Spontaneous Emission Calculator
Enter the transition frequency or wavelength. The Spontaneous Emission Calculator instantly computes the Einstein A coefficient (rate) and radiative lifetime.
About the Spontaneous Emission Calculator
The Spontaneous Emission Calculator is a precise, scientifically accurate tool that computes the spontaneous emission rate (Einstein A coefficient) and corresponding radiative lifetime for atomic and molecular transitions. This Spontaneous Emission Calculator implements the fundamental quantum electrodynamic formula derived from Einstein's 1917 work and Fermi's golden rule. Proudly supported by Agri Care Hub.
Scientific Formula
But from Einstein relations: A₂₁ = 8π h ν³ / c³ × B₂₁
Radiative lifetime τ = 1/A₂₁
Why This Calculator Is Essential
Spontaneous emission is the process by which an excited atom or molecule returns to a lower energy state by emitting a photon — without external stimulation. It is crucial in: • Fluorescence and phosphorescence • Laser physics (upper state lifetime) • Astrophysics (forbidden lines, nebulae) • Quantum optics and single-photon sources • Atomic clocks and precision spectroscopy • LED and OLED efficiency The radiative lifetime determines how long an excited state lives and is a key parameter in quantum technologies.
How to Use
- Enter either transition frequency ν (Hz) or wavelength λ (nm).
- Enter degeneracy ratio g₁/g₂ if known (often 1 for simple cases).
- Click “Calculate Spontaneous Emission”.
- Get A₂₁ rate and lifetime.
When Should You Use This Tool?
- Atomic and molecular physics research
- Laser design and excited state dynamics
- Fluorescence microscopy and spectroscopy
- Quantum optics and photon sources
- Astrophysics (line broadening, nebular emission)
- Teaching quantum transitions and Einstein coefficients
Scientific Foundation
Spontaneous emission was explained by Einstein in 1917 as a probabilistic process stimulated by vacuum fluctuations — a cornerstone of quantum electrodynamics. The rate A₂₁ is derived from the dipole matrix element and density of states. Full theory at Spontaneous Emission on Wikipedia and all quantum optics textbooks.
Conclusion
The Spontaneous Emission Calculator brings one of the most fundamental quantum processes to your browser — with perfect accuracy and beautiful design. Whether you’re a student learning quantum optics, a researcher studying atomic transitions, or an engineer designing fluorescent materials, this tool delivers precise results every time. For more physics tools, visit Agri Care Hub.