Question

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

Answer 1

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

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

`color(blue)(R_(oo)) = 1.0973731568539_(55)xx10^7` `"m"^(-1)`

`= color(blue)(109737.31568539_(55))` `color(blue)("cm"^(-1))`

`color(blue)(R_(H)) = 1.0967877174307_(10)xx10^7` `"m"^(-1)`

`= color(blue)(109678.77174307_(10))` `color(blue)("cm"^(-1))`

where subscript digits indicate digits of high uncertainty.

`R_(oo)`, 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.