Dual Nature of Radiation and Matter - Formula Sheet

Radiation as Particles (Photons)

• Photon Energy: \(E = h\nu = \frac{hc}{\lambda}\)
  (\(h\): Planck's constant \(\approx 6.626 \times 10^{-34}\) Js, \(\nu\): frequency, \(c\): speed of light, \(\lambda\): wavelength)
• Photon Momentum: \(p = \frac{E}{c} = \frac{h}{\lambda}\)
• Einstein's Photoelectric Equation: \(K_{max} = h\nu - \phi_0\)
  (\(K_{max}\): maximum kinetic energy, \(\phi_0\): work function)
• Stopping Potential Relation: \(K_{max} = eV_0\)
  (\(e\): electron charge, \(V_0\): stopping potential)
• Threshold Frequency: \(\nu_0 = \frac{\phi_0}{h}\)

Matter as Waves

• De Broglie Wavelength: \(\lambda = \frac{h}{p} = \frac{h}{mv}\)
  (\(m\): mass of the particle, \(v\): velocity)
• Wavelength in terms of Kinetic Energy (K): \(\lambda = \frac{h}{\sqrt{2mK}}\)
• Wavelength of Accelerated Electron: \(\lambda = \frac{h}{\sqrt{2meV}} \approx \frac{12.27}{\sqrt{V}}\) Å
  (\(V\): accelerating potential in Volts)

X-Ray Production

• Duane-Hunt Law (Cutoff Wavelength): \(\lambda_{min} = \frac{hc}{eV} \approx \frac{12400}{V}\) Å
  (\(V\): accelerating voltage)
• Bragg's Law (Diffraction): \(2d \sin \theta = n\lambda\)
  (\(d\): interplanar spacing, \(\theta\): glancing angle, \(n\): order of diffraction)