What is the wave number (Units cm ⁻¹ ) of the longest wave length transition in the Balmer series of Hydrogen spectrum? Z=1 for H

Step-by-step solution

The Rydberg formula for the wave number of a transition in the hydrogen spectrum is given by = R_H Z^2 ( 1 n₁^2 - 1 n₂^2 ) , where R_H = 109677 cm ⁻¹ and Z = 1 for hydrogen. For the Balmer series, the transition ends at n₁ = 2 . The longest wavelength transition corresponds to the smallest energy difference, which occurs for the transition from the nearest higher energy level, n₂ = 3 . Substituting these values into the formula: = 109677 1^2 ( 1 2^2 - 1 3^2 ) = 109677 ( 1 4 - 1 9 ) = 109677 ( 9 - 4 36 ) = 109677 5