The total spin resulting from `d^(9)` configuration is

Options

A. `(9)/( 2)`
B. 2
C. `(5)/(2)`
D. `(1)/(2)`

Answer

To find the total spin resulting from a \( d^9 \) configuration, we can follow these steps:

### Step 1: Understand the \( d \) orbital configuration
The \( d \) subshell can hold a maximum of 10 electrons, as it consists of 5 orbitals (each can hold 2 electrons). In the case of \( d^9 \), there are 9 electrons present in the \( d \) subshell.

### Step 2: Fill the \( d \) orbitals
When filling the \( d \) orbitals, we follow Hund's rule, which states that electrons will fill degenerate orbitals singly first before pairing up. The filling of the \( d \) orbitals with 9 electrons would look like this:

- Each of the 5 \( d \) orbitals will first receive 1 electron (5 electrons total).
- The next 4 electrons will pair up with the first 4 orbitals, resulting in 4 paired electrons and 1 unpaired electron.

### Step 3: Determine the spin of the electrons
- Each electron has a spin of \( +\frac{1}{2} \) or \( -\frac{1}{2} \).
- In the \( d^9 \) configuration, we have:
- 4 paired electrons: Each pair contributes \( +\frac{1}{2} \) and \( -\frac{1}{2} \), resulting in a net spin of 0 for these electrons.
- 1 unpaired electron: This contributes a spin of \( +\frac{1}{2} \).

### Step 4: Calculate the total spin
The total spin is the sum of the spins of all the electrons:
- Total spin = Spin from paired electrons + Spin from unpaired electron
- Total spin = \( 0 + \frac{1}{2} = \frac{1}{2} \)

### Conclusion
Thus, the total spin resulting from the \( d^9 \) configuration is \( \frac{1}{2} \).

### Final Answer
The correct answer is \( \frac{1}{2} \).

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