The no.of electrons involved in the change,
`Fe_(3)O_(4)rarrFe_(2)O_(3)`:

Options

A. `2`
B. `8`
C. `6`
D. `4`

Explanation

To determine the number of electrons involved in the change from \( \text{Fe}_3\text{O}_4 \) to \( \text{Fe}_2\text{O}_3 \), we will follow these steps:

### Step 1: Determine the oxidation states of iron in both compounds.
- In \( \text{Fe}_3\text{O}_4 \):
- Oxygen has an oxidation state of -2.
- Let the oxidation state of iron be \( x \).
- The equation for the oxidation states is:
\[ 3x + 4(-2) = 0 \implies 3x - 8 = 0 \implies 3x = 8 \implies x = \frac{8}{3} \approx +2.67 \]

- In \( \text{Fe}_2\text{O}_3 \):
- Again, let the oxidation state of iron be \( y \).
- The equation for the oxidation states is:
\[ 2y + 3(-2) = 0 \implies 2y - 6 = 0 \implies 2y = 6 \implies y = 3 \]

### Step 2: Calculate the change in oxidation states.
- The oxidation state of iron in \( \text{Fe}_3\text{O}_4 \) is \( +\frac{8}{3} \) and in \( \text{Fe}_2\text{O}_3 \) is \( +3 \).
- The change in oxidation state for one iron atom can be calculated as follows:
\[ \text{Change} = \left( +\frac{8}{3} - 3 \right) = \left( +\frac{8}{3} - \frac{9}{3} \right) = -\frac{1}{3} \]

### Step 3: Determine the total change for all iron atoms.
- In \( \text{Fe}_3\text{O}_4 \), there are 3 iron atoms:
\[ \text{Total change} = 3 \times \left(-\frac{1}{3}\right) = -1 \]

### Step 4: Relate the change in oxidation state to the number of electrons transferred.
- A decrease in oxidation state indicates a gain of electrons (reduction).
- Since the total change is -1, it means that 1 electron is gained in the process.

### Conclusion:
The number of electrons involved in the change from \( \text{Fe}_3\text{O}_4 \) to \( \text{Fe}_2\text{O}_3 \) is **1 electron**.