Convert energy per mole in kJ/mol, J/mol, cal/mol, or kcal/mol to energy per photon, wavelength, frequency, and approximate spectral region.
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kJ/mol To J/Photon Formula
The following formula is used to calculate the energy per photon from the energy per mole.
Variables:
- E_p is the energy per photon (J)
- E_m is the energy per mole (kJ/mol)
- N_A is Avogadro’s number (6.02214076 × 10²³ mol⁻¹)
Dividing molar energy by Avogadro’s number (6.02214076 × 10²³ mol⁻¹) gives energy per entity. It represents energy per photon only when the molar quantity describes one mole of identical photons, or an explicitly assumed equivalent photon energy. The factor of 1,000 converts kJ to J. One kJ/mol equals 1.66054 × 10⁻²¹ J per photon.
| Energy (kJ/mol) | Energy/Photon (J) | Wavelength (nm) | Spectral Region |
|---|---|---|---|
| 10 | 1.66×10⁻²⁰ | 11,963 | Mid IR |
| 25 | 4.15×10⁻²⁰ | 4,785 | Mid IR |
| 50 | 8.30×10⁻²⁰ | 2,393 | Near IR |
| 75 | 1.25×10⁻¹⁹ | 1,595 | Near IR |
| 100 | 1.66×10⁻¹⁹ | 1,196 | Near IR |
| 125 | 2.08×10⁻¹⁹ | 957 | Near IR |
| 150 | 2.49×10⁻¹⁹ | 797 | Near IR |
| 175 | 2.91×10⁻¹⁹ | 684 | Visible (red) |
| 200 | 3.32×10⁻¹⁹ | 598 | Visible (orange) |
| 250 | 4.15×10⁻¹⁹ | 479 | Visible (blue) |
| 300 | 4.98×10⁻¹⁹ | 399 | UV-A |
| 350 | 5.81×10⁻¹⁹ | 342 | UV-A |
| 400 | 6.64×10⁻¹⁹ | 299 | UV-B |
| 450 | 7.47×10⁻¹⁹ | 266 | UV-C |
| 500 | 8.30×10⁻¹⁹ | 239 | UV-C |
| 600 | 9.96×10⁻¹⁹ | 199 | UV-C |
| 700 | 1.16×10⁻¹⁸ | 171 | VUV |
| 800 | 1.33×10⁻¹⁸ | 150 | VUV |
| 900 | 1.49×10⁻¹⁸ | 133 | VUV |
| 1000 | 1.66×10⁻¹⁸ | 120 | VUV |
| λ (nm) = 119,626 / E (kJ/mol). VUV = vacuum ultraviolet (<200 nm). Visible: 400 to 700 nm. UV-A: 315 to 400 nm. UV-B: 280 to 315 nm. UV-C: 100 to 280 nm. | |||
Photon Energy and Chemical Bonds
Bond dissociation energies (BDEs) are reported in kJ/mol, placing them on the same scale this calculator uses. Comparing photon energy with a representative BDE gives a simple energy threshold; sufficient energy alone does not guarantee photolysis. The table below maps common bonds to the longest wavelength corresponding to those illustrative energy thresholds. Absorption and reaction pathways must also be considered.
| Bond | BDE (kJ/mol) | J/photon | Max. λ (nm) | UV Region |
|---|---|---|---|---|
| F–F | 159 | 2.64×10⁻¹⁹ | 753 | NIR |
| I–I | 151 | 2.51×10⁻¹⁹ | 793 | NIR |
| Br–Br | 194 | 3.22×10⁻¹⁹ | 616 | Visible |
| Cl–Cl | 243 | 4.04×10⁻¹⁹ | 492 | Visible |
| C–Cl | 339 | 5.63×10⁻¹⁹ | 353 | UV-A |
| C–C | 347 | 5.76×10⁻¹⁹ | 345 | UV-A |
| N–H | 391 | 6.49×10⁻¹⁹ | 306 | UV-B |
| C–H | 412 | 6.84×10⁻¹⁹ | 290 | UV-B |
| H–H | 436 | 7.24×10⁻¹⁹ | 274 | UV-C |
| O–H | 459 | 7.62×10⁻¹⁹ | 261 | UV-C |
| Illustrative approximate homolytic gas-phase bond energies; generic bond values vary with molecular environment. Max. λ = 119,626 / BDE (kJ/mol). Actual photolysis also requires absorption at that wavelength. Source: CRC Handbook of Chemistry and Physics. | ||||
Photon energy thresholds provide an energy comparison, not a guarantee of bond cleavage. A molecule must absorb the radiation, and its electronic states, molecular environment and competing reaction pathways affect photolysis. Generic bond energies in the table are illustrative; use molecule-specific data for reaction predictions.
Unit Equivalencies
Photon energies appear in eV in physics and semiconductor science, in kJ/mol in chemistry, and in J/photon in quantum calculations. The bridging constant is 1 eV = 96.485 kJ/mol, and the wavelength relation λ (nm) = 119,626 / E (kJ/mol) applies throughout.
| kJ/mol | eV/photon | J/photon | λ (nm) | Reference Point |
|---|---|---|---|---|
| 1 | 0.01036 | 1.661×10⁻²¹ | 119,627 | 1 kJ/mol base unit |
| 96.485 | 1.000 | 1.602×10⁻¹⁹ | 1,240 | 1 eV (semiconductor bandgap reference) |
| 175 | 1.81 | 2.91×10⁻¹⁹ | 684 | Chlorophyll-a red absorption (680 nm) |
| 278 | 2.88 | 4.62×10⁻¹⁹ | 430 | Chlorophyll-a blue absorption (430 nm) |
| 436 | 4.52 | 7.24×10⁻¹⁹ | 274 | H-H bond dissociation threshold |
| 500 | 5.18 | 8.31×10⁻¹⁹ | 239 | UV-C photolysis range |
| 1000 | 10.36 | 1.661×10⁻¹⁸ | 120 | VUV photoionization range |
| 1 eV = 96.485 kJ/mol = 1.60218×10⁻¹⁹ J. λ (nm) = 119,626/E (kJ/mol). Nₐ = 6.02214076×10²³ mol⁻¹. | ||||
How to Calculate kJ/mol To J/Photon
- Determine the energy per mole (E_m) in kJ/mol.
- Multiply E_m by 1,000 to convert from kJ to J, giving J/mol.
- Divide by Avogadro’s number (6.02214076 × 10²³) to obtain energy per photon in joules.
Example: E_m = 500 kJ/mol
E_p = (500 × 1,000) / (6.02214076 × 10²³) = 8.303 × 10⁻¹⁹ J/photon, corresponding to a UV-C photon at 239 nm, above the illustrative C-H energy threshold (412 kJ/mol, 290 nm); absorption and reaction pathways still determine whether cleavage occurs.
