Match the following: — Atomic Structure Chemistry Question

💡 Solution & Explanation

(A) 5th excited ($n=6$), 3rd excited ($n=4$). Speed $v \propto 1/n$. Ratio = $v_6/v_4 = 4/6 = 2/3$ (Q). (B) Series limit wavelength $\lambda \propto n^2$. Balmer ($n=2$), Lyman ($n=1$). Ratio = $2^2 / 1^2 = 4/1$ (P). (C) Lyman $\beta$ ($3 \to 1$): $1/\lambda_1 = R(1 - 1/9) = 8R/9 \implies \lambda_1 = 9/8R$. Paschen $\gamma$ ($6 \to 3$): $1/\lambda_2 = R(1/9 - 1/36) = R/12 \implies \lambda_2 = 12/R$. Ratio = $(9/8R) / (12/R) = 3/32$ (S). (D) $\Delta E \propto Z^2$. For H ($Z=1$) and $He^+$ ($Z=2$), ratio = $1^2 / 2^2 = 1/4$ (R). Therefore, correct answer is A-Q; B-P; C-S; D-R.