ATM-29

Einstein A lifetime

Spontaneous emission.

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AtomicEinstein A

Governing equation

\tau=1/A_{21}

$A_{21} \in \left[1\times 10^{5}, 1\times 10^{9}\right]$

where

A_{21}: A (1/s)
\tau: Lifetime (ns)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\tau=1/A_{21}

$A_{21} \in \left[1\times 10^{5}, 1\times 10^{9}\right]$

$A_{21} = 1\times 10^{5}$ $\tau = 10000$

Along the curve

②

Domain of the variable — blue

A_{21}_{\min} = 1\times 10^{5},\quad A_{21}_{\max} = 1\times 10^{9}

$A_{21} \in \left[1\times 10^{5}, 1\times 10^{9}\right]$

$A_{21} = 1\times 10^{5}$ $A_{21} = 1\times 10^{5}$

Along the curve

③

Response curve — green

\tau=1/A_{21}

$A_{21} \in \left[1\times 10^{5}, 1\times 10^{9}\right]$

$A_{21} = 1\times 10^{5}$ $\tau = 10000$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\tau}{\mathrm{d}A_{21}}

$A_{21} \in \left[1\times 10^{5}, 1\times 10^{9}\right]$

$A_{21} = 6.39\times 10^{6}$ $\tau^{\prime} = -7.89\times 10^{-4}$

Along the curve

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-29 — Einstein A lifetime) is the form associated with Einstein A. Working symbols: $A_{21}$ $\rightarrow$ $\tau$ . Spontaneous emission.

Purpose

Purpose: compute

\tau

from

A_{21}

in Atomic physics via

\tau=1/A_{21}

Spontaneous emission. 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

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

, the governing relation

\tau=1/A_{21}

yields

\tau = 10.000\,\mathrm{ns}

. Spontaneous emission. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

A A_{21}100000000 1/s

Outputs

Lifetime \tau10.000 ns

Reading speed

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Narration of this film

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