Compton Scattering formula for 180 degree scattering.

In summary, the conversation is about trying to derive a simple formula for 180° scattering. The speaker has two equations, one of which they are unsure how to simplify. They ask for help and receive a suggestion to multiply the equations together, resulting in a new equation. The speaker then explains how they derived the first equation and how it relates to the second equation from a different source. They also mention an upcoming exam.
  • #1
durand
13
0
Hi,
I'm trying to derive a simple formula for 180° scattering.

I've got to this stage and I really can't figure out how to simplify it further.

[tex]\[ \frac{1}{\lambda}-\frac{1}{\lambda'} = \frac{2m_ec}{h} \][/tex]

What I actually need is:
[tex]\[ \lambda' - \lambda = \frac{2h}{m_ec} \][/tex]

I'm pretty sure the first formula is right but I can't seem to simplify it into the second!

Thanks in advance.
 
Physics news on Phys.org
  • #2
Hi durand! :smile:

(have a lambda: λ :wink:)

If you multiply them together, you get (λ' - λ)2 = 4λ'λ, or λ'/λ = 3 ± 2√2 :redface:

How did you get your equation?
 
  • #3
Uhm, I derived the first using conservation of momentum and energy at non relativistic speeds, when the photon bounces back. The second comes from the standard compton scattering formula.
 
  • #4
CoM: h/λ = mv + h/λ'
CoE: hc/λ = hc/λ' + 0.5mv²

By substituting one into the other, I reach the formula I mentioned in my first post.
 
  • #6
Bob S said:

Yeah, I did find that, however, it uses a relativistic derivation so I can't really see how to do the last step as it's totally different to mine :/ Thanks anyway.

My exam's in an hour so it doesn't really matter now. Thanks everyone for your help :)
 

What is the Compton Scattering formula for 180 degree scattering?

The Compton Scattering formula for 180 degree scattering is used to calculate the change in energy and wavelength of a photon after it undergoes a scattering event with a free electron at a scattering angle of 180 degrees. It is given by:
\(\Delta \lambda = \frac{h}{mc}(1-cos\theta)\)
where \(\Delta \lambda\) is the change in wavelength,
h is Planck's constant,
m is the mass of the electron,
c is the speed of light, and
\(\theta\) is the scattering angle.

What is Compton Scattering and why is it important?

Compton Scattering is a phenomenon in which a photon interacts with a free electron, resulting in a change in the energy and wavelength of the photon. This process is important in understanding the behavior of electromagnetic radiation, such as X-rays, and is used in various fields such as medical imaging, astronomy, and material science.

What are the key assumptions made in the Compton Scattering formula for 180 degree scattering?

The key assumptions made in the Compton Scattering formula for 180 degree scattering are that the scattering is elastic (no energy is lost), the electron is free (not bound to an atom), and the photon has a much higher energy than the electron.

How does the Compton Scattering formula for 180 degree scattering relate to Einstein's theory of relativity?

The Compton Scattering formula for 180 degree scattering is derived from Einstein's theory of relativity, specifically the principle of conservation of energy and momentum. It takes into account the relativistic effects of the electron's mass and the change in energy and momentum of the photon after the scattering event.

What are the units of the variables in the Compton Scattering formula for 180 degree scattering?

The units of the variables in the Compton Scattering formula for 180 degree scattering are:
- \(\Delta \lambda\) is in meters (m)
- h is in joules (J)
- m is in kilograms (kg)
- c is in meters per second (m/s)
- \(\theta\) is in radians (rad)

Similar threads

Replies
1
Views
824
Replies
8
Views
854
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
10
Views
371
  • Introductory Physics Homework Help
Replies
13
Views
906
Replies
6
Views
1K
  • Quantum Physics
Replies
1
Views
529
Replies
24
Views
1K
Replies
1
Views
778
Back
Top