What is the maximum number of electrons in the M-Shell ?

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UPSC NDA-2 – 2021

Electron shells are denoted by letters K, L, M, N, … or by principal quantum numbers n = 1, 2, 3, 4, … The K-shell corresponds to n=1, the L-shell to n=2, the M-shell to n=3, and so on. The maximum number of electrons that can occupy a shell with principal quantum number ‘n’ is given by the formula $2n^2$. For the M-shell, n=3, so the maximum number of electrons is $2 \times (3)^2 = 2 \times 9 = 18$.

The formula for the maximum number of electrons in a shell with principal quantum number ‘n’ is $2n^2$.
K-shell (n=1): $2 \times 1^2 = 2$ electrons.
L-shell (n=2): $2 \times 2^2 = 8$ electrons.
M-shell (n=3): $2 \times 3^2 = 18$ electrons.
N-shell (n=4): $2 \times 4^2 = 32$ electrons.

While the formula $2n^2$ gives the maximum capacity of a shell, the actual filling of electrons follows the Aufbau principle, Hund’s rule, and the Pauli exclusion principle, which dictates the filling order based on subshells (s, p, d, f) and energy levels. The outermost shell cannot accommodate more than 8 electrons (octet rule, with some exceptions), and the second last shell cannot accommodate more than 18 electrons.

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