information:highlighting, structural:summarization
Rydberg constant

A definition based on the Rydberg constant would involve fixing the value to a certain value: R ∞ = m e e 4 8 ε 0 2 h 3 c = m e c α 2 2 h {\displaystyle R_{\infty }={\frac {m_{e}e^{4}}{8\varepsilon _{0}^{2}h^{3}c}}={\frac {m_{e}c\alpha ^{2}}{2h}}}. The Rydberg constant describes the energy levels in a hydrogen atom with the nonrelativistic approximation E n ≈ − R ∞ c h n 2 {\displaystyle E_{n}\approx -{\frac {R_{\infty }ch}{n^{2}}}}.

The only viable way to fix the Rydberg constant involves trapping and cooling hydrogen. Unfortunately, this is difficult because it is very light and the atoms move very fast, causing Doppler shifts. The radiation needed to cool the hydrogen — 121.5 nm — is also difficult. Another hurdle involves improving the uncertainty in quantum electrodynamics /QED calculations.

In the Report of the 25th meeting of the Consultative Committee for Units (2021), 3 options were considered for the redefinition of the second sometime around 2026, 2030, or 2034. The first redefinition approach considered was a definition based on a single atomic reference transition. The second redefinition approach considered was a definition based on a collection of frequencies. The third redefinition approach considered was a definition based on fixing the numerical value of a fundamental constant, such as making the Rydberg constant the basis for the definition. The committee concluded there was no feasible way to redefine the second with the third option, since no physical constant is known to enough digits currently to enable realizing the second with a constant.