The magnetic moment and nature for isolated gaseous ion `Au^(3+)` is 

Options

A. zero and diamagnetic.
B. 2.82 BM and diamagnetic.
C. 2.82 BM and paramagnetic.
D. None of these.

Answer

To determine the magnetic moment and nature of the isolated gaseous ion \( \text{Au}^{3+} \), we can follow these steps:

### Step 1: Determine the Electronic Configuration of Gold (Au)
Gold (Au) has an atomic number of 79. The electronic configuration of neutral gold is:
\[ \text{Au}: [\text{Xe}] 4f^{14} 5d^{10} 6s^1 \]

### Step 2: Determine the Electronic Configuration of \( \text{Au}^{3+} \)
The \( \text{Au}^{3+} \) ion is formed by losing 3 electrons from the neutral gold atom. The electrons are removed first from the outermost shell (6s) and then from the 5d subshell. Thus, the electronic configuration for \( \text{Au}^{3+} \) is:
\[ \text{Au}^{3+}: [\text{Xe}] 4f^{14} 5d^8 \]

### Step 3: Analyze the 5d Orbital
In the \( 5d \) subshell, there are 8 electrons. The \( d \) subshell can hold a maximum of 10 electrons and has 5 orbitals. The distribution of electrons in the \( 5d \) orbitals can be visualized as follows:

- Each of the 5 orbitals can hold 2 electrons (one with spin up and one with spin down).
- With 8 electrons, we can fill the 5 orbitals as follows: 4 orbitals will have 2 electrons each, and 1 orbital will have 2 electrons (which means there will be 2 unpaired electrons).

### Step 4: Determine the Number of Unpaired Electrons
From the configuration \( 5d^8 \), we see that there are 2 unpaired electrons.

### Step 5: Calculate the Magnetic Moment
The magnetic moment (\( \mu \)) can be calculated using the formula:
\[ \mu = \sqrt{n(n + 2)} \text{ Bohr magnetons} \]
where \( n \) is the number of unpaired electrons. In this case, \( n = 2 \):
\[ \mu = \sqrt{2(2 + 2)} = \sqrt{2 \times 4} = \sqrt{8} \approx 2.83 \text{ Bohr magnetons} \]

### Step 6: Determine the Nature of the Ion
Since \( \text{Au}^{3+} \) has unpaired electrons, it is classified as **paramagnetic**.

### Final Answer
- **Magnetic Moment**: Approximately \( 2.83 \) Bohr magnetons
- **Nature**: Paramagnetic

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