Photon Momentum Calculator

Photons carry momentum despite having zero rest mass. Photon momentum p = h/lambda = E/c. This causes radiation pressure, enables solar sails, and was confirmed by Compton scattering.

💡 Quantum Physics📐 p = h/λ⚛️ Wave-Particle Duality
Wavelength (nm)
Or Photon Energy (eV)
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Formula & Reference

VariableSymbolFormulaUnits
Momentumpp = h/λ = E/ckg·m/s
Wavelengthλλ = h/pm
EnergyEE = pc = hfJ
Planck Constanth6.626 × 10⁻³⁴ J·sJ·s

Step-by-Step Examples

Example 1
Visible Light

Green photon lambda=500 nm.

  • p = h/lambda = 6.626e-34/500e-9 = 1.325e-27 kg*m/s
  • E = p*c = 2.48 eV
✓ 1.325e-27 kg*m/s — tiny but real momentum
Example 2
X-Ray Photon

X-ray lambda=0.1 nm.

  • p = 6.626e-34/0.1e-9 = 6.626e-24 kg*m/s
  • E = 12.4 keV
✓ 6.626e-24 kg*m/s — 5000x more than visible
Example 3
Radiation Pressure

1 W laser beam. Force = P/c.

  • p per second = P/c = 1/3e8 = 3.33e-9 kg*m/s^2
  • Force = 3.33 nN
✓ 3.33 nN force from 1 W laser

Real-World Applications

🛸
Solar Sails
Radiation pressure from sunlight provides thrust: F = P/c per square meter.
⚛️
Laser Cooling
Atom absorbs photon momentum, slowing down. Multiple photons cool atoms to nanokelvin temperatures.
📡
Optical Tweezers
Focused laser momentum transfer can trap and manipulate microscopic particles and cells.
☢️
Compton Effect
Photon momentum transfer to electrons explained Compton wavelength shift.

Common Mistakes to Avoid

⚠️
Photon momentum is not zero

Photons have zero rest mass but carry momentum p = h/lambda = E/c. This is not classical momentum.

⚠️
Higher frequency means more momentum

p = h/lambda = hf/c. X-rays carry ~5000x more momentum than visible photons.

⚠️
Radiation pressure is real

The momentum of light creates measurable force on surfaces. Confirmed by Nichols and Hull (1901).

Frequently Asked Questions

How can photons have momentum without mass? ▾
In special relativity, momentum E = sqrt((pc)^2 + (mc^2)^2). For m=0: E = pc, so p = E/c. Photons have energy, and thus momentum.
What is radiation pressure? ▾
Force per unit area from photon momentum transfer: P = I/c (absorption) or P = 2I/c (reflection). For 1 kW/m^2 sunlight: ~3.3 microN/m^2.
How does laser cooling work? ▾
Atom moving toward laser absorbs photon (gains photon momentum opposing motion), then emits in random direction. Net effect: atom slows down. Requires many millions of cycles.
What is optical angular momentum? ▾
Circularly polarized photons carry spin angular momentum hbar per photon. Structured light beams can carry orbital angular momentum n*hbar per photon.
What is the photon de Broglie wavelength? ▾
For photons, the de Broglie wavelength equals the photon wavelength: lambda_dB = h/p = lambda. They are the same thing.

Related Physics Calculators

☢️ Compton Scattering💡 Photoelectric Effect⚛️ Heisenberg Uncertainty🌊 de Broglie Wavelength🌈 Wavelength Energy

Formula Explorer connections

Interpretation: This relationship connects motion, force, momentum, work or energy in a mechanical system. Assumption: Choose a consistent reference direction and unit system. The model may assume constant acceleration, rigid bodies, negligible losses or an isolated system.

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