One mole of carbon atom weighs 12g, the number of atoms in it is equal to, ( Mass of carbon-12 is `1.9926xx10^(-23)g`)

Options

A. `1.2xx10^(23)`
B. `6.022xx10^(22)`
C. `12xx10^(22)`
D. `6.022xx10^(23)`

Answer

To solve the question regarding the number of atoms in one mole of carbon, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- We know that one mole of carbon weighs 12 grams.
- The mass of a single carbon-12 atom is given as \(1.9926 \times 10^{-23}\) grams.

2. **Calculate the Number of Atoms in One Gram**:
- To find out how many carbon atoms are in one gram, we can use the formula:
\[ \text{Number of atoms in 1 gram} = \frac{1 \text{ gram}}{\text{mass of one atom in grams}} \]
- Substituting the mass of one carbon atom:
\[ \text{Number of atoms in 1 gram} = \frac{1}{1.9926 \times 10^{-23}} \]

3. **Calculate the Number of Atoms in 12 Grams**:
- Since we need the number of atoms in 12 grams, we multiply the number of atoms in 1 gram by 12:
\[ \text{Number of atoms in 12 grams} = \left(\frac{1}{1.9926 \times 10^{-23}}\right) \times 12 \]

4. **Perform the Calculation**:
- First, calculate \(\frac{1}{1.9926 \times 10^{-23}}\):
\[ \frac{1}{1.9926 \times 10^{-23}} \approx 5.02 \times 10^{22} \]
- Now multiply by 12:
\[ \text{Number of atoms in 12 grams} = 5.02 \times 10^{22} \times 12 \approx 6.022 \times 10^{23} \]

5. **Final Result**:
- Therefore, the number of atoms in one mole of carbon is:
\[ \text{Number of atoms} = 6.022 \times 10^{23} \]

### Conclusion:
The number of atoms in one mole of carbon is \(6.022 \times 10^{23}\).

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