What range of values can L take based on the principal quantum number (n)?

The principal quantum number (n) indicates the energy level of an electron in an atom and can take positive integer values (1, 2, 3, ...). The azimuthal quantum number (L), which defines the shape of an orbital, must conform to specific rules relative to n.

For a given principal quantum number n, the values that L can take are whole numbers starting from 0 up to ( n-1 ). This means if n is 1, L can only be 0; if n is 2, L can take values of 0 or 1; if n is 3, it can take values of 0, 1, or 2; and so forth. Therefore, the range of values for L is properly described as 0 through ( n-1 ).

By understanding this relationship, one can accurately determine the possible values of L based on the principal quantum number, reinforcing the foundational principles of quantum mechanics that govern electron configuration in atoms.