What is the wave number of lowest transition associated with Paschen series?

Step-by-step solution

The wave number v for a transition in a hydrogen atom is given by the Rydberg formula: v = R_H ( 1 n₁^2 - 1 n₂^2 ) For the Paschen series, the lower energy level is n₁ = 3 . The lowest transition corresponds to the minimum energy difference, which occurs for the transition from the immediately higher energy level, n₂ = 4 . Substituting these values into the formula: v = R_H ( 1 3^2 - 1 4^2 ) v = R_H ( 1 9 - 1 16 ) v = R_H ( 16 - 9 144 ) v = R_H ( 7 144 ) cm ⁻¹ Answer: R_H ( 7 144 ) cm ⁻¹