Energy of a photon scattered due to the Compton Effect

[PhysicsTruth]

Homework Statement

Show that the maximum energy of a scattered photon in Compton experiment is 2moc^2(mo=rest mass of electron). Also find the corresponding angle at which this max energy occurs.

Relevant Equations

Delta lambda=h/moc (1-cos(theta))

I don't really know how to proceed. Can someone help me out in this?

 

[Abhishek11235]

I don't really know how to proceed. Can someone help me out in this?

You can't get any help from anyone here if you say this. This is just $\textbf{put-into-the-formula}$ problem

 

[PhysicsTruth]

No it really isn't ! I'm not that dumb really. I had tried using the relativistic energies of photon and electron, and the fact that delta lambda should be minimum for the scattered photon to have max energy, but to no avail.

 

[phyzguy]

Do you know how to use calculus to maximize a function?

 

[PhysicsTruth]

Yeah, but on which formula should I use it? I'm confused. For delta lambda to be minimum, theta had to be 0. But then, how is the energy moc^2? Really, I don't get it.

 

[PhysicsTruth]

Yeah, but on which formula should I use it? I'm confused. For delta lambda to be minimum, theta had to be 0. But then, how is the energy moc^2? Really, I don't get it.

2moc^2, my bad.

 

[jtbell]

Do you know how to use calculus to maximize a function?

Yeah, but on which formula should I use it?

From the problem statement, it should be apparent that the relevant function is the energy of the scattered photon as a function of angle. Call the energy of the incoming photon $E_0$, and call the energy of the scattered photon $E$. Can you come up with a function $E(\theta)$?

Hint: what is the relationship between $E$ and $\lambda$?

 

[PhysicsTruth]

From the problem statement, it should be apparent that the relevant function is the energy of the scattered photon as a function of angle. Call the energy of the incoming photon $E_0$, and call the energy of the scattered photon $E$. Can you come up with a function $E(\theta)$?

Hint: what is the relationship between $E$ and $\lambda$?

I get: $1/E$= $1/E_0$ + (1-cos(theta))/moc^2
But for E to be max, theta should be 0,so how to do it now?

 

[PhysicsTruth]

I get: $1/E$= $1/E_0$ + (1-cos(theta))/moc^2
But for E to be max, theta should be 0,so how to do it now?

Can you please guide me how should I proceed further?

 

[PhysicsTruth]

Please help someone!

 

[jtbell]

But for E to be max, theta should be 0

Indeed! and what does E equal in that case?

Hmmm... are you sure you copied the problem statement correctly and completely?

 

[PhysicsTruth]

The question says- **Show that the maximum energy of the scattered photon will be 2moc^2, irrespective of the energy of the incident photon.**

 

[vela]

I imagine most of the helpers here think that question is obviously wrong, which may be why you're a little confused as to what to do. You may want to check with your instructor if it was worded correctly.