What is the Compton effect?

The Compton effect is the rise in wavelengths in X-rays as well as other powerful electromagnetic radiations that were elastically scattering through electrons, this is a major mode of radiant energy absorption in the matter. This phenomenon has been shown as one of the foundations of quantum physics, account including both waves as well as particles aspects of radiation and matter. Also see earlier particle & waves concepts of light. Compton effect is a type of inelastic light scattering by such a free-charged particle in which the scattering has a wavelength that differs from the incoming radiation. The energy of an X-ray photon (17 keV) was substantially higher than that of the binding energy of an atom particle in Compton's initial experiment. Therefore the electrons could be viewed as free following scatter. The Compton shifting is the proportion whereby the wavelength of light varies. While nucleus Compton scatter does exist, Compton scattering usually refers to an atom's ions exclusively. Arthur Holly Compton who discovered the Compton effect got Nobel Prize in 1927 in Physics.

History and experimental setup

Around early 1923, renowned Dutch physical scientist Peter Debye discovered the Compton impact. The wavelength expansion was described by Holly Compton (American physicist at 1922-1923) by treating X-rays as discrete pulses of electromagnetic fields. The name photon was later invented by Gilbert Lewis (an American chemist) to describe light quantum states. Photons, like material particles, contain energy and velocity, as well as wave properties like wavelength and frequency. Relatively low photons possess low frequency and greater wavelength because their energy is proportional to their frequency & negatively related to their wavelength. Individual photons hit into single electrons within atoms of substance which are free or very loosely bound in the Compton effect. When photons collide, some of their energy and momentum are transferred to electrons, which recoil. Additional photons with less momentum and energy are produced at the time of the impact, scattering at angles whose magnitude is determined by the amount of power dissipated to the recoiling electrons.

The scattering photons have such a longer wavelength due to the relationship between energy and wavelength, which is also dependent on the magnitude of the angle by which the X-rays had diverted. The wavelength shift, also Compton shift, is independent of the incoming photon's wavelength. Compton provided a quantum interpretation, dependent upon that quantum theory of light. As per the quantum theory, whenever photon energy collides with such a substance, part of the photon's energy is transferred to electrons, reducing the photon's energy (and frequency) thus increasing the wavelength.

The following assumptions were made to explain the effect:

1. The Compton Phenomenon is caused by the interaction of a single particle with a shooter's free electron.
2. The impact is both relativistic & elastic.
3. The rules of conservation of energy states are still valid.

Compton Scattering

The Compton effect, also known as Compton scattering, is among the most common types of photon interaction. In such a material, it is the primary source of scattered radiation. This happens when a photon (e.g. X-ray or gamma) interacts with free electrons (atoms that aren't bonded to them) or weakly bound valence shell (or outer shell) electrons. Photon scatters & provides energy towards the electron as a result (i.e. recoil electron). The dispersed photon will also have a different frequency and hence varied energy i.e. $E=\frac{hc}{\lambda }$(observed phenomenon). This technique conserves both energy and momentum.

A Compton impact is a partly absorption process that results in a Compton shifting (i.e. a wavelength/frequency shifting) when the original photon loses energy and where the scattered photon angle, can be used to estimate the wavelength variation of the scattered photon. As a result, the scattered photon angle increases, and the energy of scattered photon drops.

$\lambda \text{'}-\lambda =\frac{h}{m_{e}c}(1-\cos \theta )$

Where

• $\lambda$ = initial wavelength
• $\lambda \text{'}$ = wavelength after scattering
• $h$ = Planck constant
• $m_e$ = electron mass
• $c$ = speed of light
• $\theta$ = scattering angle

It can further be seen that the angle φ of the outgoing electron with the direction of the incoming photon is specified by 

$cot \phi =(1+\frac{hf}{m_e{c}^2})\tan \left(\frac{\theta }{2}\right)$.

In other terms, the possibility of the Compton impact is determined by the number of electrons per gram in the absorbing medium, which would be generally the same as most substances. The only exception is hydrogen, which has no neutrons in its nucleus and hence has an electron density double that of all other atoms making the Compton effect irrespective of the absorber's number of atoms (Z). Whenever human tissues are bombarded in the 30-30000 MeV range of energies, which would be the diagnosis and therapy radiation range, the Compton impact is becoming the dominating mechanism.

