The isotopic abundance of `C-12` and `C-14 "is" 98%` and `2%` respectively. What would be the number of `C-14` isotope
in `12 g` carbon sample?

Options

A. `1.032xx10^(22)`
B. `3.01xx10^(23)`
C. `5.88xx10^(23)`
D. `6.02xx10^(23)`

Explanation

To find the number of C-14 isotopes in a 12 g carbon sample, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the isotopic abundances**:
- C-12 abundance = 98%
- C-14 abundance = 2%

2. **Calculate the mass of C-14 in a 12 g carbon sample**:
- Since the abundance of C-14 is 2%, the mass of C-14 in 12 g of carbon can be calculated as:
\[ \text{Mass of C-14} = \left(\frac{2}{100}\right) \times 12 \text{ g} = 0.24 \text{ g} \]

3. **Calculate the number of moles of C-14**:
- The molar mass of C-14 is approximately 14 g/mol. To find the number of moles of C-14 in 0.24 g, we use the formula:
\[ \text{Number of moles of C-14} = \frac{\text{mass of C-14}}{\text{molar mass of C-14}} = \frac{0.24 \text{ g}}{14 \text{ g/mol}} \approx 0.01714 \text{ mol} \]

4. **Use Avogadro's number to find the number of C-14 atoms**:
- Avogadro's number (N_A) is \(6.022 \times 10^{23}\) atoms/mol. Therefore, the number of C-14 isotopes can be calculated as:
\[ \text{Number of C-14 atoms} = \text{Number of moles of C-14} \times N_A = 0.01714 \text{ mol} \times 6.022 \times 10^{23} \text{ atoms/mol} \approx 1.032 \times 10^{22} \text{ atoms} \]

### Final Answer:
The number of C-14 isotopes in a 12 g carbon sample is approximately \(1.032 \times 10^{22}\) atoms.

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