How many different values of the magnetic quantum number (m_l) are possible in the 5d sublevel?

• A. 3
• B. 7
• C. 10
• D. 5

Answer: (D)

Verified step by step guidance

1. Recall that the magnetic quantum number \(m_l\) depends on the azimuthal quantum number \(l\), which defines the sublevel type (s, p, d, f, etc.).
2. Identify the value of \(l\) for the 5d sublevel. Since 'd' corresponds to \(l = 2\), this is the key quantum number for the sublevel.
3. Understand that \(m_l\) can take integer values ranging from \(-l\) to \(+l\), including zero. So, \(m_l = -l, -(l-1), ..., 0, ..., (l-1), l\).
4. List all possible \(m_l\) values for \(l = 2\): \(-2, -1, 0, +1, +2\).
5. Count the total number of possible \(m_l\) values, which is the number of integers from \(-2\) to \(+2\), inclusive. This gives the total number of different \(m_l\) values possible in the 5d sublevel.