Formula & Calculator
Photon Momentum
Calculates the momentum carried by a single photon, despite having zero rest mass, from its wavelength.
Interpretation
p = h/λ. Momentum of a photon. Used in radiation pressure, Compton scattering, and gravitational lensing.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| p | Photon momentum | kg*m/s |
| h | Planck's constant | J*s |
| λ | Wavelength | m |
What it means
A photon has momentum inversely proportional to its wavelength. This is used to explain radiation pressure (solar sails), the Compton effect, and gravitational lensing (light bending due to gravity). Understanding this is essential for quantum mechanics and for applications like laser cooling and trapping of atoms. The formula is derived from the de Broglie relation and Planck’s law.
Worked example
Photon Momentum – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| λ (nm) | 400 |
| Parameter | Value |
|---|---|
| λ | 500 |
Common mistakes
- Photon momentum: p = h / λ – the momentum of a photon.
- Units: h in J·s, λ in m → p in kg·m/s.
- Alternatively: p = E / c – consistent with relativity.
- Radiation pressure: Light exerts pressure due to photon momentum – pressure = intensity / c for absorbing surfaces.
- Quantum mechanics: Photons have momentum despite having zero rest mass.
Applications
Photon momentum, p = h/λ, describes the momentum of a photon as inversely proportional to its wavelength. This concept is key in understanding radiation pressure, laser cooling, and atomic physics. Engineers use it in designing optical tweezers, in spacecraft solar sails, and in atom interferometry. By calculating photon momentum, they can predict the force exerted by light on particles. This is also used in quantum optics for understanding the recoil effect in absorption and emission. Understanding photon momentum is essential for advanced photonics and quantum technology applications.
- Optical trapping and tweezers for manipulating particles
- Solar sail propulsion for spacecraft
- Laser cooling and trapping of atoms
- Quantum optics and atom interferometry
- Education on the dual nature of light
Frequently Asked Questions
It calculates the momentum carried by a photon, despite its zero rest mass: p = h / λ.
p = photon momentum (kg·m/s).
h = Planck's constant.
λ = wavelength.
From the de Broglie relation p = h/λ, which applies to all quantum particles, including massless photons.
For a photon, E = pc, since E = hc/λ and p = h/λ.
It explains radiation pressure, the photoelectric effect (momentum transfer), and the Compton effect.
For λ = 500 nm, p = 6.626×10⁻³⁴ / (500×10⁻⁹) = 1.325×10⁻²⁷ kg·m/s.
- Assuming photon momentum requires mass; it comes from the wave nature.
- Confusing momentum with energy.
- Using the wrong units for λ.
When a photon is absorbed or reflected, its momentum changes, exerting a force on the surface.
In Compton scattering, a photon transfers momentum and energy to an electron, resulting in a wavelength shift.
Momentum transfer from photons to atoms can slow down atoms, cooling them to very low temperatures.