Brief description of the Compton phenomenon

The study into the impact of X-rays on the matter was very well established in the early twentieth century. Whenever X-rays of certain wavelengths engage with particles, they are dispersed via an angle then emerge at a wavelength that is dependent on the angle. Despite the fact that classical electromagnetism anticipated that perhaps the wavelength of the scattered beams would be the same as the beginning wavelength, several investigations revealed that the wavelength of the scattered beams was longer (and so had lesser energy) than that of the starting wavelength.

Compton wrote a statement in 1923 describing the X-ray shifting by assigning atom momentum on light quanta which include the idea of Einstein hypothesized light quanta done in 1905 in an attempt to elucidate the photoelectric phenomenon. However, Compton did not expand on Einstein's study. The energy of light quanta is solely determined by the light's frequency. Compton used the assumption that each scattered X-ray photon interacts with only a single electron to determine the statistical link between both the change in wavelength as well as the scattering direction of the X-rays for their work. The study closes with a description of trials that corroborated his calculated relationship.

The incoming photons' energy must be in the range of an X-ray frequency to generate the Compton effect. The electron does not lose enough energy that reduces the wavelength of scattered photons towards the visible spectrum. As a result, with visible lights, the Compton effect is missing.

Wien’s displacement law

This law states that the black-body radiation curve for various temperatures peaks at different wavelengths. The peak wavelength is inversely proportional to the temperature. According to this, the product of the peak wavelength ($\lambda$),  and the corresponding temperature (T) is constant, i.e.,

$$\begin{gathered} \lambda T=\text{constant} \\ \text{or} \\ \lambda =\frac{\text{constant}}{T} \end{gathered}$$

Where $\lambda$ is the peak wavelength at a given temperature and $T$ is the temperature.

Formulae

• Change in wavelength of the scattered photon
  $∆\lambda =\frac{h}{mc}(1-\cos \theta )$

• Wien’s displacement law
  $\lambda T=\text{constant}$

Context and Applications

Compton scattering has several applications. Compton scattering is essential to radiobiology as it belongs to the interaction of gamma rays & strong X-rays involving atoms in organisms, and it is used in chemo and radiation treatment. For astrophysics, Inverse Compton scattering (ICS) is crucial which is an accretion disc encircling a black hole that is thought to provide a thermal spectrum for X-ray astronomy. In general, relativity electrons in the nearby corona scatter the reduced energy photons generated by such a spectrum into higher energies. Mostly the Inverse Compton scattering is used with the non-linearity concept.

This topic is useful for the students who are undergoing the following courses:

● Bachelors in Technology in Civil engineering
● Masters in Technology in Mechanical engineering
● Bachelors in Science in Chemical engineering
● Masters in Science in Chemical engineering

Practice Problems

1. Which of the following is the characteristic of a black body?

1. A perfect absorber but an imperfect radiator.
2. A perfect radiator but an imperfect absorber.
3. A perfect radiator and a perfect absorber.
4. A perfect conductor.
   

Answer- c

Explanation: When the radiations are made to pass through a black body, it undergoes multiple reflections and is completely absorbed. When it is placed in a temperature bath of fixed temperature, the heat radiations will come out. Thus a black body is a perfect absorber and a perfect reflector.

2. Rayleigh-Jeans law holds good for which of the following?

1. Shorter wavelength
2. Longer wavelength
3. High temperature
4. High energy
   

Answer- b

Explanation: According to this law, the energy distribution is directly proportional to the absolute temperature and is inversely proportional to the fourth power of the wavelength. Therefore the longer the wavelength, the greater is the energy distribution.

3. Which of the following does not affect the photon?

1. Magnetic or electric field
2. Light waves
3. Gravity
4. Current
   

Answer- a

Explanation: Photons have no charge. They can interact with charged particles but not with themselves. This is why photons are neutral and not affected by magnetic or electric fields.

4. Which of the following are called non-mechanical waves?

1. Magnetic waves
2. Electromagnetic waves
3. Electrical waves
4. Matter waves
   

Answer- b

Explanation: The waves which travel in the form of oscillating electric and magnetic waves are called electromagnetic waves. Such waves do not require any material for their propagation and are called non-mechanical waves.

5. Which of the following is associated with an electron microscope?

1. Matter waves
2. Electrical waves
3. Magnetic waves
4. Electromagnetic waves
   

Answer- a
Explanation: The waves associated with microscopic particles when they are in motion are called matter waves. Electron microscope makes use of the matter waves associated with fast-moving electrons.

Related Concepts

• Compton Effect
• Compton shift
• Wien’s displacement formulae
• History of the brief description and experiment setup
• Application