Compton Effect

The Compton effect explains the change in wavelength of photons after colliding with an object (and transferring energy). It further supports the particle nature of Light through means of X-ray radiation.

Definition §

The X-rays are emitted as high-energy photons. When they collide with an electron, they transfer a quantised amount of energy to the electron, and lost that energy, due to the Conservation of Energy. The angle of scattering is accounted for by the conservation of Momentum.

The change in energy (of the photon), also results in a change of wavelength.

Formulae §

Compton Effect ^formula

$$\Delta \lambda ={\lambda }_f-{\lambda }_i={\lambda }_{compton}(1-\cos (\varphi ))=\frac{h}{m_{e}c}(1-\cos (\varphi ))$$

• $\Delta \lambda$ = Change in Wavelength of the photon (in $\text{m}$)
  • ${\lambda }_i$ = Wavelength before collision with electron
  • ${\lambda }_f$ = Wavelength after collision
• $h$ = Planck’s Constant $\approx 6.63\times 10^{-34}\text{ Js}$
• $m_e$ = Mass of an Electron (in $\text{kg}$)
• $c$ = Speed of light $\approx 3\times 10^8\text{ m/s}$
• $\varphi$ = Angle of photon deflection (NOT ELECTRON!)

Derivation §

Electron has non-zero momentum due to Heisenberg principle. #TODO