How this instrument works
Max Planck introduced energy quanta in 1900 as mathematical scaffolding to make blackbody radiation curves come out right; he did not believe light itself was lumpy. Einstein did. His 1905 photoelectric paper argued that radiation arrives in discrete packets worth hc/λ apiece, which explained why a feeble ultraviolet lamp ejects electrons from metal while a blazing red one ejects none. Energy set by colour rather than by brightness — that claim earned a Nobel Prize in 1921 and handed quantum mechanics its first hard experimental footing. Gilbert Lewis named those packets photons in 1926.
Magnitudes here are small and worth memorising. Visible quanta span roughly 1.8 electronvolts at deep red to 3.1 at violet, or 2.8 × 10⁻¹⁹ up to 5.0 × 10⁻¹⁹ joules. One shortcut spectroscopists live by: hc equals 1239.84 eV·nm, so dividing 1240 by wavelength in nanometres gives electronvolts to four figures. Silicon's 1.12 eV bandgap lands at 1107 nm, which is precisely why silicon solar cells throw away every infrared quantum past that line — however many arrive, not one of them can lift an electron across.
Two assumptions hide inside E = hc/λ. First, λ must be a vacuum wavelength. Inside glass or water light slows and its wave contracts by its refractive index, yet its energy does not shift at all; frequency is what survives crossing a boundary, so E = hν is the primary statement and hc/λ merely a vacuum convenience. Second, energy depends on who is looking. A quantum emitted at 500 nm by a distant galaxy reaches us stretched and softened — cosmological redshift is no illusion painted over some fixed value, but a genuine reduction measured in our frame.
- Set Wavelength and pick the unit — nm suits lasers and spectral lines, mm suits microwave and terahertz work.
- Use vacuum figures. Quoted emission lines such as 589 nm may be air values; air shifts results by 0.03%.
- Read Photon energy in joules, or switch that field to kJ when scaling up toward a mole of quanta.
- Divide the joules answer by 1.602176634 × 10⁻¹⁹ for electronvolts, the unit spectroscopists actually speak.
- For beams rather than one quantum, multiply this per-photon figure by how many arrive each second.
Worked example — one green photon at 500 nm
Set Wavelength to 500 nm, mid-green and close to where daylight vision peaks. In SI that is 5 × 10⁻⁷ m. Substituting: E = (6.62607015 × 10⁻³⁴ × 299792458) ⁄ 5 × 10⁻⁷, so E = 1.986445857 × 10⁻²⁵ J·m ÷ 5 × 10⁻⁷ m = 3.9728917143 × 10⁻¹⁹ J.
Divide by an elementary charge and you get 2.48 electronvolts, exactly what spectroscopy tables print for green. That number also sizes a laser pointer: 1 mW at this colour is a millijoule each second, and a millijoule divided by 3.9729 × 10⁻¹⁹ comes to roughly 2.5 × 10¹⁵ quanta leaving that aperture per second — which is why single-photon counting demands heavy attenuation before any detector will cope.
Questions
Should I enter the wavelength in air or in vacuum?
Vacuum. Refraction shortens waves inside glass or water while leaving their frequency, and therefore their energy, untouched. Air is close enough for most purposes — refractive index near 1.0003 moves an answer by 0.03% — but published spectral lines sometimes come as air values, so check your source. Sodium's D2 line is 588.995 nm in air and 589.158 nm in vacuum.
How do I convert the answer into electronvolts?
Divide joules by 1.602176634 × 10⁻¹⁹, an elementary charge, exact by SI definition since 2019. Faster still, skip joules: energy in electronvolts equals 1239.84 divided by wavelength in nanometres. Green at 500 nm gives 2.48 eV, red at 650 nm gives 1.91 eV, and a 10 keV medical X-ray sits at 0.124 nm.
Does a brighter lamp emit more energetic photons?
No. Brightness fixes how many quanta arrive per second; colour fixes what each one carries. That distinction is precisely what Einstein resolved in 1905 — dim ultraviolet frees electrons from metal surfaces while intense red frees none, because no pile-up of weak quanta substitutes for one single quantum above threshold. Turning up a red lamp only sends more red.
When does this relation stop being true?
For a lone quantum in vacuum it never breaks; E = hν is exact, not an approximation. What breaks is single-wavelength thinking. Real sources carry bandwidth — a 100 fs pulse near 500 nm spans several nanometres by its time–bandwidth limit — so feeding a centre wavelength gives an average, not a value every quantum in that pulse shares.
How is photon energy related to momentum?
Momentum follows p = h/λ = E/c, so one wavelength fixes both quantities. A massless quantum still pushes: sunlight exerts roughly 9 micronewtons per square metre against a perfect reflector at Earth's orbit. That tiny pressure drives solar sails, and IKAROS in 2010 became first to cross interplanetary space on it.
Why are h and c quoted without any uncertainty?
Since 20 May 2019 Planck's constant has been defined as exactly 6.62607015 × 10⁻³⁴ J·s, and that definition is what now fixes a kilogram. Redefinition of a metre had already pinned c at exactly 299792458 m/s back in 1983. Their product is therefore an exact number, meaning every digit returned here traces to your wavelength alone.