For a given value of the angular momentum quantum number l, what are the possible values of the magnetic quantum number m_l?

• A. Only positive integer values up to l
• B. All integer values from 0 to l
• C. All integer values from -l to +l, including zero
• D. All integer values from -l to l, excluding zero

Answer: (C)

Verified step by step guidance

1. Recall that the magnetic quantum number \(m_l\) describes the orientation of the orbital angular momentum in space relative to an external magnetic field.
2. For a given angular momentum quantum number \(l\), the magnetic quantum number \(m_l\) can take on integer values that range from \(-l\) to \(+l\).
3. This means \(m_l\) includes zero and all integer values in between, so the set of possible \(m_l\) values is \(\{ -l, -(l-1), ..., -1, 0, 1, ..., (l-1), l \}\).
4. The total number of possible \(m_l\) values for a given \(l\) is therefore \$2l + 1$.
5. Thus, the correct description of the possible \(m_l\) values is: all integer values from \(-l\) to \(+l\), including zero.