October 1970
WAVE NUMBER
Always treated as a physical constant rather than a unit, and denoted by italic R (more specifically R∞, RH, etc.). Examples of usage:
$R=R_∞(1+m/M), R_∞=2\pi^2me^4 / ch^2 ≈ 1.1 × 10^{−5} cm^{−1}; \overline {\upsilon}_{mn} = R(1/m^2−1/n^2)$.
$\overline {\upsilon}=R, \overline {\upsilon}=0.25R, \overline {\upsilon}=(0.25±0.01)R$.
ENERGY
May be treated as a physical constant or as a unit. One or the other should be done consistently to avoid confusion.
Physical constant. A one-letter symbol should be defined–usually script R $\mathcal{R}_∞$, etc.). Examples:
$\mathcal{R}_∞=hcR_∞=2π^2me^4/h^2≈13.6 eV; Emn=\mathcal{R}(1/m^2−1/n^2)$.
$E=\mathcal{R}, E=0.25\mathcal{R}, E=(0.25±0.01)\mathcal{R}; ε=E/\mathcal{R}=0.25$.
Unit. The abbreviation Ry (Ry∞, etc.) should be used and need not be defined. Examples:
$1Ry =\frac{1}{2} a.u. = \frac{1}{2} hartree ≈13.6 eV; Emn = 1/m^2 − 1/n^2 Ry$.
$E = 1 Ry, E = 0.25 Ry, E = 0.25 ± 0.01 Ry$.
Frequency (Rare)
The unit abbreviation Ry may be used, but it should be pointed out that it represents a frequency.
$1 Ry = 1/4π a.u$.