What is the maximum number of electrons that can occupy a shell according to the formula 2n^2?

The maximum number of electrons that can occupy a shell is determined by the formula 2n^2, where n represents the principal quantum number of the shell. This formula arises from quantum mechanics and indicates that as the principal quantum number increases, the capacity of the shell to hold electrons also increases quadratically.

To break it down further, the principal quantum number (n) characterizes the energy level and size of the electron shell in an atom. For each shell number n, the formula shows the maximum number of electrons that can be present based on energy levels and orbital arrangements. For instance, when n equals 1, the maximum number of electrons is 2(1^2) = 2. When n equals 2, it is 2(2^2) = 8, and so forth.

This understanding that the capacity grows as per the n^2 factor, and then multiplied by 2, explains why D, which states 2n^2, accurately reflects the maximum number of electrons a shell can accommodate. The other options do not represent this relationship correctly.