Particle Nature of Light

Photoelectric Effect

Theorem

Thrm Planck–Einstein Relation According to special relativity, photon energy is directly proportional to frequency:$E=h\nu =\hslash \omega =\frac{hc}{\lambda }$

Corollary

Corollary The momentum of a photon is then given by $p=\hslash k=\frac{h}{\lambda }$.

The Compton Effect

Theorem

Thrm Compton Scattering Formula The Compton scattering formula is:$\omega -{\omega }^{\prime }=\frac{2\hslash }{m{c}^2}\omega {\omega }^{\prime }{\sin }^2\frac{\theta }{2}$ which is equivalent in terms of wavelength: ${\lambda }^{\prime }-\lambda =2\frac{2\pi \hslash }{mc}{\sin }^2\frac{\theta }{2}$where ${\lambda }_c=\frac{2\pi \hslash }{mc}$ is the Compton wavelength of a particle with mass $m$.