Step 1: Recollect the Rydberg constant expression in energy units.
RH = (me e⁴) / (8 ε₀² h³ c) which approximates to 2.18 × 10⁻¹⁸ J.
Step 2: Connection to energy states.
Hydrogen atom energy levels follow En = -RH / n².
Step 3: Validating the numerical value.
Both theoretical derivation and experimental measurement yield RH ≈ 2.18 × 10⁻¹⁸ J.
Step 4: Unit consistency check.
The Rydberg constant here is expressed in joules, representing the energy per photon emitted.
Step 5: Cross-referencing.
This aligns with the known energy gap between n = ∞ and n = 1 in the hydrogen atom.
Step 6: Deduction.
Thus, the correct value of the Rydberg constant in joules is 2.18 × 10⁻¹⁸.