# What is the difference between the Rydberg constants R_H = "109678.77 cm"^(-1) and R_(oo) = "109737.32 cm"^(-1)?

Jan 5, 2017

It just depends on what kinds of atoms you use it for.

These Rydberg constants are (Inorganic Chemistry, Miessler et al.):

$\textcolor{b l u e}{{R}_{\infty}} = {1.0973731568539}_{55} \times {10}^{7}$ ${\text{m}}^{- 1}$

$= \textcolor{b l u e}{{109737.31568539}_{55}}$ $\textcolor{b l u e}{{\text{cm}}^{- 1}}$

$\textcolor{b l u e}{{R}_{H}} = {1.0967877174307}_{10} \times {10}^{7}$ ${\text{m}}^{- 1}$

$= \textcolor{b l u e}{{109678.77174307}_{10}}$ $\textcolor{b l u e}{{\text{cm}}^{- 1}}$

where subscript digits indicate digits of high uncertainty.

${R}_{\infty}$, the constant for the limit of "infinite" nuclear mass, is used for heavy atoms, which have a heavy nucleus, considered to be "infinitely" heavier than the mass of each electron.

${R}_{H}$, the constant for the proton nuclear mass, is used for hydrogen atom only, because its nucleus is only one proton, which is about $1836.15$ times as heavy as an electron, but not "infinitely" heavier.