ATM-12

Spin–orbit interval

E_{SO} = (A/2) [J(J+1) − L(L+1) − S(S+1)]. Landé interval rule.

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StructureSpin–orbit

Governing equation

E=\dfrac{A}{2}\bigl[J(J+1)-L(L+1)-S(S+1)\bigr]

where

A: Interval A (cm^{-1})
L: L (—)
S: S (—)
J: J (—)
E_{SO}: Fine-structure energy (cm^{-1})

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-12 — Spin–orbit interval) is the form associated with Spin–orbit. Working symbols: $A$ , $L$ , $S$ , $J$ $\rightarrow$ $E_{SO}$ . A ∝ Z⁴ α² Rydberg. Fine-structure splitting of alkali D lines is this plus core penetration.

Purpose

Purpose: compute

E_{SO}

from

A

L

S

J

in Atomic physics via

E=\dfrac{A}{2}\bigl[J(J+1)-L(L+1)-S(S+1)\bigr]

E_{SO} = (A/2) [J(J+1) − L(L+1) − S(S+1)]. Landé interval rule. 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 = 20.000\,\mathrm{cm^-1}

L = 1.000\,\mathrm{—}

S = 0.500\,\mathrm{—}

J = 1.500\,\mathrm{—}

, the governing relation

E=\dfrac{A}{2}\bigl[J(J+1)-L(L+1)-S(S+1)\bigr]

yields

E_{SO} = 10.000\,\mathrm{cm^-1}

. A term that splits into J levels. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Interval A A20 cm^{-1}L L1 —S S0.5 —J J1.5 —

Outputs

Fine-structure energy E_{SO}10.000 cm^{-1}

Reading speed

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Narration of this film

A term that splits into J levels.

A ∝ Z⁴ α² Rydberg. Fine-structure splitting of alkali D lines is this plus core penetration.

Reading speed

Watch on YouTube