If avogadro number `N_(A)` is changed from `6.022 xx10^(23)mol ^(-1) ` to `6.022xx10^(26)mol ^(-1),` then the mass of 1 mole carbon becomes :-

Options

A. 12 mg
B. 12 gm
C. 12 kg
D. none of these

Answer

To solve the problem, we need to understand how the change in Avogadro's number affects the mass of one mole of carbon.

### Step-by-Step Solution:

1. **Understand the current Avogadro's number**:
The current Avogadro's number \( N_A \) is \( 6.022 \times 10^{23} \, \text{mol}^{-1} \). This means that one mole of any substance contains \( 6.022 \times 10^{23} \) entities (atoms, molecules, etc.).

2. **Determine the mass of one mole of carbon**:
The atomic mass of carbon is 12 g/mol. Therefore, one mole of carbon weighs 12 grams.

3. **Calculate the mass of one atom of carbon**:
The mass of one atom of carbon can be calculated using the formula:
\[ \text{Mass of one atom} = \frac{\text{Mass of one mole}}{N_A} = \frac{12 \, \text{g}}{6.022 \times 10^{23}} \, \text{g} \]

4. **Change Avogadro's number**:
Now, if \( N_A \) changes to \( 6.022 \times 10^{26} \, \text{mol}^{-1} \), we need to find the new mass of one mole of carbon using the new Avogadro's number \( N_A' \).

5. **Calculate the mass of one atom of carbon with the new Avogadro's number**:
Using the new Avogadro's number:
\[ \text{Mass of one atom} = \frac{12 \, \text{g}}{6.022 \times 10^{26}} \, \text{g} \]

6. **Relate the mass of one mole of carbon with the new Avogadro's number**:
The mass of one mole of carbon with the new Avogadro's number can be calculated as follows:
\[ \text{Mass of one mole} = \text{Mass of one atom} \times N_A' = \left(\frac{12 \, \text{g}}{6.022 \times 10^{26}}\right) \times (6.022 \times 10^{23}) \]

7. **Simplify the expression**:
\[ \text{Mass of one mole} = 12 \, \text{g} \times \frac{6.022 \times 10^{23}}{6.022 \times 10^{26}} = 12 \, \text{g} \times 10^{-3} = 12 \, \text{mg} \]

### Final Answer:
The mass of 1 mole of carbon becomes **12 mg**.