Final answer:
For n = 4, the maximum allowed value for l is 3. The principal quantum number n specifies the shell, and l can take on values from 0 to n - 1, resulting in the subshells within that shell.
Step-by-step explanation:
If n = 4, the maximum allowed value for l (the angular momentum quantum number) is 3. Quantum numbers determine the properties of an electron in an atom's orbital. The principal quantum number (n) denotes the shell number of an electron in an atom.
The azimuthal or angular momentum quantum number (l) can have integral values ranging from 0 to n − 1. Hence, for n = 4, the possible values for l are 0, 1, 2, and 3. Each of these corresponds to different subshells within the shell, with each subshell containing a different number of orbitals and therefore a different maximum number of electrons.
The maximum number of electrons in the n-th shell is calculated using the formula 2n².