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The wave number of the first line of the Balmer series of a hydrogen atom is . What is the wave numbAtomic Structure Chemistry Question

Question

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

Answer: C

💡 Solution & Explanation

Wave number $\bar{\nu}$ is proportional to $Z^2$. For Hydrogen, $Z=1$. For $Li^{2+}$, $Z=3$, so $Z^2 = 9$. The corresponding wave number for $Li^{2+} = 15200 \times 9 = 136800 \text{ cm}^{-1}$.

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