Formula: Compton Scattering Wavelength before Scattering angle
$$\lambda' ~-~ \lambda ~=~ \frac{h}{m \, c } \, \left( 1 ~-~ \cos(\theta) \right)$$
$$\lambda ~=~ \lambda' - \frac{h}{m\,c} \, \left( 1 - \cos(\theta) \right)$$
$$\lambda' ~=~ \frac{h}{m\,c} \, \left( 1 - \cos(\theta) \right) + \lambda$$
$$\theta ~=~ \arccos\left( 1 - \frac{h}{m\,c}\,(\lambda - \lambda') \right)$$
Wavelength before
$$ \lambda $$ Unit $$ \mathrm{m} $$
Wavelength of the photon before the collision.
Wavelength after
$$ \lambda' $$ Unit $$ \mathrm{m} $$
Wellenlänge des Photons nach dem Stoß.
Scattering angle
$$ \theta $$ Unit $$ - $$
Scattering angle between the two momentum vectors of the photon after and before the collision.
Mass
$$ \class{brown}{m} $$ Unit $$ \mathrm{kg} $$
Mass of the particle (e.g. an electron) at which the photon is scattered.
Planck's Constant
$$ h $$ Unit $$ \mathrm{Js} $$
Planck's constant \( h \) is a physical constant from quantum mechanics and has the following exact value:
$$ h ~=~ 6.626 \, 070 \, 15 ~\cdot~ 10^{-34} \, \mathrm{Js} $$
Speed of light
$$ c $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$
Speed of light is a physical constant and indicates how fast light travels in empty space (vacuum). It has the following exact value in vacuum:
$$ c ~=~ 299 \, 792 \, 458 \, \frac{ \mathrm{m} }{ \mathrm{s} } $$