Which set of quantum numbers is consistent with a 3p orbital?

• A. n = 3, l = 2, m_l = 1
• B. n = 3, l = 1, m_l = 0
• C. n = 2, l = 0, m_l = 0
• D. n = 1, l = 0, m_l = 0

Answer: (B)

Verified step by step guidance

1. Recall the meaning of each quantum number: the principal quantum number \(n\) indicates the energy level or shell, the azimuthal quantum number \(l\) indicates the subshell or orbital shape, and the magnetic quantum number \(m_l\) indicates the orientation of the orbital within the subshell.
2. For a 3p orbital, the principal quantum number \(n\) must be 3, since it is in the third energy level.
3. The azimuthal quantum number \(l\) for a p orbital is 1 (where \(l = 0\) corresponds to s, \(l = 1\) to p, \(l = 2\) to d, and so on). So for a 3p orbital, \(l\) must be 1.
4. The magnetic quantum number \(m_l\) can take integer values from \(-l\) to \(+l\), including zero. For \(l = 1\), \(m_l\) can be \(-1\), \$0\(, or \)+1$. Therefore, any of these values are valid for a 3p orbital.
5. Check each given set of quantum numbers to see if they satisfy these conditions: \(n = 3\), \(l = 1\), and \(m_l\) between \(-1\) and \(+1\). The set that meets all these criteria corresponds to a 3p orbital.