Q. The wavelength of the first line of Lyman series for hydrogen atom is equal to that of the second line of Balmer series for a hydrogen like ion. The atomic number Z of hydrogen like ion is
A) 2
B) 3
C) 4
D) 1
Explanation
[Solution from source] Lyman first line: 1/λ = R(1 − 1/4) = 3R/4. Balmer second line (n = 4 → 2) for the ion: 1/λ = Z²R(1/4 − 1/16) = 3Z²R/16. Equating gives Z² = 4, Z = 2 (He⁺). Using n = 3 → 2 as the second Balmer line gives a non-integer Z. Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.