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 problem of finding the number of atoms in one mole of carbon, we can follow these steps:

### Step-by-Step Solution:

1. **Given Data**:
- Mass of one mole of carbon atoms = 12 grams
- Mass of one carbon-12 atom = \(1.9926 \times 10^{-23}\) grams

2. **Concept**:
- One mole of any substance contains Avogadro's number (\(N_A\)) of particles (atoms, molecules, etc.). Avogadro's number is \(6.022 \times 10^{23}\).

3. **Calculation**:
- To find the number of atoms in one mole of carbon, we use the relationship between the mass of one mole of carbon and the mass of a single carbon atom.

4. **Formula**:
- Number of atoms in one mole = \(\frac{\text{Mass of one mole of carbon}}{\text{Mass of one carbon atom}}\)

5. **Substitute the values**:
\[ \text{Number of atoms} = \frac{12 \text{ grams}}{1.9926 \times 10^{-23} \text{ grams/atom}} \]

6. **Perform the division**:
\[ \text{Number of atoms} = \frac{12}{1.9926 \times 10^{-23}} \]

7. **Simplify the calculation**:
\[ \text{Number of atoms} = 6.022 \times 10^{23} \]

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