The carbon-based reduction method is NOT used for the extraction of

Options

A. Tin from `SnO_(2)`
B. Iron from `Fe_(2)O_(3)`
C. Aluminium from `Al_(2)O_(3)`
D. Magnesium from `MgCO_(3).CaCO_(3)`

Explanation

To solve the question regarding which metal cannot be extracted using the carbon-based reduction method, we will analyze the extraction methods for each of the given metals: tin, iron, aluminum, and magnesium.

### Step-by-Step Solution:

1. **Understanding Carbon-Based Reduction**:
Carbon-based reduction involves using carbon (usually in the form of coke) to reduce metal oxides or carbonates to their respective metals. This method is effective for certain metals but not for all.

2. **Analyzing Tin (Sn)**:
- Tin oxide (SnO2) can be reduced using carbon.
- The reaction is:
\[ \text{SnO}_2 + 2\text{C} \rightarrow \text{Sn} + 2\text{CO} \]
- Therefore, carbon-based reduction can be used for tin.

3. **Analyzing Iron (Fe)**:
- Iron oxide (Fe2O3) can also be reduced using carbon.
- The reaction is:
\[ \text{Fe}_2\text{O}_3 + 3\text{C} \rightarrow 2\text{Fe} + 3\text{CO} \]
- Thus, carbon-based reduction is applicable for iron as well.

4. **Analyzing Aluminum (Al)**:
- Aluminum oxide (Al2O3) has a higher affinity for oxygen than carbon.
- Attempting to reduce Al2O3 with carbon results in the formation of aluminum carbide (Al4C3) and oxygen instead of aluminum:
\[ 2\text{Al}_2\text{O}_3 + 6\text{C} \rightarrow 4\text{Al}_4\text{C}_3 + 3\text{O}_2 \]
- Therefore, aluminum cannot be extracted using carbon-based reduction.

5. **Analyzing Magnesium (Mg)**:
- Similar to aluminum, magnesium oxide (MgO) cannot be reduced by carbon effectively.
- The reaction typically yields magnesium carbide and carbon dioxide:
\[ \text{MgO} + \text{C} \rightarrow \text{Mg}_2\text{C}_2 + \text{CO}_2 \]
- Hence, magnesium also cannot be extracted using carbon-based reduction.

### Conclusion:
From the analysis, we conclude that the carbon-based reduction method is not used for the extraction of aluminum and magnesium. Therefore, the answer to the question is:

**Answer**: Aluminum (Al) and Magnesium (Mg) cannot be extracted using carbon-based reduction.