The maximum number of electrons that can be accommodated in a shell is determined by the formula 2n^2, where n is the principal quantum number. By setting this formula equal to 32, we can solve for n:
2n^2 = 32
Dividing both sides by 2:
n^2 = 16
Taking the square root of both sides:
n = ±4
Since the principal quantum number (n) cannot be negative, the value for n is 4. Therefore, the principal quantum number for a shell containing 32 electrons is 4.
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