Wave number of the first line in the Balmer series of Be^3+ is 2.5 * 10^5 cm^-1. Wave number of the — Atomic Structure Chemistry Question

💡 Solution & Explanation

First Balmer of Be^3+ (Z=4, n=3→2): ν̄_1 = 16R*(5/36) = 20R/9 = 2.5*10^5 cm^-1. Second Paschen of Li^2+ (Z=3, n=5→3): ν̄_2 = 9R*(16/225) = 16R/25. Ratio ν̄_2/ν̄_1 = (16R/25)/(20R/9) = 144/500 = 0.288. ν̄_2 = 0.288 * 2.5*10^5 = 7.2*10^4 cm^-1.