Question

Which of the following is a correct set of four quantum numbers for a 4d orbital?

• A. \( (4, 3, 2, 1/2) \)
• B. \( (4, 2, 1, 1/2) \)
• C. \( (4, 1, 2, 1/2) \)
• D. None of these

Hint:

Always remember: \[ |m_l| \leq l \] If \(m_l\) is greater than \(l\), the quantum number set is invalid.

Answer 1

The Correct Option is B

Concept: Quantum numbers describe the position and state of an electron in an atom.
• Principal quantum number \(n\): Specifies shell.
• Azimuthal quantum number \(l\): Specifies orbital shape.
• Magnetic quantum number \(m_l\): Specifies orientation.
• Spin quantum number \(m_s\): Specifies spin direction. For orbital notation: \[ s \rightarrow 0, \quad p \rightarrow 1, \quad d \rightarrow 2, \quad f \rightarrow 3 \]

Step 1: Determining \(n\) and \(l\) for 4d orbital.
For a 4d orbital: \[ n = 4, \qquad l = 2 \]

Step 2: Determining allowed values of \(m_l\) and \(m_s\).
For \(l = 2\): \[ m_l = -2, -1, 0, +1, +2 \] and \[ m_s = \pm \frac{1}{2} \]

Step 3: Checking the options.

• \( (4,3,2,1/2) \): Represents 4f orbital.
• \( (4,2,1,1/2) \): All values are valid.
• \( (4,1,2,1/2) \): Invalid because for \(l=1\), \(m_l\) cannot be 2. Hence, the correct answer is option (2).