pauli exclusion principle

Question

According to Pauli's exclusion principle, the maximum number of electrons in an atom that can have the quantum numbers n = 4 and m = -2 is:

RankGuru · Accepted Answer

**Pauli's Exclusion Principle** states that no two electrons in an atom can have the same four quantum numbers $(n, l, m, s)$.
- Given: $n = 4$ and $m = -2$.
- For $n=4$, the allowed values of $l$ are $0, 1, 2, 3$.
- For $m = -2$, the allowed values of $l$ must satisfy $|m| \le l$, so $l$ can be $2$ ($4d$) or $3$ ($4f$).
- This gives **two distinct orbitals** with $(n=4, m=-2)$: the $(4,2,-2)$ orbital in the $4d$ subshell and the $(4,3,-2)$ orbital in the $4f$ subshell.
- Each orbital can accommodate a maximum of **2 electrons** (with opposite spins, $s = +1/2$ or $-1/2$).
- Therefore, the maximum number of electrons with $n=4$ and $m=-2$ is $2 + 2 = 4$.

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pauli exclusion principle

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