Does Recoiling Electrons Have 0 Energy When Photon is Scattered 180°?

[MostlyHarmless]

I'm pretty sure this is a fairly obvious question, but I can't ever be sure..

So, if a photon is "scattered" 180 degrees. Its not being scattered at all, correct? So, then the energy of the "recoiling electrons" would be 0.

It makes sense mathematically if I'm doing it right.

${\lambda}_2-{\lambda}_1={\frac{h}{m_ec}}(1-cos{\theta})$

$h$ is Planck's constant, $m_e$ is electron mass, c, speed of light. If theta is 180, change is wavelength is 0, so then there is no scattering? Is the all consistent?

The reason I'm so hesitant, is because this is a homework problem, and the only one assigned dealing with recoiling electrons, so I figured it would be... less trivial.Note: Excuse the lack of homework template, I'm posting this off of my phone, which does not give me the template.

 

[George Jones]

So, if a photon is "scattered" 180 degrees. Its not being scattered at all, correct?

Not correct.

So, then the energy of the "recoiling electrons" would be 0.

It makes sense mathematically if I'm doing it right.

${\lambda}_2-{\lambda}_1={\frac{h}{m_ec}}(1-cos{\theta})$

$h$ is Planck's constant, $m_e$ is electron mass, c, speed of light. If theta is 180, change is wavelength is 0, so then there is no scattering?

What is cos(180)?

 

[MostlyHarmless]

>.< Doh. That's what I get for just punching it my calculator and then not writing it down.

hen it says, 180, its "scattering" back in the direction if the incident photon?

So the change in wave length should be $2h/(m_ec)$?

 

[vela]

Right. The angle $\theta$ is the angle by which the photon is deflected.

 

[HalfLostAndSearching]

I would like to clarify that the concept of recoiling electrons and their energy in the context of photon scattering is not a trivial matter. It involves a complex interplay between the energy and momentum of the photon and the electrons involved in the scattering process.

Firstly, let's define what we mean by a "scattered" photon. In this case, we are referring to the process of Compton scattering, where a photon is absorbed by an electron and then re-emitted in a different direction. This process results in a change in the photon's energy and wavelength, as well as a change in the momentum of the recoiling electron.

Now, let's consider the scenario where the photon is scattered at an angle of 180 degrees. In this case, the change in the wavelength of the photon, as shown in the equation provided, is indeed 0. However, this does not mean that the photon is not scattered at all. It simply means that the photon is scattered back in the same direction from which it came, with no change in its energy or wavelength.

As for the recoiling electron, it does not have 0 energy in this scenario. While the change in its momentum may be 0, it still retains its initial energy before the scattering event. This is because the energy of the electron is not solely dependent on its momentum, but also on its mass and speed.

In conclusion, the concept of recoiling electrons and their energy in the context of photon scattering is not a trivial matter and requires a deeper understanding of the underlying principles of quantum mechanics. It is important to approach such problems with a critical mindset and to seek further clarification if needed.