How the conversions work
Each field is a different way of writing the same energy \(E\). For a photon,
Molar energy multiplies by Avogadro's number, \(E_m = N_A E\). The temperature equivalent divides by Boltzmann's constant, \(T = E/k_B\): it is the temperature at which \(k_BT\) equals the energy. Wavelength and energy are inversely proportional, so the converter works through energy internally and is exact in both directions.
Quick reference
| eV | cm⁻¹ | kJ/mol | kcal/mol | K | |
|---|---|---|---|---|---|
| 1 eV | 1 | 8065.544 | 96.4853 | 23.0605 | 11604.52 |
| 1 Eh | 27.21139 | 219474.63 | 2625.500 | 627.5095 | 315775.0 |
| 1 cm⁻¹ | 1.239842 × 10⁻⁴ | 1 | 0.0119627 | 0.00285914 | 1.438777 |
| 1 kJ/mol | 0.0103643 | 83.5935 | 1 | 0.239006 | 120.272 |
| 1 kcal/mol | 0.0433641 | 349.755 | 4.184 | 1 | 503.217 |
Useful anchors: \(hc = 1239.842\) eV·nm, so a 1240 nm photon carries about 1 eV. One wavenumber corresponds to 29.979 GHz. Thermal energy at room temperature (298.15 K) is \(k_BT \approx 207.2\) cm⁻¹ = 25.69 meV = 2.479 kJ/mol.
Why spectroscopists use wavenumbers
The wavenumber \(\tilde\nu\) is proportional to energy, unlike wavelength, so spacings between levels add and subtract linearly. A vibrational fundamental at 3000 cm⁻¹ and its overtone near 6000 cm⁻¹ sit at proportional positions, while in wavelength they appear at 3.33 µm and 1.67 µm. Wavenumbers are also measured directly by interferometric (FTIR) and grating instruments, and they are easy to read for chemists: 1 kcal/mol ≈ 350 cm⁻¹.
Vacuum versus air wavelengths
The converter works with vacuum wavelengths. Visible and near-IR lines are often tabulated in standard air, where \(\lambda_\text{air} = \lambda_\text{vac}/n\) and \(n - 1 \approx 2.7\text{–}2.9 \times 10^{-4}\). The difference is about 0.18 nm at 633 nm, which matters for line identification and spectrometer calibration but not for most laser-process work. For 300–1690 nm the panel above shows the standard-air wavelength from Ciddor's dispersion equation (15 °C, 101.325 kPa, dry, 450 ppm CO₂).
Constants used
| Quantity | Symbol | Value |
|---|---|---|
| Speed of light | c | 299 792 458 m/s (exact) |
| Planck constant | h | 6.626 070 15 × 10⁻³⁴ J·s (exact) |
| Elementary charge | e | 1.602 176 634 × 10⁻¹⁹ C (exact) |
| Boltzmann constant | kB | 1.380 649 × 10⁻²³ J/K (exact) |
| Avogadro constant | NA | 6.022 140 76 × 10²³ mol⁻¹ (exact) |
| Hartree energy | Eh | 4.359 744 722 2071 × 10⁻¹⁸ J |
| Thermochemical calorie | cal | 4.184 J (exact) |
References
- E. Tiesinga, P. J. Mohr, D. B. Newell, B. N. Taylor, “CODATA recommended values of the fundamental physical constants: 2018,” Rev. Mod. Phys. 93, 025010 (2021).
- P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” Appl. Opt. 35, 1566–1573 (1996).
- ISO 21348:2007, Space environment — Process for determining solar irradiances (UV, VUV, and EUV category definitions). The infrared band labels on this page follow common photonics usage (NIR to 1.4 µm, SWIR to 3 µm, MWIR 3–8 µm, LWIR 8–15 µm) rather than ISO's IR-A/B/C.