To determine how many atoms of carbon are in Rachel's sample, we need to use Avogadro's number, which is approximately [tex]\(6.022 \times 10^{23}\)[/tex] atoms per mole. Rachel has a sample containing 2 moles of carbon.
Here's the step-by-step solution:
1. Identify the number of moles of carbon in the sample:
- Rachel's sample contains 2 moles of carbon.
2. Use Avogadro's number to find the number of atoms in one mole of carbon:
- Avogadro's number is [tex]\(6.022 \times 10^{23}\)[/tex] atoms/mole.
3. Multiply the number of moles by Avogadro's number to find the total number of atoms:
- Total number of atoms = (number of moles) × (Avogadro's number)
- Total number of atoms = [tex]\(2 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mole}\)[/tex]
4. Perform the multiplication:
- Total number of atoms = [tex]\(1.2044 \times 10^{24}\)[/tex] atoms
After completing the calculation, we find that the number of atoms of carbon in Rachel's sample is:
[tex]\[ \boxed{1.204 \times 10^{24} \text{ atoms}} \][/tex]
Therefore, the correct answer is:
C. [tex]\(1.204 \times 10^{24}\)[/tex] atoms
