A sample of He ⁺ ions emits radiation of wavelength 180 nm . Which spectral series and specific transition is responsible for this emission? (Given: Rydberg constant R_H = 10^5 cm ⁻¹ )

Step-by-step solution

For a hydrogen-like species, the Rydberg equation is given by: 1 = R_H Z^2 ( 1 n₁^2 - 1 n₂^2 ) Given = 180 nm = 180 10⁻⁷ cm = 1.8 10⁻⁵ cm and for He ⁺ , Z = 2 . Substituting the values: 1 1.8 10⁻⁵ cm = 10^5 cm ⁻¹ (2)^2 ( 1 n₁^2 - 1 n₂^2 ) 10^5 1.8 = 4 10^5 ( 1 n₁^2 - 1 n₂^2 ) 1 n₁^2 - 1 n₂^2 = 1 1.8 4 = 1 7.2 = 10 72 = 5 36 We know that 5 36 = 9 - 4 36 = 1 4 - 1 9 = 1 2^2 - 1 3^2 Thus, n₁ = 2 and n₂ = 3 . Since it is an emission, the transition is from n₂ = 3 to n₁ = 2 . The transition to n₁ = 2 corresponds to the