Final answer:
For n = 4, the maximum allowed value for l is 3. This is because l can range from 0 to n − 1, which in this case results in l being 0, 1, 2, or 3, corresponding to s, p, d, and f orbitals respectively, and determining the subshell and the shape of the orbitals.
Step-by-step explanation:
If n = 4, the maximum allowed value for l (the azimuthal quantum number or angular momentum quantum number) is determined by the rule that l can have all integral values from 0 to n − 1.
Therefore, for n = 4, the possible values of l are 0, 1, 2, or 3. The quantum number l indicates the subshell type and directly relates to the shape of the orbital within an atom. For example, l = 0 corresponds to an s subshell, l = 1 corresponds to a p subshell, l = 2 corresponds to a d subshell, and l = 3 corresponds to an f subshell.
Each subshell can contain a different number of orbitals associated with different values of the magnetic quantum number, ml. These orbitals are represented spatially where electrons can be found.
For instance, the s subshell (with l = 0) has 1 orbital, the p subshell (with l = 1) has 3 orbitals, the d subshell (with l = 2) has 5 orbitals, and the f subshell (with l = 3) has 7 orbitals. Given these values and the fact that each orbital can hold 2 electrons, the shell with n = 4 will have a total maximum of 32 electrons.
The concept of orbitals and quantum numbers is fundamental to the understanding of electronic structure in atoms, as outlined by the quantum mechanical model of the atom.