Assertion (A): Both `138 g` of `K_(2)CO_(3)` and `12 g` of carbon have some number of carbon atoms.
Resaon (R ): Both contains `1 g` atom of carbon which contains `6.022 xx 10^(23)` carbon atoms.

Options

A. If both (A) and (R ) are correct and (R ) is the correct explantion for (A)
B. If both (A) and (R ) are correct but (R ) is not the correct explantion for (A)
C. If (A) is correct but (R ) is incorrect.
D. If (A) and (R ) are incorrect.

Explanation

To solve the question, we need to analyze both the assertion and the reasoning provided.

### Step 1: Analyze the Assertion
The assertion states that both `138 g` of `K2CO3` (potassium carbonate) and `12 g` of carbon have some number of carbon atoms.

**Calculation for K2CO3:**
- Molar mass of K2CO3 = 138 g/mol
- Given mass = 138 g

Using the formula for moles:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} = \frac{138 \, \text{g}}{138 \, \text{g/mol}} = 1 \, \text{mol} \]

Since 1 mole of K2CO3 contains 1 mole of carbon atoms (as there is one carbon atom in each molecule of K2CO3), we have:
\[ \text{Number of carbon atoms in K2CO3} = 1 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} = 6.022 \times 10^{23} \, \text{atoms} \]

### Step 2: Analyze the Reasoning
The reasoning states that both substances contain `1 g atom` of carbon, which corresponds to `6.022 x 10^23` carbon atoms.

**Calculation for Carbon:**
- Molar mass of carbon = 12 g/mol
- Given mass = 12 g

Using the formula for moles:
\[ \text{Number of moles of carbon} = \frac{12 \, \text{g}}{12 \, \text{g/mol}} = 1 \, \text{mol} \]

Thus, the number of carbon atoms in 12 g of carbon is:
\[ \text{Number of carbon atoms} = 1 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} = 6.022 \times 10^{23} \, \text{atoms} \]

### Step 3: Conclusion
Both the assertion and the reasoning are correct:
- The assertion is true because both `138 g` of K2CO3 and `12 g` of carbon contain the same number of carbon atoms, which is `6.022 x 10^23`.
- The reasoning is also true as both substances contain `1 mole` of carbon atoms.

Thus, the correct conclusion is that both A and R are correct, and R is the correct explanation of A.

### Final Answer:
Both the assertion (A) and the reasoning (R) are correct, and R is the correct explanation of A.

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