ATM-19

Thomas–Reiche–Kuhn sum

Σ f = Z. The remaining oscillator strength after two known lines.

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SpectraThomas–Reiche–Kuhn

Governing equation

\sum_n f_{gn}=Z

where

Z: Electrons Z (—)
f_1: Line 1 (—)
f_2: Line 2 (—)
f_{rest}: Remaining f (—)

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-19 — Thomas–Reiche–Kuhn sum) is the form associated with Thomas–Reiche–Kuhn. Working symbols: $Z$ , $f_1$ , $f_2$ $\rightarrow$ $f_{rest}$ . A direct consequence of the double commutator [x,[H,x]]. Bound plus continuum.

Purpose

Purpose: compute

f_{rest}

from

Z

f_1

f_2

in Atomic physics via

\sum_n f_{gn}=Z

Σ f = Z. The remaining oscillator strength after two known lines. 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

Z = 2.000\,\mathrm{—}

f_1 = 0.400\,\mathrm{—}

f_2 = 0.200\,\mathrm{—}

, the governing relation

\sum_n f_{gn}=Z

yields

f_{rest} = 1.400\,\mathrm{—}

. A stack of f bars that must fill Z. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Electrons Z Z2 —Line 1 f_10.4 —Line 2 f_20.2 —

Outputs

Remaining f f_{rest}1.400 —

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Narration of this film

A stack of f bars that must fill Z.

A direct consequence of the double commutator [x,[H,x]]. Bound plus continuum.

Reading speed

Watch on YouTube