Appendix B — Physical Constants and Unit Conversions
The values below are rounded to six significant figures, which is more than enough for every calculation in this book. Exact values (marked with *) are fixed by the definition of the SI units. For the full list with all digits, see the NIST reference on constants (National Institute of Standards and Technology, n.d.).
| Constant | Symbol | Value |
|---|---|---|
| Planck constant* | \(h\) | \(6.62607\times10^{-34}\;\text{J s}\) |
| Reduced Planck constant | \(\hbar=h/2\pi\) | \(1.05457\times10^{-34}\;\text{J s}\) |
| Speed of light in vacuum* | \(c\) | \(2.99792\times10^{8}\;\text{m s}^{-1}\) |
| Elementary charge* | \(e\) | \(1.60218\times10^{-19}\;\text{C}\) |
| Electron mass | \(m_e\) | \(9.10938\times10^{-31}\;\text{kg}\) |
| Proton mass | \(m_p\) | \(1.67262\times10^{-27}\;\text{kg}\) |
| Atomic mass unit | \(\text{u}\) | \(1.66054\times10^{-27}\;\text{kg}\) |
| Vacuum permittivity | \(\varepsilon_0\) | \(8.85419\times10^{-12}\;\text{C}^2\,\text{J}^{-1}\,\text{m}^{-1}\) |
| Avogadro constant* | \(N_A\) | \(6.02214\times10^{23}\;\text{mol}^{-1}\) |
| Boltzmann constant* | \(k_B\) | \(1.38065\times10^{-23}\;\text{J K}^{-1}\) |
| Bohr radius | \(a_0\) | \(5.29177\times10^{-11}\;\text{m} = 0.529177\;\text{Å}\) |
| Hartree energy | \(E_h\) | \(4.35974\times10^{-18}\;\text{J}\) |
| Rydberg constant | \(R_\infty\) | \(1.09737\times10^{5}\;\text{cm}^{-1}\) |
Spectroscopists, chemists, and computational chemists all use different energy units. Table B.2 converts between the ones used in this book. To use it, read across a row: for example, \(1\;\text{eV} = 96.4853\;\text{kJ/mol}\).
| \(E_h\) | eV | kJ/mol | cm\(^{-1}\) | |
|---|---|---|---|---|
| 1 \(E_h\) | 1 | 27.2114 | 2625.50 | 219475 |
| 1 eV | 0.0367493 | 1 | 96.4853 | 8065.54 |
| 1 kJ/mol | \(3.80880\cdot10^{-4}\) | 0.0103643 | 1 | 83.5935 |
| 1 cm\(^{-1}\) | \(4.55634\cdot10^{-6}\) | \(1.23984\cdot10^{-4}\) | 0.0119627 | 1 |
A few more relations that are useful in practice:
- Photon energy and wavelength: \(E=hc/\lambda\), with \(hc = 1239.84\;\text{eV nm}\). A photon of \(500\;\text{nm}\) therefore carries \(2.48\;\text{eV}\).
- Wavenumbers: \(\tilde{\nu} = 1/\lambda\), so a wavelength of \(1\;\mu\text{m}\) corresponds to \(10{,}000\;\text{cm}^{-1}\).
- Thermal energy at room temperature (\(298\;\text{K}\)): \(k_BT = 0.0257\;\text{eV} = 207\;\text{cm}^{-1}\), and \(RT = 2.48\;\text{kJ/mol}\).
- Lengths: \(1\;\text{Å} = 10^{-10}\;\text{m} = 100\;\text{pm}\), and \(1\;a_0 = 0.529177\;\text{Å}\).