How is L value assigned in a multi-electron system?

In a multi-electron system, the total orbital angular momentum quantum number, L, is determined by combining the individual orbital angular momentum quantum numbers of the electrons involved. Each electron has an associated quantum number, denoted as l, which corresponds to its orbital shape (such as s, p, d, etc.).

For multiple electrons, when adding angular momenta, the resultant total angular momentum quantum number, L, can take on a range of values that start from the maximum achievable value (the sum of the individual l values) and decrease in integer steps down to the absolute value of the difference between the two angular momentum components. This means that if you have two electrons with angular momentum quantum numbers l1 and l2, the possible values for L would indeed range from l1 + l2 down to |l1 - l2| in integer steps.

This correct understanding aligns with the principle of angular momentum coupling, where all combinations of the individual angular momentum quantum numbers are considered. Therefore, the statement that L can take values down to the lower limit of |l1 - l2| and includes all integers in between is foundational in quantum mechanics for describing systems with multiple angular momenta, making the choice demonstrating this range the appropriate one.