Dual Nature of Matter and Radiation Cheatsheet

Cheat Codes & Shortcuts

• Photoelectric Effect: \( E = h \nu \), where \( E \) is photon energy, \( h \) Planck’s constant, \( \nu \) frequency.
• Work Function: \( \phi = h \nu_0 \), minimum energy to eject an electron.
• Einstein’s Photoelectric Equation: \( h \nu = \phi + \frac{1}{2} m v_{\text{max}}^2 \).
• de Broglie Wavelength: \( \lambda = \frac{h}{p} = \frac{h}{m v} \), where \( p \) is momentum.
• Photon Momentum: \( p = \frac{h}{\lambda} = \frac{E}{c} \).
• Wave-Particle Duality: Matter exhibits both particle and wave-like properties.
• Uncertainty Principle: \( \Delta x \cdot \Delta p \geq \frac{h}{4 \pi} \).
• Planck’s Constant: \( h = 6.626 \times 10^{-34} \, \text{J·s} \).
• Stopping Potential: \( e V_s = \frac{1}{2} m v_{\text{max}}^2 \).
• Davisson-Germer Experiment: Confirms electron wave nature via diffraction.

Quick Reference Table

Advice

Dual Nature Quick Tips

• Photoelectric Effect: Use \( h \nu = \phi + \frac{1}{2} m v_{\text{max}}^2 \) for electron emission problems.
• de Broglie Wavelength: Apply \( \lambda = \frac{h}{p} \) for particles like electrons or protons.
• Photon Energy: Calculate energy using \( E = h \nu \) or \( E = \frac{h c}{\lambda} \).
• Uncertainty Principle: Use \( \Delta x \cdot \Delta p \geq \frac{h}{4 \pi} \) for position-momentum problems.
• Stopping Potential: Relate to kinetic energy via \( e V_s = \frac{1}{2} m v_{\text{max}}^2 \).