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The wave number of the first line of the Balmer series for a hydrogen atom is experimentally found tAtomic Structure Chemistry Question

Question

The wave number of the first line of the Balmer series for a hydrogen atom is experimentally found to be $15200 \text{ cm}^{-1}$. What is the corresponding wave number of the first line of the Balmer series for a $Li^{2+}$ ion?

Answer: D

💡 Solution & Explanation

The wave number $\bar{ u}$ is proportional to $Z^2$. For hydrogen $Z=1$, and for $Li^{2+}$ $Z=3$. Therefore, $\bar{ u}_{Li^{2+}} = \bar{ u}_H \times Z^2 = 15200 \text{ cm}^{-1} \times (3)^2 = 15200 \times 9 = 136800 \text{ cm}^{-1}$.

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