Discussion
The possible values of j and mj for a single d electron system would be :
Answer: B
The values are \( j = \frac{5}{2} \) and \( \frac{3}{2} \), with \( m_{j} = \pm\frac{5}{2}, \pm\frac{3}{2}, \pm\frac{1}{2} \).
A d electron has \( l = 2 \) and \( s = \frac{1}{2} \), so \( j = l \pm s = \frac{5}{2} \) or \( \frac{3}{2} \). For each \( j \), \( m_{j} \) runs from \( -j \) to \( +j \) in steps of 1, so together the values are \( \pm\frac{5}{2}, \pm\frac{3}{2}, \pm\frac{1}{2} \).
Integer \( j \) values such as 2, 1 or 3 are impossible for a single electron, whose half-integer spin makes \( j \) half-integral. \( m_{j} = 5, 3, 1, \ldots \) doubles the correct values, and \( m_{j} \) must lie between \( -j \) and \( +j \).
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