Final answer:
A maximum of 32 electrons can populate the n = 4 shell of an atom, as determined by the formula 2n², where n represents the principal quantum number of the energy level.
Step-by-step explanation:
According to the quantum model of the atom, the maximum number of electrons in the nth shell is given by 2n². For n = 4, we can calculate the maximum number of electrons using this formula:
2(4)² = 2(16) = 32 electrons The principal quantum number, denoted as n, specifies the energy level or shell of an atom in which electrons reside. For n = 4, the number of electrons that can be accommodated in this shell can be calculated using the formula 2n². Substituting the value of n into the formula gives us:
2n² = 2(4)² = 2(16) = 32.
Therefore, a maximum of 32 electrons can fit into the n = 4 energy level of an atom. This includes the 4s, 4p, 4d, and 4f subshells, which contain a total of 16 orbitals where each orbital can hold 2 electrons.