Question

The incorrect set of quantum numbers \((n,l,m,s)\) for an electron in \(3p\) orbital is:

• A. \(3,\ 1,\ -1,\ \dfrac{1}{2}\)
• B. \(3,\ 1,\ -2,\ -\dfrac{1}{2}\)
• C. \(3,\ 1,\ 1,\ \dfrac{1}{2}\)
• D. \(3,\ 1,\ +1,\ -\dfrac{1}{2}\)

Hint:

For any orbital, \[ m=-l \text{ to } +l \] For a \(p\)-orbital where \(l=1\), \[ m=-1,\ 0,\ +1 \] only.

Answer 1

The Correct Option is B

Step 1: Identify the quantum numbers for a \(3p\) orbital.
For a \(3p\) orbital: \[ n=3 \] Since it is a \(p\)-orbital, \[ l=1 \]

Step 2: Determine the possible values of magnetic quantum number.
The magnetic quantum number \(m\) can take values from \[ -l \text{ to } +l \] Thus, \[ m=-1,\ 0,\ +1 \]

Step 3: Check the spin quantum number.
The spin quantum number can have only two values: \[ s=+\frac{1}{2} \] or \[ s=-\frac{1}{2} \]

Step 4: Analyze the options.

Option (1): \[ (3,1,-1,\tfrac{1}{2}) \] All values are allowed. Hence, correct.

Option (2): \[ (3,1,-2,-\tfrac{1}{2}) \] Here, \[ m=-2 \] which is not allowed for \[ l=1 \] Hence, this set is incorrect.

Option (3): \[ (3,1,1,\tfrac{1}{2}) \] All values are allowed.

Option (4): \[ (3,1,+1,-\tfrac{1}{2}) \] All values are allowed.

Step 5: Final conclusion.
Therefore, the incorrect set of quantum numbers is \[ \boxed{(3,\ 1,\ -2,\ -\frac{1}{2})} \] Hence, the correct option is \[ \boxed{(2)} \]