The wavelengths of the first Lyman lines of hydrogen, He and Li ions are . The ratio of these wavele — Atomic Structure Chemistry Question
Question
The wavelengths of the first Lyman lines of hydrogen, He$^+$ and Li$^{2+}$ ions are $\lambda_1, \lambda_2, \lambda_3$. The ratio of these wavelengths is
Answer: C
💡 Solution & Explanation
Wavelength $\lambda \propto \frac{1}{Z^2}$. For H ($Z=1$), He$^+$ ($Z=2$), Li$^{2+}$ ($Z=3$), the ratio $\lambda_1 : \lambda_2 : \lambda_3 = \frac{1}{1^2} : \frac{1}{2^2} : \frac{1}{3^2} = 1 : \frac{1}{4} : \frac{1}{9}$. Multiplying by 36 gives $36 : 9 : 4$. Therefore, correct answer is C.
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