Answer: n(n-1)/2.
- A n
- B n-1
- C n(n-1)/2
- D n²
Correct answer: C. n(n-1)/2
Explanation: Transitions possible from n levels: any pair can transition. Total lines = n(n-1)/2 (combinations of 2 from n levels). Wait, for transitions from nth orbit to 1: possible intermediate stops give n(n-1)/2 total lines.

The Geiger–Marsden alpha-scattering result: a few alpha particles bounce back at large angles, which rules out Thomson’s diffuse model and demands a tiny, massive, positively charged nucleus. Image: Kurzon, CC BY 3.0, via Wikimedia Commons.
Concept context
Thomson's plum-pudding model, Rutherford's nuclear model from alpha-scattering, Bohr's postulates and hydrogen spectrum, spectral series (Lyman to Pfund), Rydberg formula, and limitations of each model.