To determine the number of atoms in a 0.635 gram sample of copper, we can follow these steps:
1. Identify the given data:
- Mass of the copper sample ([tex]\( m \)[/tex]): 0.635 grams
- The approximate molar mass of copper ([tex]\( M \)[/tex]): 63.546 grams per mole (commonly approximated to [tex]\( 63.5 \)[/tex] grams per mole for simplified calculations)
- Avogadro's number ([tex]\( N_A \)[/tex]): [tex]\( 6.022 \times 10^{23} \)[/tex] atoms per mole
2. Calculate the number of moles of copper:
The number of moles ([tex]\( n \)[/tex]) can be found using the formula:
[tex]\[
n = \frac{m}{M}
\][/tex]
Substituting the given values:
[tex]\[
n = \frac{0.635}{63.546}
\][/tex]
3. Estimated number of moles:
[tex]\[
n \approx 0.009992761
\][/tex]
4. Calculate the number of atoms:
The number of atoms can be found by multiplying the number of moles by Avogadro's number:
[tex]\[
\text{Number of atoms} = n \times N_A
\][/tex]
Substituting the values we have:
[tex]\[
\text{Number of atoms} = 0.009992761 \times 6.022 \times 10^{23}
\][/tex]
5. Calculate the result:
[tex]\[
\text{Number of atoms} \approx 6.017 \times 10^{21}
\][/tex]
Hence, the number of atoms in a 0.635 gram sample of copper is approximately [tex]\( 6.017 \times 10^{21} \)[/tex] atoms.
