Question

Evaluate Rydberg constant by putting the values of the fundamental constants in its expression.

Answer 1

Expression of Rydberg constant (R) is given by
$R=\frac{m{e}^4}{8h^{2}c{\in }_0^2}$
Mass of electron, m_e = 9.31$\times$10²¹ kg
Charge, e = 1.6 × 10⁻¹⁹ C
Planck's constant, h = 6.63 × 10⁻³⁴ J-s,
Speed of light, c = 3 × 10⁸ m/s,
Permittivity of vacuum, ∈₀ = 8.85 × 10⁻¹² C²N^$-1$m
On substituting the values in the expression, we get
^{$$\begin{gathered} R=\frac{\left(9.31\times {10}^{-31}\right)\times {\left(1.6\times {10}^{-19}\right)}^4}{8\times {\left(6.63\times {10}^{-34}\right)}^2\times \left(3\times {10}^8\right)\times {\left(8.85\times {10}^{-12}\right)}^2} \\ \Rightarrow R=1.097\times {10}^7{\mathrm{m}}^{-1} \end{gathered}$$}