Which of the following spectral transitions in a hydrogen atom emit a photon of the EXACT SAME energ — Atomic Structure Chemistry Question

💡 Solution & Explanation

Energy $\Delta E \propto Z^2 (\frac{1}{n_1^2} - \frac{1}{n_2^2})$. For H ($2 \to 1$), $\Delta E \propto 1^2(\frac{1}{1} - \frac{1}{4}) = \frac{3}{4}$. For $He^+$ ($4 \to 2$), $\Delta E \propto 2^2(\frac{1}{4} - \frac{1}{16}) = 4(\frac{3}{16}) = \frac{3}{4}$. For $Li^{2+}$ ($6 \to 3$), $\Delta E \propto 3^2(\frac{1}{9} - \frac{1}{36}) = 9(\frac{3}{36}) = \frac{3}{4}$. For $Be^{3+}$ ($8 \to 4$), $\Delta E \propto 4^2(\frac{1}{16} - \frac{1}{64}) = 16(\frac{3}{64}) = \frac{3}{4}$. All except C match precisely.