If the atomic weight of carbon is set at 24 amu, the value of the avogadro constant would be :-

Options

A. `6.022xx10^(23)`
B. `12.044xx10^(23)`
C. `3.011xx10^(23)`
D. none of these

Explanation

To find the value of the Avogadro constant when the atomic weight of carbon is set at 24 amu, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Atomic Mass Unit (amu)**:
- The atomic mass unit is defined based on the carbon-12 isotope. Specifically, 1 amu is defined as 1/12 of the mass of a carbon-12 atom.

2. **Setting the New Atomic Mass Unit**:
- If the atomic weight of carbon is set to 24 amu, we can express this in terms of the standard atomic mass unit. We can say:
\[ 1 \text{ amu} = \frac{1}{24} \times \text{mass of carbon-12} \]

3. **Relating Old and New Atomic Mass Units**:
- The old atomic mass unit (1 amu) corresponds to the mass of carbon-12, while the new atomic mass unit corresponds to the new definition (24 amu). Therefore, we can express the relationship as:
\[ \text{Old amu} = 2 \times \text{New amu} \]

4. **Expressing Avogadro's Number**:
- We know that 1 amu is also equal to \( \frac{1}{N_A} \), where \( N_A \) is Avogadro's number. Thus, we can write:
\[ \text{New amu} = \frac{1}{N_A'} \quad \text{(where \( N_A' \) is the new Avogadro's number)} \]

5. **Setting Up the Equation**:
- From the previous steps, we have:
\[ \frac{1}{N_A'} = \frac{1}{2N_A} \]
- Rearranging gives:
\[ N_A' = 2N_A \]

6. **Calculating the New Avogadro's Number**:
- The original Avogadro's number \( N_A \) is approximately \( 6.022 \times 10^{23} \). Therefore:
\[ N_A' = 2 \times 6.022 \times 10^{23} = 12.044 \times 10^{23} \]

7. **Final Result**:
- Thus, the value of the Avogadro constant when the atomic weight of carbon is set at 24 amu is:
\[ N_A' = 12.044 \times 10^{23} \text{ molecules/mol} \]