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9.9: Summary of Relations Between f, A and S

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In this section I use ϖf to mean either ϖ1f12 or ϖ2f21, since these are equal; likewise I use ϖB to mean either ϖ1B12 or ϖ2B21. The Einstein A coefficient is used exclusively in connection with emission spectroscopy. The B coefficient is defined here in terms of radiation energy density per unit wavelength interval; that is, it is the Ba of section 9.4. The relations between the possible definitions of B are given in equations 9.4.1-4.

The following relations for electric dipole radiation may be useful. In these, ε0 is the “rationalized” definition of free space permittivity, and the formulas are suitable for use with SI units.

ϖ2A21=8πhcλ5ϖB=2πe2ε0mcλ2ϖf=16π33hε0λ3S;

ϖB=e2λ34hε0mc2ϖf=2π2λ23h2ε0cS=λ58πhcϖ2A21;

ϖf=8π2mc3he2λS=ε0mcλ22πe2ϖ2A21=4hε0mc2e2λ3ϖB;

S=3hε0λ316π3ϖ2A21=3h2ε0c2π2λ2ϖB=3he2λ8π2mcϖf.

For electric quadrupole radiation:

ϖ2A21=8π55ε0hλ5S.

For magnetic dipole radiation:

ϖ2A21=16π3μ03hλ3S,

in which μ0 is the free space permeability.


This page titled 9.9: Summary of Relations Between f, A and S is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform.

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