Dual Nature of Radiation and Matter — Formula Sheet

E = h\nu

h\nu = \phi_0 + K_{\max}

K_{\max} = eV_0

K_{\max} = h(\nu - \nu_0)

\lambda = \frac{h}{p}

\lambda = \frac{h}{\sqrt{2mqV}}

\lambda = \frac{12.3}{\sqrt{V}} \ \text{Å}

p = \frac{h\nu}{c}

p = \frac{h}{\lambda}

The wavelength associated with a moving particle is given by λ = h/p.

eV₀ = (1/2)mv_max²: kinetic energy of fastest electron equals work done against stopping potential.

Einstein’s equation

hν = φ₀ + K_max.

K_max = h(ν − ν₀): kinetic energy depends on frequency, not intensity.

Einstein proposed that light consists of photons, each carrying energy E = hν.