Final answer:
To determine the maximum number of electrons in a shell, use the formula 2n², and for a specific subshell within that shell, use 2(2l + 1), where n is the principal quantum number and l is the azimuthal quantum number.
Step-by-step explanation:
To find the maximum number of electrons that can be held in a given shell when provided with quantum numbers, you would use the formula 2n², where n represents the principal quantum number corresponding to the shell number. This formula takes into account all the subshells within a particular shell. For example, when n = 3, there are three subshells (3s, 3p, and 3d) which, when applying the formula 2n², results in a total capacity of 18 electrons for the n = 3 shell.
Additionally, if you are calculating the maximum number of electrons within an individual subshell, the formula 2(2l + 1) is used, where l is the azimuthal quantum number for the subshell. This formula calculates the maximum number of electrons for a specific subshell designated by l. So, for the 3d subshell where l = 2, the maximum number of electrons would be 10, as calculated by 2(2(2) + 1).