The magnetic moment of `KO_(2)` at room temperature is ---------- BM.

Options

A. `1.41`
B. `1.73`
C. `2.23`
D. `2.64`

Explanation

To find the magnetic moment of KO₂ (potassium superoxide) at room temperature, we will follow these steps:

### Step 1: Understand the magnetic moment formula
The magnetic moment (μ) can be calculated using the formula:
\[ \mu = \sqrt{n(n + 2)} \]
where \( n \) is the number of unpaired electrons.

### Step 2: Identify the oxidation state of potassium in KO₂
In KO₂, potassium (K) is in the +1 oxidation state. Therefore, we can represent it as K⁺.

### Step 3: Determine the number of unpaired electrons in K⁺
Potassium in its elemental form has the electronic configuration of [Ar] 4s¹. When it loses one electron to form K⁺, it has no unpaired electrons:
- K⁺ has 0 unpaired electrons.

### Step 4: Analyze the superoxide ion (O₂⁻)
The superoxide ion (O₂⁻) has a specific electronic configuration. The molecular orbital configuration for O₂⁻ is:
\[ \sigma 1s^2 \sigma^* 1s^2 \sigma 2s^2 \sigma^* 2s^2 \sigma 2p_z^2 \pi 2p_x^2 \pi 2p_y^2 \pi^* 2p_x^2 \pi^* 2p_y^1 \]
From this configuration, we can see that there is 1 unpaired electron in the π* orbitals.

### Step 5: Calculate the total number of unpaired electrons
Since K⁺ has 0 unpaired electrons and O₂⁻ has 1 unpaired electron, the total number of unpaired electrons in KO₂ is:
\[ n = 0 + 1 = 1 \]

### Step 6: Substitute \( n \) into the magnetic moment formula
Now we substitute \( n = 1 \) into the magnetic moment formula:
\[ \mu = \sqrt{1(1 + 2)} = \sqrt{1 \times 3} = \sqrt{3} \]

### Step 7: Calculate the value of the magnetic moment
Calculating the square root gives:
\[ \mu = \sqrt{3} \approx 1.73 \text{ Bohr magneton (BM)} \]

### Final Answer
The magnetic moment of KO₂ at room temperature is approximately **1.73 BM**.

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