# Particle-like Photon Processes

Wednesday, February 2, 2022

## What did experiments show?

Experiments repeatedly showed that many phenomena to do with electromagnetic radiation cannot be explained by the classical wave theory. Such experiments include, but are not limited to, thermal radiation, the photoelectric effect, and the Compton effect.

## Photons and atoms

Atoms sometimes emit electromagnetic radiation, but only in discrete amounts (photons). When an atom releases a photon of energy $E$, it also has some small amount of energy, $K$, which is recoil kinetic energy to conserve momentum after emitting the photon.

When an atom absorbs a photon, the same recoil kinetic energy $K$ exists, but now it conserves momentum in the opposite direction. So therefore, the energy the atom adds to its internal structural energy is equal to the energy of the photon minus the small recoil kinetic energy.

## Bremsstrahlung and X-Rays

Accelerating electric charges, such as electrons, emit electromagnetic radiation in discrete amounts (photons). For instance, an electron accelerated through a voltage potential $\Delta V$ loses potential energy $-e\Delta V$ and has potential energy $K=e\Delta V$.

An electron being accelerated into an atom initially has kinetic energy $K$ and after has kinetic energy $K'$. Therefore, since the energy essentially only goes into emitting photons (there is some small recoil kinetic energy of the atom, but it is often ignored), the light can be described as such:

$hf=\frac{hc}{\lambda}=K-K'$

Since the electron often makes many collisions, there are many values for $K'$, and therefore many different wavelengths of light are often emitted.

If an electron loses all of its kinetic energy in one interaction, it emits a photon with wavelength $\lambda_{max}$, which can be found as such:

$\lambda_{max}=\frac{hc}{K}=\frac{hc}{e\Delta V}$

$\lambda_{max}$ is often in the x-ray range, and this constant emission of x-rays is called *bremsstrahlung*.

## Pair Production and Annihilation

**Pair production** is when a photon interacts with an atom and two particles—an electron and a positron—are created.

A positron is an anti-electron. It has the same mass as an electron but has a +1 electric charge.

The electron and positron did not exist before the photon interaction created them. Therefore, the photon energy, $hf$, equates to the energies of the two new particles:

$hf=E_++E_-=\left(m_ec^2+K_+\right)+\left(m_ec^2+K_-\right)$

Since the kinetic energies of the electron and positron are always positive, the photon needs to have the energy of at least $2m_ec^2$, or about 1.02MeV (typically nuclear gamma rays).

The reverse process can also happen, when an electron and a positron annihilate and form a photon. Due to conservation of energy and conservation of momentum, an electron and positron annihilating form two photons with equal energies $m_ec^2$ each (about 0.511MeV) and the photons must move in opposite directions.