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If and are, respectively, the principal and azimuthal quantum numbers, then the expression for calcuAtomic Structure Chemistry Question

Question

If $n$ and $l$ are, respectively, the principal and azimuthal quantum numbers, then the expression for calculating the total number of electrons in any energy level is

Answer: D

💡 Solution & Explanation

For a given shell $n$, the azimuthal quantum number $l$ ranges from $0$ to $n-1$. The number of electrons in a subshell is $2(2l+1)$. Therefore, the total number of electrons is the sum over all permissible $l$: $\sum_{l=0}^{n-1} 2(2l+1)$. Therefore, correct answer is D.

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