Formula used
- Energy–frequency: E = h·f
- Vacuum wavelength: λ₀ = c / f
- Photon momentum (vacuum): p = E / c = h / λ₀
- Wave‑vector form: p = ħ·k, where k = 2π/λ₀
- Medium reference models (optional): Abraham p = E/(n·c), Minkowski p = n·E/c
- Radiation pressure (optional): absorber prad = I/c, reflector prad = 2I/c, with I = Power/Area
How to use this calculator
- Select an input mode: wavelength, frequency, or energy.
- Enter the value and choose its unit.
- Set refractive index n if you need medium references.
- Pick a momentum model and output unit.
- Optionally set N to compute total momentum.
- If needed, add power and area for radiation pressure.
- Press Calculate to view results above the form.
- Use the CSV or PDF buttons to export results.
Example data table
| Input | Value | Computed energy | Vacuum momentum (E/c) |
|---|---|---|---|
| Wavelength | 532 nm | ≈ 2.33 eV | ≈ 1.24×10⁻²⁷ kg·m/s |
| Frequency | 500 THz | ≈ 2.07 eV | ≈ 1.11×10⁻²⁷ kg·m/s |
| Energy | 1 keV | 1000 eV | ≈ 5.34×10⁻²⁵ kg·m/s |
Photon momentum in modern physics
Photons carry energy and momentum even though they have zero rest mass. In vacuum, the momentum magnitude is tied directly to energy by p = E/c. For a green laser at 532 nm, this gives a momentum near 1.25×10⁻²⁷ kg·m/s per photon, tiny but measurable through radiation pressure and recoil.
Core relations used by the calculator
The calculator connects three equivalent descriptions: wavelength, frequency, and energy. It uses E = h·f, f = c/λ₀, and p = h/λ₀, where λ₀ is the vacuum wavelength. It also shows the wave‑vector view p = ħk with k = 2π/λ₀.
Wavelength mode with medium option
If you enter wavelength, you can mark it as a value inside a material. In that case the calculator computes frequency as f = c/(n·λ). This is helpful for optics where the wavelength shortens in a medium while frequency stays constant across boundaries.
Frequency mode for broadband sources
Frequency is often the cleanest input for spectroscopy. Visible light spans roughly 430–770 THz. When you enter a frequency, the tool computes energy and the corresponding vacuum wavelength automatically, maintaining consistent SI units under the hood.
Energy mode and convenient units
Photon energy is commonly reported in electronvolts. For example, 2.0 eV corresponds to about 620 nm, while 1 keV X‑rays have much larger momentum. The calculator supports eV, keV, MeV, and joules, and can report momentum in eV/c for particle‑style work.
Momentum in media: reference models
For light in a dielectric, momentum definitions can differ depending on the chosen model. The calculator offers two common references: Abraham (E/(n·c)) and Minkowski (n·E/c). These options are provided for comparison and sensitivity checks when modeling materials.
Many‑photon totals and scaling
Real beams contain huge photon counts. Total momentum scales linearly as Ptotal = N·p. If a pulse contains 10¹⁸ photons at 2 eV, the summed momentum becomes macroscopic enough to matter for micro‑mechanics, optical trapping, and precision force experiments.
Radiation pressure and force extension
The optional pressure block uses intensity I = Power/Area. For a perfect absorber, pressure = I/c; for a perfect reflector, pressure = 2I/c. A 10 W beam spread over 1 cm² produces an intensity of 10⁵ W/m² and pressure on the order of 3.3×10⁻⁴ Pa.
FAQs
1) Why is photon momentum not zero?
Photons have no rest mass, but they carry energy. Relativity links energy flow to momentum, giving p = E/c in vacuum. This momentum enables light to exert radiation pressure and transfer recoil to matter.
2) Which input mode should I use?
Use wavelength for lasers and optics datasheets, frequency for spectroscopy, and energy for X‑ray or particle contexts. All three routes are equivalent once units are consistent.
3) What does “wavelength is in medium” mean?
If checked, the entered wavelength is treated as the shortened wavelength inside a material with refractive index n. The calculator then uses f = c/(n·λ) to keep frequency consistent.
4) What is the difference between Abraham and Minkowski?
They are two commonly cited momentum definitions for light in media. Abraham scales as E/(n·c), while Minkowski scales as n·E/c. The calculator provides both as reference comparisons.
5) How do I compute total momentum for a pulse?
Enter the photon count N. The calculator multiplies the per‑photon momentum by N to return total momentum. This is useful when you know pulse energy and can estimate N from E.
6) When is eV/c output useful?
eV/c is convenient when comparing photon momentum with particle momenta commonly reported in high‑energy physics. It avoids very small SI numbers while preserving correct physical dimensions.
7) How is radiation pressure computed here?
The tool uses pressure = I/c for an absorbing surface and 2I/c for a reflecting surface, with I = Power/Area. It then multiplies pressure by area to estimate force.