#### neilparker62

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- Question about the Rydberg Constant.

**Summary:**Question about the Rydberg Constant.

The Rydberg constant is essentially a 'relic' of a now obsolete model (the Bohr model) of the Hydrogen atom. So my question is why do scientists keep trying to measure it to greater and greater degrees of precision?

Also I thought that the Rydberg constant / Rydberg energy would relate directly to accurately obtained values of atomic hydrogen ionization energy. But this does not seem to be the case. So what 'correction' needs to be applied to the Rydberg constant (adjusted for Hydrogen) such that it agrees with an accurately obtained value of ionization energy for the same atom ? Why do we keep it , if it is no longer directly reflective of the physical quantity it was designed to determine (via calculation of 1 - infinity transition) ?

R

_{H}= 109677.576 cm-1.

E

_{i}(H) = 109678.7717426 (10) cm−1.

I know my R

_{H}is showing way less significant figures than for E

_{i}(H) but the difference is already evident in the units column.

Formulations of the Dirac energy equation I have seen appear to depend only upon mc^2 and the fine structure constant although elsewhere it appears there are more complex versions which somehow 'reincorporate' the Rydberg constant. Why ?

### Solution of the Dirac Equation for Hydrogen

Solution of the Dirac Equation for Hydrogen

quantummechanics.ucsd.edu

Disclaimer: I have no idea what's going on in the Maths per above link - was just interested in the formula at the end of it!