Atomic StructurehardNUMERICAL

In a sample of hydrogen atoms, an electronic transition from a particular excited state to the grounAtomic Structure Chemistry Question

Question

In a sample of hydrogen atoms, an electronic transition from a particular excited state to the ground state in one or more steps gives rise to exactly $4$ lines in the ultraviolet region of the spectrum. How many total distinct lines does this transition sequence produce in the infrared region of the spectrum?

Answer: 3

💡 Solution & Explanation

Ultraviolet lines belong to the Lyman series, which terminate at $n_1=1$. The number of Lyman lines is $(n-1) = 4$, which means the excited state is $n=5$. Infrared lines belong to Paschen ($n \to 3$), Brackett ($n \to 4$), and Pfund ($n \to 5$). The possible IR transitions from $n=5$ are: Paschen ($5 \to 3$ and $4 \to 3$), Brackett ($5 \to 4$). Total IR lines = $2 + 1 = 3$.

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