In summary: Plugging these values into the expression for the components of the momentum of the photon before and after the collision, we get:\begin{equation}\vec p_{pre} = \left(\frac{p'y - p'x}{2}, \frac{p'x + p'y}{2}\right)\end{equation}\begin{equation}\vec p_{post} = \left(\frac{p'y + p'x}{2}, \frac{p'x - p'y}{2}\right)\end{equation} Taking the dot product of these two vectors, we can determine the change in momentum of the photon as:\begin{equation}\Delta \vec p = \vec p_{post
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Introduction
In a previous article entitled “Alternate Approach to 2D Collisions” we analyzed collisions between a moving and stationary object by defining the co-ordinate axes as being respectively parallel and perpendicular to the post-collision direction of motion of the stationary object. In this article, we will be adopting the same approach to analyze the well known physical phenomenon known as Compton scattering in which a photon collides with a stationary electron, imparts momentum to the latter, and hence loses momentum and energy which manifests in a change of direction (‘scattering’ angle) and wavelength (of the photon).
The established physics of Compton scattering relates the scattering angle (angle of deflection) to the change in wavelength of the incident photon  according to the following expression...

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\begin{equation}\Delta \lambda = \frac{h}{m_e c}\left(1 - \cos(\theta)\right)\end{equation}where $\Delta \lambda$ is the change in wavelength of the incident photon, $h$ is Planck’s constant, $m_e$ is the mass of the electron, and $\theta$ is the scattering angle.To determine the scattering angle using the alternate approach, let us consider a point $(x,y)$ on the co-ordinate plane representing the photon's pre-collision position and direction of motion. The post-collision position and direction of motion can be represented by $(x',y')$. The co-ordinate axes are parallel and perpendicular to the post-collision direction of motion of the electron. Therefore, the components of the momentum of the photon before and after the collision can be written as:\begin{equation}\vec p_{pre} = (px,py)\end{equation}\begin{equation}\vec p_{post} = (p'x,p'y)\end{equation}where $px$ and $py$ are the components of the momentum of the photon in the pre-collision direction of motion and $p'x$ and $p'y$ are the components of the momentum of the photon in the post-collision direction of motion.Since the momentum of the photon is conserved during the collision, we have:\begin{equation}px + py = p'x + p'y\end{equation}Also, since the change in momentum of the electron is equal and opposite to the change in momentum of the photon, we can write:\begin{equation}p'x - px = -(p'y - py)\end{equation}Rearranging the equations for $px$ and $py$, we get:\begin{equation}px = \frac{p'y - p'x}{2}\end{equation}\begin{equation}py = \frac{p'x + p'y}{2}\end{equation
 

1. What is Compton scattering?

Compton scattering is a phenomenon in which a photon (massless particle of light) collides with an electron (massive particle) and transfers some of its energy to the electron. This results in a change in the wavelength and direction of the photon.

2. How is Compton scattering related to the concept of massless meets massive?

Compton scattering is a perfect example of the interaction between a massless particle (photon) and a massive particle (electron). It demonstrates the transfer of energy between these two types of particles and the resulting change in their properties.

3. What is the significance of revisiting Compton scattering?

Revisiting Compton scattering allows scientists to further understand the fundamental properties of particles and their interactions. It also allows for the improvement and refinement of theoretical models and experimental techniques.

4. How is Compton scattering used in scientific research?

Compton scattering is used in a variety of fields, including nuclear physics, astrophysics, and medical imaging. It is a valuable tool for studying the properties of particles and their interactions, as well as for developing new technologies and treatments.

5. Can Compton scattering be observed in everyday life?

Yes, Compton scattering can be observed in everyday life through phenomena such as the blue color of the sky and the X-rays used in medical imaging. These are both examples of the scattering of photons by electrons in the atmosphere and human tissue, respectively.

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