ATM-16

Einstein A coefficient

A_{21} = 1/τ. Spontaneous emission rate from a lifetime.

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SpectraEinstein A

Governing equation

A_{21}=1/\tau

where

\tau: Lifetime (ns)
A_{21}: Einstein A (1/s)
\Gamma: Natural width ħ (MHz)

Lecture brief

Historical brief

Balmer, Rydberg, Bohr (1913), fine structure, Zeeman and Stern–Gerlach built the spectrum of one atom. The lab computes levels, selection and magnetic splitting. This sheet (ATM-16 — Einstein A coefficient) is the form associated with Einstein A. Working symbols: $\tau$ $\rightarrow$ $A_{21}$ , $\Gamma$ . Related to f by A = (2π e² ν² / ε₀ m c³) f. B coefficients follow from detailed balance.

Purpose

Purpose: compute

A_{21}

\Gamma

from

\tau

in Atomic physics via

A_{21}=1/\tau

A_{21} = 1/τ. Spontaneous emission rate from a lifetime. Use it when a real atomic physics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\tau = 10.000\,\mathrm{ns}

, the governing relation

A_{21}=1/\tau

yields

A_{21} = 1.000e+8\,\mathrm{1/s}

\Gamma = 15.9155\,\mathrm{MHz}

. An excited atom, a ticking decay. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Lifetime \tau10 ns

Outputs

Einstein A A_{21}100000000.000 1/s
Natural width ħ \Gamma15.9155 MHz

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Narration of this film

An excited atom, a ticking decay.

Related to f by A = (2π e² ν² / ε₀ m c³) f. B coefficients follow from detailed balance.

Reading speed

Watch on YouTube