Final answer:
The principal quantum number (n) defines the main energy level of an electron and its average distance from the nucleus. Electrons in the outermost principal shell have the highest n. A shell that holds up to 32 electrons corresponds to the fourth energy level, n=4.
Step-by-step explanation:
The principal quantum number (n) signifies the main energy level occupied by an electron within an atom, determining its average distance from the nucleus. As n increases, the electron is farther away from the nucleus, exhibiting higher energy levels and being less tightly bound to the nucleus. Each principal shell is denoted by a specific value of n, with electrons in the outermost shell possessing the highest principal quantum number.
Regarding the question about a shell containing a maximum of 32 electrons, one can deduce the principal quantum number by understanding the electron capacity of shells. Specifically, the capacity of each principal shell is given by the formula 2n2, so by solving 2n2 = 32, we find that n = 4. This is because the fourth shell has the capacity to hold up to 32 electrons, aligning with the quantum mechanical model of the atom that describes the discrete energy levels where electrons can reside.