago

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

Nishu sharma - 6 years, 1 month ago

This is the original problem:

11.13 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 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 wave length is λ1, the particle is nearer the origin than when its value is λ2.

(d) When the de Broglic wavelength is λ2, the particle is nearer the origin than when its value is λ1.

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

Raghav Vaidyanathan - 6 years, 1 month ago

@Nishu sharma @Ronak Agarwal

Raghav Vaidyanathan - 6 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$