Atoms and Nuclei Cheatsheet

Cheat Codes & Shortcuts

• Bohr’s Model: Electron orbits nucleus in discrete energy levels, \( E_n = -\frac{13.6}{n^2} \, \text{eV} \).
• Radius of Orbit: \( r_n = \frac{n^2 h^2 \epsilon_0}{\pi m e^2} \), where \( n \) is principal quantum number.
• Energy of Photon: \( E = h \nu = \frac{h c}{\lambda} \), emitted/absorbed during transitions.
• Rydberg Formula: \( \frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \), \( R = 1.097 \times 10^7 \, \text{m}^{-1} \).
• Nuclear Mass Defect: \( \Delta m = [Z m_p + (A-Z) m_n] - M \), where \( M \) is nuclear mass.
• Binding Energy: \( BE = \Delta m c^2 \), energy required to separate nucleons.
• Radioactive Decay Law: \( N = N_0 e^{-\lambda t} \), where \( \lambda \) is decay constant.
• Half-Life: \( T_{1/2} = \frac{\ln 2}{\lambda} \approx \frac{0.693}{\lambda} \).
• Alpha Decay: \( _Z^A X \to _{Z-2}^{A-4} Y + _2^4 \text{He} \).
• Beta Decay (β⁻): \( _Z^A X \to _{Z+1}^A Y + _{-1}^0 e + \bar{\nu}_e \).

Quick Reference Table

Advice

Atoms and Nuclei Quick Tips

• Bohr’s Model: Use \( E_n = -\frac{13.6}{n^2} \, \text{eV} \) for hydrogen atom energy levels.
• Rydberg Formula: Apply \( \frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \) for spectral lines.
• Binding Energy: Calculate mass defect first, then use \( BE = \Delta m c^2 \).
• Decay Constant: Relate to half-life via \( T_{1/2} = \frac{\ln 2}{\lambda} \).
• Nuclear Reactions: Ensure conservation of atomic and mass numbers in alpha and beta decay.