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Index/Atomic physics/ATM-34

ATM-34

Natural width

Lifetime broadening.

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Atomicnatural width

Governing equation

Γ=ℏA\Gamma=\hbar A

A∈[1×106,1×109]A \in \left[1\times 10^{6}, 1\times 10^{9}\right]

where

A
A (1/s)
\Gamma
Width (µeV)

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ATM-34 · spectrum
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①

Governing law — red

Γ=ℏA\Gamma=\hbar A

A∈[1×106,1×109]A \in \left[1\times 10^{6}, 1\times 10^{9}\right]

A=1×106A = 1\times 10^{6}Γ=6.58×10−4\Gamma = 6.58\times 10^{-4}

②

Domain of the variable — blue

Amin⁡=1×106,Amax⁡=1×109A_{\min} = 1\times 10^{6},\quad A_{\max} = 1\times 10^{9}

A∈[1×106,1×109]A \in \left[1\times 10^{6}, 1\times 10^{9}\right]

A=1×106A = 1\times 10^{6}A=1×106A = 1\times 10^{6}

③

Response curve — green

Γ=ℏA\Gamma=\hbar A

A∈[1×106,1×109]A \in \left[1\times 10^{6}, 1\times 10^{9}\right]

A=1×106A = 1\times 10^{6}Γ=6.58×10−4\Gamma = 6.58\times 10^{-4}

④

Rate of change — amber

dΓdA\frac{\mathrm{d}\Gamma}{\mathrm{d}A}

A∈[1×106,1×109]A \in \left[1\times 10^{6}, 1\times 10^{9}\right]

A=7.28×106A = 7.28\times 10^{6}Γ′=6.58×10−10\Gamma^{\prime} = 6.58\times 10^{-10}

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-34 — Natural width) is the form associated with natural width. Working symbols: AA →\rightarrow Γ\Gamma. Lifetime broadening.

Purpose

Purpose: compute Γ\Gamma from AA in Atomic physics via Γ=ℏA\Gamma=\hbar A Lifetime broadening. 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=1.000e+8 1/sA = 1.000e+8\,\mathrm{1/s}, the governing relation Γ=ℏA\Gamma=\hbar A yields Γ=0.0658 μeV\Gamma = 0.0658\,\mathrm{\mu eV}. Lifetime broadening. Move a slider: the numbers are this situation, not a canned story.

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Outputs

  • Width \Gamma0.0658 µeV
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ATM-34 · spectrum
00:0 / 00:08

Narration of this film

Lifetime broadening.

Lifetime broadening.

Reading speed

Watch on YouTube