ATM-04

Fine-structure constant

α = e² / (4π ε₀ ħ c) ≈ 1/137. The dimensionless electromagnetic coupling.

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StructureFine structure

Governing equation

\alpha=e^2/(4\pi\varepsilon_0\hbar c)

where

s: Scale vs SI (—)
\alpha: α (—)
1/\alpha: 1/α (—)

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-04 — Fine-structure constant) is the form associated with Fine structure. Working symbols: $s$ $\rightarrow$ $\alpha$ , $1/\alpha$ . Fine-structure splits ~ α². This sheet just evaluates α from the SI constants you set.

Purpose

Purpose: compute

\alpha

1/\alpha

from

s

in Atomic physics via

\alpha=e^2/(4\pi\varepsilon_0\hbar c)

α = e² / (4π ε₀ ħ c) ≈ 1/137. The dimensionless electromagnetic coupling. 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

s = 1.000\,\mathrm{—}

, the governing relation

\alpha=e^2/(4\pi\varepsilon_0\hbar c)

yields

\alpha = 0.007297\,\mathrm{—}

1/\alpha = 137.0360\,\mathrm{—}

. Four constants combining into a pure number. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Scale vs SI s1 —

Outputs

α \alpha0.007297 —
1/α 1/\alpha137.0360 —

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Narration of this film

Four constants combining into a pure number.

Fine-structure splits ~ α². This sheet just evaluates α from the SI constants you set.

Reading speed

Watch on YouTube