Multiple Choice
Which of the following best explains whether the quantum state n=3, l=3, m_l=-2, m_s=1/2 is an allowable state for an electron in an atom?
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9. Quantum Mechanics
Quantum Numbers: Principal Quantum Number
Multiple Choice
Which set of quantum numbers correctly describes a 3p orbital?
A
n = 3, l = 1, m_l = 0
B
n = 3, l = 2, m_l = 1
C
n = 3, l = 0, m_l = 0
D
n = 2, l = 1, m_l = 0
Verified step by step guidance1
Recall that the principal quantum number \(n\) indicates the energy level or shell of the electron. For a 3p orbital, \(n\) must be 3.
Understand that the azimuthal quantum number \(l\) defines the subshell or shape of the orbital: \(l = 0\) corresponds to an s orbital, \(l = 1\) to a p orbital, \(l = 2\) to a d orbital, and so on. Since we are dealing with a 3p orbital, \(l\) must be 1.
The magnetic quantum number \(m_l\) describes the orientation of the orbital in space and can take integer values from \(-l\) to \(+l\). For \(l = 1\), \(m_l\) can be \(-1\), \$0\(, or \)+1\(. Therefore, \)m_l = 0$ is a valid value for a 3p orbital.
Check each given set of quantum numbers against these rules: the correct set must have \(n = 3\), \(l = 1\), and \(m_l\) within the allowed range for \(l = 1\).
Conclude that the set \(n = 3\), \(l = 1\), \(m_l = 0\) correctly describes a 3p orbital because it satisfies all the quantum number conditions for that orbital.
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