Compton used photons of wavelength 0.0711 nm (a) What is the energy of these photons? (b) What i

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Compton used photons of wavelength 0.0711 nm (a) What is the...

Compton used photons of wavelength $0.0711 \mathrm{nm}$ (a) What is the energy of these photons? (b) What is the wavelength of the photons scattered at an angle of $180^{\circ}$ (backscattering case)? (c) What is the energy of the backscattered photons? (d) What is the recoil energy of the electrons in this case?

Compton used photons of wavelength $0.0711 \mathrm{nm}$
(a) What is the energy of these photons? (b) What is the wavelength of the photons scattered at an angle of $180^{\circ}$ (backscattering case)? (c) What is the energy of the backscattered photons? (d) What is the recoil energy of the electrons in this case?

Key Concepts

Recoil Energy of Electrons

The recoil energy of electrons in Compton scattering comes from the energy transferred from the photon to the electron during the interaction. This energy transfer is determined by the difference between the initial photon energy and the energy of the scattered photon, illustrating how kinetic energy is imparted to the electron as a result of momentum conservation during the collision.

Compton Wavelength Shift

The Compton wavelength shift is given by the formula ?? = ?_C (1 - cos?), where ?_C is the Compton wavelength of the electron and ? is the scattering angle. This relation quantifies the increase in the photon’s wavelength as a result of its collision with an electron, with the maximum shift occurring for a scattering angle of 180° (backscattering).

Photon Energy

This concept involves the quantization of electromagnetic radiation, where the energy of a photon is calculated using the relation E = hc/?. Here, h is Planck’s constant and c is the speed of light. The energy of a photon is inversely proportional to its wavelength, meaning that shorter wavelengths correspond to higher energies.

Compton Scattering

Compton scattering describes the inelastic scattering of a photon by a charged particle, typically an electron, resulting in a transfer of energy and momentum. This process is governed by the principles of conservation of energy and momentum, leading to a change in the wavelength of the scattered photon compared to the incident photon.

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