Energy of a 656 nm Photon in eV, Joules and kJ/mol

The calculator below is set to a wavelength of 656 nm, with the unit nm already chosen. It works out the energy of one photon of that light in electronvolts and joules, the energy of a mole of such photons in kJ/mol, and the photon momentum.

The formula is E = h × c / wavelength. With the wavelength in nanometers, the energy in electronvolts is simply 1239.84 divided by 656, and multiplying by 96.49 gives kJ/mol. The Planck constant, the speed of light, the electron charge and the Avogadro constant are all exact in today's SI, so none of these conversions carries rounding from the constants.

Add the power of a light source to count photons per second, or pick a metal to see whether this light can free electrons from its surface.

What one photon carries, and what a beam of them adds up to

A green laser pointer sold in the US must stay under 5 mW, and at that limit a 532 nm beam still fires 1.339 × 10¹⁶ photons every second, each carrying 2.331 eV. From a wavelength, a frequency or an energy in eV, joules or kJ/mol it gives one photon's energy, a mole's worth and the momentum; add a power to count photons per second, or a metal to test the photoelectric effect.

Working through the form

1
You know the - wavelength, frequency or photon energy. Only the matching boxes stay on screen.
2
Value and unit - nm, pm, angstroms, µm, mm or m; Hz to PHz; or meV, eV, keV, MeV, kJ/mol and joules × 10⁻¹⁹. A frequency may be typed as 5.45e14 or with grouped digits.
3
Light power (optional) - µW, mW or W from the label of the laser or LED. Leave it empty if you only need one photon.
4
Metal surface (optional) - one of fourteen metals for the photoelectric check, or No metal.
5
Read the result - energy in eV and joules, wavelength and frequency, kJ/mol, momentum, photons per joule, and the two optional blocks.

Electronvolts, joules or kJ/mol: three units for one number

The same 550 nm photon, three ways. Mixing up eV and joules puts an answer off by 6.242 × 10¹⁸, the number of electronvolts in one joule.

Parameter	eV	Joules	kJ/mol
A 550 nm photon	2.254 eV	3.612 × 10⁻¹⁹ J	217.50 kJ/mol
What it counts	one photon	one photon	6.02214076 × 10²³ photons
Exact link	1 eV = 1.602176634 × 10⁻¹⁹ J	SI unit	1 eV = 96.49 kJ/mol
Handy when	work functions	counting photons from watts	chemistry
Verdict	Keep the unit your other number is in; the result prints all three.

The formulas, and three photons worked by hand

E = h × f = h × c / λ p = h / λ = E / c photons per second = P / E
h = 6.62607015 × 10⁻³⁴ J·s, c = 299,792,458 m/s, N_A = 6.02214076 × 10²³ per mol, all exact

All four constants are exact in today's SI. With nanometers, h × c / e is 1239.84 eV·nm, and times 96.49 it gives 119,626.57 for kJ/mol.

A 532 nm photon. 1239.84 / 532 = 2.331 eV, which is 3.734 × 10⁻¹⁹ J; a mole of them is 224.86 kJ/mol, and each one pushes with a momentum of 1.246 × 10⁻²⁷ kg·m/s.

From kJ/mol back to a wavelength. 119,626.57 / 250 = 478.51 nm. Typed as an energy of 250 kJ/mol, the calculator shows 2.591 eV at 626.52 THz.

Photons in a 5 mW beam. 0.005 W / (3.734 × 10⁻¹⁹ J) = 1.339 × 10¹⁶ photons per second at 532 nm. The same power at 650 nm is 1.636 × 10¹⁶, because redder photons are smaller packets and it takes more of them.

Photoelectric thresholds for fourteen metals

A photon frees an electron only if it carries at least the metal's work function. Values are from the work function table in Wikipedia, which gives several metals a range rather than one number; the longest wavelength is 1239.84 divided by each value. Anything longer does nothing, whatever the power.

Metal	Work function	Longest wavelength that works
Caesium	1.95 eV	635.82 nm
Potassium	2.29 eV	541.42 nm
Sodium	2.75 eV	450.85 nm
Calcium	2.87 eV	432.00 nm
Lithium	2.9 eV	427.53 nm
Zinc	3.63 to 4.9 eV	253.03 to 341.55 nm
Aluminum	4.06 to 4.26 eV	291.04 to 305.38 nm
Silver	4.26 to 4.74 eV	261.57 to 291.04 nm
Tungsten	4.32 to 4.55 eV	272.49 to 287.00 nm
Copper	4.53 to 5.10 eV	243.11 to 273.70 nm
Iron	4.67 to 4.81 eV	257.76 to 265.49 nm
Nickel	5.04 to 5.35 eV	231.75 to 246.00 nm
Gold	5.10 to 5.47 eV	226.66 to 243.11 nm
Platinum	5.12 to 5.93 eV	209.08 to 242.16 nm

So a 532 nm pointer frees electrons from caesium, fastest at 380.530 meV, and from potassium at 40.530 meV, but falls 419.470 meV short on sodium. A 253.7 nm germicidal line is enough for some copper and zinc surfaces and 212.960 meV short on gold. Inside a range the result says borderline rather than guess.

Slips that give the wrong photon energy

Reading kJ/mol as energy per photon. 217.50 kJ/mol is a mole of 550 nm photons. Per photon it is 3.612 × 10⁻¹⁹ J, a factor of 6.02214076 × 10²⁰ smaller once the kilo is included.

Expecting brighter light to free faster electrons. The Wikipedia article on the photoelectric effect is explicit: more intensity raises the number of electrons, not their kinetic energy. A full watt of 650 nm light on gold frees none at all; each photon is 3.193 eV short.

Treating a work function as one fixed number. Copper spans 4.53 to 5.10 eV in the table, so a photon of 4.887 eV works on some copper and not on other copper. The result says borderline for exactly this case.

Photon questions, answered with numbers

What is the energy of a 405 nm photon?

3.061 eV, or 4.905 × 10⁻¹⁹ J, at 740.23 THz. A mole of them is 295.37 kJ/mol.

How do I convert eV to kJ/mol?

Multiply by 96.49. That factor is the charge of the electron times Avogadro's number divided by 1,000, both exact, so 1 eV is 96.49 kJ/mol and 13.6 eV is 1,312.20 kJ/mol.

How many photons per second does a 1 W source emit?

At 550 nm, 2.769 × 10¹⁸ per second, which is 4.598 × 10⁻⁶ mol/s. The same watt at 650 nm is 3.272 × 10¹⁸. Use the light output, not the electrical power drawn.

Does a photon have momentum if it has no mass?

Yes: p = h / λ with zero rest mass, per Wikipedia's photon article. At 550 nm that is 1.205 × 10⁻²⁷ kg·m/s.

What wavelength is a 13.6 eV photon?

91.16 nm, in the extreme ultraviolet, at 3.29 PHz. It carries about 6.033 times the energy of a 550 nm photon.

Does the calculator tell me the color?

No, it stays with energy. The Wavelength to Color Calculator takes the same inputs and names the band of the spectrum and the color, with the edges of each band converted.

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What is the energy of a photon with a wavelength of 656 nm?

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