For any given series of spectral lines of atomic hydrogen, let Δ v - = v - m a x - v - m i n be the difference in maximum and minimum wave number in c m - 1 . The ratio Δ v - L y m a n / Δ v - B a l m a r is

Step-by-step solution

= v m a x - v m i n l y m a n v m a x - v m i n B a l m a r   ∵ ν = 1 λ = E ch = E m a x - E m i n l y m a n E m a x - E m i n B a l m a r   E = h ν , ν = E h = E 1 → ∞ -   E 1 → 2 E 2 → ∞ -   E 2 → 3   = 13.6   1 1 - 1 ∞ - 13.6   1 1 - 1 4 13.6   1 4 - 1 ∞ - 13.6   1 4 - 1 9 = 1 - 0 - 1 + 1 4 1 4 - 0 - 1 4 + 1 9 = 1 / 4 1 / 9 = 9 4