Compton Effect | Quantum mechanics | Physical basis of quantum mechanics

Compton Effect (Quantum nature of light)

• Compton effect was discovered by A.H. Compton.
• When a beam of monochromatic X-rays of wavelength λ is scattered by a light element (carbon), then the scattered X-rays have maximum intensities at two wavelengths, one of them at the same wavelength λ and the other at slightly longer wavelength λ՛. This effect is known as Compton effect.
• The difference in wavelength (λ - λ՛) is known as Compton shift.

Theory 

• The energy of incident photon, E₁ = hν
• Momentum of incident photon, p₁ = hν/c
• This photon strikes with an electron at rest.

Before collision

• Momentum of electron, p₂ = 0
• Energy of electron (rest mass energy), E₂ = m₀c²

After collision

• The photon scattered from its original path by giving some of its kinetic energy to the electron and the electron recoils.
• Energy of scattered photon, E₁՛ = hν՛
• Momentum of scattered photon, p₁՛ = hν՛/c
• The scattered photon move in a direction making an angle θ with the X-axis.
• The energy of electron, E₂՛ = mc²
• Momentum of electron, p₂՛ = mv
• This electron moves in a direction making an angle ϕ with the X-axis.

From the law of conservation of energy

            E₁ + E₂ = E₁՛ + E₂՛

            hν + m₀c² = hν՛ + mc²

            mc² = h (ν - ν՛) + m₀c²

From the law of conservation of momentum 

• Momentum along X-axis

• Momentum along Y-axis

• From relativistic formula

• This is the change in wavelength of X-rays and is known as Compton shift in the wavelength of X-rays.
• Here λ_c is Compton wavelength and its value is given by
• λ_c = h / m₀c = 0.0242Å

Conclusion

• Compton shift is independent of the wavelength of the incident radiation and nature of the scattering substance.
• It depends only on the scattering angle θ.

Special cases

• It is the maximum value of Compton shift.

Experimental setup

Experimental setup of Compton effect

Relative intensities versus wavelength curve of Compton effect at different angles

• The excellent agreement between the Compton shift obtained from Compton theory and the experimental results confirms that the elastic collision between a photon and an electron is just like an elastic collision between two particles.
• The Compton effect proves the quantum theory (particle nature) of radiation.
• To know more about Compton effect, please click on the link https://youtu.be/hwQaqo6Gwz4 and for bilingual lecture (Hindi/English) https://youtu.be/KNiPYOq274U