Find the total spin and spin magnetic moment of following ion.
(i) `Fe^(+3)` (ii) `Cu^(+)`

Explanation

To find the total spin and spin magnetic moment of the ions \( \text{Fe}^{+3} \) and \( \text{Cu}^{+} \), we will follow these steps:

### Step 1: Determine the electronic configuration of \( \text{Fe}^{+3} \)

1. **Identify the atomic number of iron (Fe)**: Iron has an atomic number of 26.
2. **Write the electronic configuration of neutral iron**: The electronic configuration is \( [\text{Ar}] 4s^2 3d^6 \).
3. **Account for the +3 charge**: Removing 3 electrons (2 from 4s and 1 from 3d) gives us the configuration \( [\text{Ar}] 3d^5 \).

### Step 2: Count the unpaired electrons in \( \text{Fe}^{+3} \)

1. **Identify the number of electrons in the d-orbital**: There are 5 electrons in the \( 3d \) subshell.
2. **Determine the number of unpaired electrons**: In a \( 3d^5 \) configuration, all 5 electrons are unpaired (following Hund's rule).

### Step 3: Calculate the total spin for \( \text{Fe}^{+3} \)

1. **Use the formula for total spin \( S \)**:
\[ S = \frac{n}{2} \]
where \( n \) is the number of unpaired electrons.
2. **Substituting the value**:
\[ S = \frac{5}{2} = 2.5 \]

### Step 4: Calculate the spin magnetic moment for \( \text{Fe}^{+3} \)

1. **Use the formula for magnetic moment \( \mu \)**:
\[ \mu = \sqrt{n(n + 2)} \]
where \( n \) is the number of unpaired electrons.
2. **Substituting the value**:
\[ \mu = \sqrt{5(5 + 2)} = \sqrt{35} \text{ B.M.} \]

### Step 5: Determine the electronic configuration of \( \text{Cu}^{+} \)

1. **Identify the atomic number of copper (Cu)**: Copper has an atomic number of 29.
2. **Write the electronic configuration of neutral copper**: The electronic configuration is \( [\text{Ar}] 4s^2 3d^{10} \).
3. **Account for the +1 charge**: Removing 1 electron (from 4s) gives us the configuration \( [\text{Ar}] 3d^{10} \).

### Step 6: Count the unpaired electrons in \( \text{Cu}^{+} \)

1. **Identify the number of electrons in the d-orbital**: There are 10 electrons in the \( 3d \) subshell.
2. **Determine the number of unpaired electrons**: In a \( 3d^{10} \) configuration, all 10 electrons are paired.

### Step 7: Calculate the total spin for \( \text{Cu}^{+} \)

1. **Since there are no unpaired electrons**:
\[ S = 0 \]

### Step 8: Calculate the spin magnetic moment for \( \text{Cu}^{+} \)

1. **Since there are no unpaired electrons**:
\[ \mu = 0 \text{ B.M.} \]

### Final Results:

- For \( \text{Fe}^{+3} \):
- Total Spin \( S = 2.5 \)
- Spin Magnetic Moment \( \mu = \sqrt{35} \text{ B.M.} \)

- For \( \text{Cu}^{+} \):
- Total Spin \( S = 0 \)
- Spin Magnetic Moment \( \mu = 0 \text{ B.M.} \)