• Tags: rydberg, constant, formula
• Difficulty: Moderate

The Rydberg constant R = $me^{4}$/(8ε_{0}^{2}$h^{3}$c) = $1.097 \times 10^{7}$$m^{-1}$. In energy units: Ry = 13.6 eV = hcR. The Rydberg formula: 1/λ =$RZ^{2}(1/n_f^{2} - 1/n_i^{2}$) is the most used equation in atomic physics for JEE. Useful derived values: R × hc = 13.6 eV, 1/R = 911.6 Å (this is the series limit of the Lyman series). For the first Balmer line: 1/λ = R(1/4 - 1/9) = 5R/36, giving λ = 36/(5R) = 6563 Å. The Rydberg constant changes slightly for different elements due to the reduced mass correction: R_atom = R_∞ × μ/m_e, where R_∞ is the Rydberg constant for infinite nuclear mass.$