Enter the energy per mole and Avogadro’s number into the calculator to determine the energy per photon.
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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.
E_p = (E_m * 1000) / N_A
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) converts a bulk thermodynamic quantity to the energy carried by a single photon. 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. For direct photolysis, a photon must carry energy equal to or greater than the BDE per molecule. The table below maps common bonds to the minimum photon wavelength required to break them.
| Bond | BDE (kJ/mol) | J/photon | Min. 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 |
| Homolytic gas-phase BDE values. Min. λ = 119,626 / BDE (kJ/mol). Actual photolysis also requires absorption at that wavelength. Source: CRC Handbook of Chemistry and Physics. | ||||
Visible photons (170 to 300 kJ/mol, 400 to 700 nm) cannot directly break most covalent bonds. UV-A photons (300 to 380 kJ/mol, 315 to 400 nm) cleave weak C-Cl and C-Br bonds, explaining why chlorofluorocarbons photolyze in the stratosphere above the ozone layer. UV-C photons below 280 nm carry more than 430 kJ/mol, sufficient to break H-H, C-H, and N-H bonds in atmospheric molecules. Ozone absorbs UV-C strongly for this reason, since photons in that range exceed the O-O bond energy in ozone (approximately 105 kJ/mol for the weak terminal bond).
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 = 8.306 × 10⁻¹⁹ J/photon, corresponding to a UV-C photon at 239 nm, which exceeds the C-H bond dissociation energy (412 kJ/mol, 290 nm).