How many electrons can the third shell of an atom accommodate at maximum?

The third shell of an atom can accommodate a maximum of 18 electrons. This is derived from the formula used to determine the maximum number of electrons that can fill a shell, which is given by (2n^2), where (n) is the principal quantum number representing the shell level. For the third shell, (n) equals 3:

[ 2n^2 = 2(3^2) = 2 \times 9 = 18 ]

Thus, according to this formula, the third shell can hold up to 18 electrons. In contrast, the innermost shells (first and second) can hold 2 and 8 electrons, respectively. The fourth shell and beyond continue to increase in capacity, but specifically for the third shell, the maximum is firmly established at 18 electrons.