Home / Topics / Quantum Mechanics
Einstein coefficients
Advanced
Rates of absorption, spontaneous and stimulated emission.
Einstein defined rates of absorption B₁₂, stimulated emission B₂₁ = B₁₂ and spontaneous emission A₂₁ and derived Planck's law from them, introducing stimulated emission.
A/B = 8πhν³/c³.
Spontaneous emission dominates at high frequencies.
In more detail
Einstein's coefficients A and B describe spontaneous emission, absorption and stimulated emission of light by atoms. They connect the rates of these processes and explain blackbody radiation.
Real-world uses
- Laser design uses Einstein coefficients to predict gain.
- Astrophysicists use them to interpret spectral lines.
- Physicists use Einstein's coefficients to describe how atoms absorb and emit light at a given frequency.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
What is spontaneous emission?
An excited atom emits a photon on its own, without an incoming photon.
What is stimulated emission?
An incoming photon triggers an excited atom to emit an identical photon.
What are the three processes?
Absorption, spontaneous emission and stimulated emission, each with its own rate coefficient.
Related topics in Quantum Mechanics
Quantum teleportation · Lasers · Population inversion · Blackbody and Planck's law · Quantum statistics of light · Quantum field theory intro