How many orbitals can have quantum numbers n = 2 and l = 1?

• A. 3
• B. 2
• C. 6
• D. 1

Answer: (A)

Verified step by step guidance

1. Understand the meaning of the quantum numbers: \(n\) is the principal quantum number indicating the energy level, and \(l\) is the azimuthal (angular momentum) quantum number indicating the subshell or shape of the orbital.
2. Given \(n = 2\) and \(l = 1\), identify the type of orbital: \(l = 1\) corresponds to the p-subshell.
3. Recall that the magnetic quantum number \(m_l\) can take integer values from \(-l\) to \(+l\), inclusive. For \(l = 1\), \(m_l\) can be \(-1\), \$0\(, or \)+1$.
4. Each unique value of \(m_l\) corresponds to one orbital. Therefore, the number of orbitals for \(l = 1\) is the number of possible \(m_l\) values.
5. Count the possible \(m_l\) values: \(-1\), \$0\(, and \)+1$, which gives a total of 3 orbitals.