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The maximum number of electrons that can be accommodated in a shell with principal quantum number $$n$$ is given by
$$N = 2n^2$$For $$n = 4$$,
$$N = 2 \times 4^2 = 2 \times 16 = 32$$We can verify this by counting the subshells in the 4th shell: 4s has 2 electrons, 4p has 6, 4d has 10, and 4f has 14, giving a total of $$2 + 6 + 10 + 14 = 32$$ electrons.
So, the answer is $$32$$.
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