Calculate the Rydberg constant by substituting the values of the fundamental constants into its expression.

Step-by-step solution

The expression for the Rydberg constant is given by: R = m e^4 8 ₀^2 h^3 c Substituting the values of the fundamental constants: m = 9.1 10⁻³¹ kg e = 1.6 10⁻¹⁹ C ₀ = 8.85 10⁻¹² F m ⁻¹ h = 6.63 10⁻³⁴ J s c = 3 10^8 m s ⁻¹ R = (9.1 10⁻³¹) (1.6 10⁻¹⁹)^4 8 (8.85 10⁻¹²)^2 (6.63 10⁻³⁴)^3 (3 10^8) R = 1.097 10^7 m ⁻¹