MHT CET202519 Apr 2025Evening ShiftChemistryStructure of AtomActual
What is the wavenumber of the photon emitted during transition from the orbit n =5 to that of n =2 in hydrogen atom? [ R _ H =109677 ~cm ⁻¹ ]
Options
- A23032 ~cm ⁻¹
- B46064 ~cm ⁻¹
- C69096 ~cm ⁻¹
- D92128 ~cm ⁻¹
Correct answer
A. 23032 ~cm ⁻¹
Step-by-step solution
The wavenumber for a hydrogen transition is determined by the Rydberg formula: = R_H Z^2 ( 1 n₁^2 - 1 n₂^2 ) , where R_H = 109677 cm ⁻¹ and Z = 1 . For the n = 5 to n = 2 transition, = 109677 ( 1 4 - 1 25 ) . Simplifying, 1 4 - 1 25 = 25 - 4 100 = 21 100 . Thus, = 109677 21 100 = 23032.17 cm ⁻¹ . Comparing with the options, the value corresponds to A 23032 cm ⁻¹ . The correct choice is A .