Which of the following best describes the allowed values for the magnetic quantum number, ml, for a given value of the angular momentum quantum number, l?

• A. ml can take any integer value
• B. ml can only be positive integers up to l
• C. ml can only be zero
• D. ml can take integer values from -l to +l, including zero

Answer: (D)

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. Understand that for a given angular momentum quantum number \(l\), the possible values of \(m_l\) are quantized and depend on \(l\).
3. The allowed values of \(m_l\) are all the integer values starting from \(-l\) up to \(+l\), including zero. This means \(m_l\) can be \(-l, -(l-1), ..., -1, 0, 1, ..., (l-1), l\).
4. This range arises because the magnetic quantum number corresponds to the projection of the angular momentum along a chosen axis, and the quantization reflects the discrete orientations possible.
5. Therefore, the best description is that \(m_l\) can take integer values from \(-l\) to \(+l\), including zero.