To solve the problem of determining how many moles are in a sample of neon containing [tex]\(8.6 \cdot 10^{24}\)[/tex] atoms, follow these steps:
1. Understand the Problem:
- You are given the number of atoms in the sample: [tex]\(8.6 \cdot 10^{24}\)[/tex] atoms.
- You need to find out how many moles this amount of atoms corresponds to.
2. Know the Relevant Concept:
- One mole of any substance contains [tex]\(6.022 \cdot 10^{23}\)[/tex] atoms (known as Avogadro's number).
3. Use the Formula for Moles:
- The formula to convert between the number of atoms and the number of moles is:
[tex]\[
\text{Number of moles} = \frac{\text{Number of atoms}}{\text{Avogadro's number}}
\][/tex]
4. Substitute the Given Values:
- Number of atoms given: [tex]\(8.6 \cdot 10^{24}\)[/tex]
- Avogadro's number: [tex]\(6.022 \cdot 10^{23}\)[/tex]
5. Perform the Calculation:
[tex]\[
\text{Number of moles} = \frac{8.6 \cdot 10^{24}}{6.022 \cdot 10^{23}}
\][/tex]
6. Evaluate the Expression:
- Calculate the division:
[tex]\[
\frac{8.6 \cdot 10^{24}}{6.022 \cdot 10^{23}} \approx 14.280969777482564
\][/tex]
Therefore, a sample of neon containing [tex]\(8.6 \cdot 10^{24}\)[/tex] atoms corresponds to approximately 14.28 moles.
7. Compare the Answer with the Given Options:
- The closest answer to 14.280969777482564 is 14 moles.
Conclusion:
Thus, the correct answer is 14 moles.
