Library / Foundations: Physics / FPH-61
Foundations: Physics
Photon energy from frequency
Energy of one photon of light or other electromagnetic radiation, equal to Planck’s constant times the frequency.
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- FPH-61
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- Foundations: Physics
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- E [J]
Planck’s constant h is 6.626 × 10⁻³⁴ J·s. The photon energy is h times the frequency, in joules; divide by 1.602 × 10⁻¹⁹ to get electronvolts. To start from wavelength instead of frequency, use the photon energy page.
Energy of one photon of light or other electromagnetic radiation, equal to Planck’s constant times the frequency. Higher frequency means more energy per photon.
Calculator
- Energy in electronvolts2.068 eV
- Wavelength, c/ν599.6 nm
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- A photon of 500 THz carries 2.068 eV, which corresponds to a wavelength of 599.6 nm.
- Energy is directly proportional to frequency: doubling the frequency doubles each photon’s energy.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (J) | Local step | Change in result |
|---|---|---|---|---|---|---|
| ν Frequency | 1e9 to 1e20 Hz | 6.626e-25 | 6.626e-14 | 6.626e-14 | +10% | +10 % |
Sweep of Frequency
| Frequency (Hz) | Photon energy (J) |
|---|---|
| 1e9 | 6.626e-25 |
| 2.371e10 | 1.571e-23 |
| 5.623e11 | 3.726e-22 |
| 1.334e13 | 8.836e-21 |
| 3.162e14 | 2.095e-19 |
| 7.499e15 | 4.969e-18 |
| 1.778e17 | 1.178e-16 |
| 4.217e18 | 2.794e-15 |
| 1e20 | 6.626e-14 |
Sweep one variable
Variables and how each one contributes
Photon energy
What the equation gives you. Everything else feeds it.
Frequency
The frequency of the radiation, in Hz. Raises the photon energy in direct proportion. Raising it by 10 % (to 5.5×1014) moves the result by +10 %, from 3.313×10−19 to 3.644×10−19 J.
Worked example with the values above
- h = 6.626 × 10⁻³⁴ J·s.
- E = hν = 6.626 × 10⁻³⁴ × 5×1014.
- E = 3.31304×10−19 J, which is 2.0678 eV.
Assumptions and limits
- A single photon of one frequency.
- Frequency measured in hertz, not angular frequency.
Common mistakes
- Using angular frequency ω in place of ν (that needs ħ, not h).
- Mixing joules and electronvolts.
- Putting a wavelength in the frequency box.
Statistics and uncertainty
The formula is exact. The uncertainty is that of the frequency, which can be measured to extremely high precision for lasers and atomic transitions.
Where it is used
- Comparing LED, laser and X-ray photon energies.
- Checking photoelectric and band-gap thresholds.
Maths you need
- Frequency and wavelength: c = fλ
- Electronvolt: energy gained by an electron through 1 V