Photon Energy
Light consists of photons — discrete packets of energy. A photon's energy depends on its frequency: higher frequency (shorter wavelength) = more energy per photon.
Planck's Equations
E = h × f
E = h × c / λ
h = 6.626×10⁻³⁴ J·s (Planck's constant)
c = 3×10⁸ m/s (speed of light)
f = frequency (Hz)
λ = wavelength (m)Worked Examples
Green light (λ=550 nm = 5.5×10⁻⁷ m):
E = 6.626×10⁻³⁴ × 3×10⁸ / 5.5×10⁻⁷
E = 3.61×10⁻¹⁹ J = 2.26 eV
X-ray (λ=0.1 nm = 10⁻¹⁰ m):
E = 1.99×10⁻¹⁵ J = 12,400 eV = 12.4 keVJoules to Electron-Volts
1 eV = 1.602×10⁻¹⁹ J
E (eV) = E (J) / 1.602×10⁻¹⁹
Visible light: 1.7 eV (red) to 3.3 eV (violet)
UV photon: 3.4–124 eV
Gamma ray: >100 keVCalculate photon energy: Free Photon Energy Calculator
Photon Wavelength–Energy Quick-Reference Table
| Type | Wavelength | Frequency (Hz) | Energy per photon (eV) |
|---|---|---|---|
| Radio | >1 m | <3×10⁸ | <1.24×10⁻⁶ |
| Infrared | 700 nm–1 mm | 3×10¹¹–4×10¹⁴ | 0.001–1.77 |
| Red light | 700 nm | 4.28×10¹⁴ | 1.77 |
| Violet light | 400 nm | 7.49×10¹⁴ | 3.10 |
| UV-C | 100–280 nm | 10¹⁵–3×10¹⁵ | 4.4–12.4 |
| X-ray (medical) | 0.01–10 nm | 3×10¹⁶–3×10¹⁹ | 100–100,000 |
How Wavelength and Photon Energy Relate
Every photon carries energy E = hf = hc/λ, where h = 6.626×10⁻³⁴ J·s (Planck's constant), c = 3×10⁸ m/s (speed of light in vacuum), and λ is wavelength. Shorter wavelength = higher frequency = higher energy per photon. Visible light (400–700 nm) carries 1.77–3.10 eV per photon. This is why ultraviolet light can break chemical bonds and cause sunburn while visible light cannot.
The electron-volt (eV) is convenient: 1 eV = 1.602×10⁻¹⁹ J. Typical chemical bond energies are 1–5 eV, which explains why UV photons can initiate photochemical reactions while IR photons (< 1 eV) only cause molecular vibration (heat). Photovoltaic cells need photons with E ≥ band gap (≈1.1 eV for silicon) to excite electrons into the conduction band.
Common Mistakes
- Wrong wavelength unit: λ must be in metres in E = hc/λ. Plugging in nanometres directly gives answers 10⁹ times too large.
- Confusing energy of one photon with beam power: E = hf is per photon. A laser with 1 mW power emits many billions of photons per second; divide power by E per photon to find photon flux.
- Mixing eV and Joules: Be consistent — if using eV, note h = 4.136×10⁻¹⁵ eV·s. If using Joules, h = 6.626×10⁻³⁴ J·s.
Frequently Asked Questions
X-ray photons (1–100 keV) have enough energy to overcome the binding energy of inner-shell electrons, causing photoionisation. Visible light photons (1.77–3.1 eV) interact with outer electrons and are absorbed or reflected by the molecular bonds of skin and tissue. The high energy of X-rays also means fewer are absorbed per unit thickness, allowing transmission through soft tissue while being blocked by dense bone.
The photoelectric effect (Nobel Prize, Einstein 1921) shows that light ejects electrons from metals only when photon energy exceeds the material's work function, regardless of intensity. For sodium (work function 2.3 eV), only photons with λ < 540 nm can eject electrons. This proved light's quantum (particle) nature and underpins photomultiplier tubes, CCD image sensors, and solar cells.
A blackbody radiator's spectrum peaks at λ_peak = 2,898 μm·K / T (Wien's displacement law). The Sun (5,778 K) peaks at 500 nm (green), matching peak human visual sensitivity. A tungsten bulb filament (2,700 K) peaks at 1,070 nm (near-IR), making it thermally inefficient — most energy is emitted as heat. LED lights tune their emission to match human vision more efficiently.