ATM-15

Oscillator strength

f = (8π² m ν / 3 h e²) |μ|² × (degeneracy sketch). Dimensionless line strength.

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SpectraOscillator strength

Governing equation

f=\dfrac{8\pi^2 m\nu}{3he^2}|\mu|^2

$\mu \in \left[0.01, 10\right]$

where

\nu: Frequency (PHz)
\mu: Dipole (D)
f: Oscillator strength (—)

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

f=\dfrac{8\pi^2 m\nu}{3he^2}|\mu|^2

$\mu \in \left[0.01, 10\right]$

$\mu = 0.01$ $f = 9.66\times 10^{-7}$

Along the curve

②

Domain of the variable — blue

\mu_{\min} = 0.01,\quad \mu_{\max} = 10

$\mu \in \left[0.01, 10\right]$

$\mu = 0.01$ $\mu = 0.01$

Along the curve

③

Response curve — green

f=\dfrac{8\pi^2 m\nu}{3he^2}|\mu|^2

$\mu \in \left[0.01, 10\right]$

$\mu = 0.01$ $f = 9.66\times 10^{-7}$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}f}{\mathrm{d}\mu}

$\mu \in \left[0.01, 10\right]$

$\mu = 0.073$ $f^{\prime} = 0.001$

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-15 — Oscillator strength) is the form associated with Oscillator strength. Working symbols: $\nu$ , $\mu$ $\rightarrow$ $f$ . f ~ 1 is a strong allowed line. TRK says the sum of f from a given level is Z.

Purpose

Purpose: compute

f

from

\nu

\mu

in Atomic physics via

f=\dfrac{8\pi^2 m\nu}{3he^2}|\mu|^2

f = (8π² m ν / 3 h e²) |μ|² × (degeneracy sketch). Dimensionless line strength. 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

\nu = 0.616\,\mathrm{PHz}

\mu = 1.500\,\mathrm{D}

, the governing relation

f=\dfrac{8\pi^2 m\nu}{3he^2}|\mu|^2

yields

f = 0.0217\,\mathrm{—}

. A dipole, a line, an f bar. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Frequency \nu0.616 PHzDipole \mu1.5 D

Outputs

Oscillator strength f0.0217 —

Reading speed

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Narration of this film

A dipole, a line, an f bar.

f ~ 1 is a strong allowed line. TRK says the sum of f from a given level is Z.

Reading speed

Watch on YouTube