How many different values of the magnetic quantum number (m_l) are possible in the 2p sublevel?

• A. 2
• B. 6
• C. 1
• D. 3

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).
2. For the 2p sublevel, the principal quantum number \(n\) is 2, and the azimuthal quantum number \(l\) for a p sublevel is 1.
3. The magnetic quantum number \(m_l\) can take integer values from \(-l\) to \(+l\), including zero. So for \(l = 1\), \(m_l\) can be \(-1\), \$0\(, or \)+1$.
4. Count the number of possible \(m_l\) values: \(-1\), \$0\(, and \)+1$ gives a total of 3 possible values.
5. Therefore, the number of different values of \(m_l\) possible in the 2p sublevel is 3.