To calculate the relative atomic mass (RAM) of element A, we follow these detailed steps:
1. Identify the given values:
- Number of atoms of element A: [tex]\(1.58 \times 10^{19}\)[/tex]
- Mass of the sample: [tex]\(1.05 \times 10^{-3}\)[/tex] grams
2. Recall Avogadro's number:
- Avogadro's number is approximately [tex]\(6.022 \times 10^{23}\)[/tex] atoms/mol. This number represents the quantity of atoms in one mole of any substance.
3. Calculate the relative atomic mass:
- The formula to calculate the relative atomic mass (RAM) is given by:
[tex]\[
\text{RAM} = \left( \frac{\text{mass of the sample (in grams)}}{\text{number of atoms}} \right) \times \text{Avogadro's number}
\][/tex]
4. Substitute the given values into the formula:
- Mass of the sample [tex]\( m = 1.05 \times 10^{-3} \, \text{g} \)[/tex]
- Number of atoms [tex]\( N = 1.58 \times 10^{19} \)[/tex]
- Avogadro's number [tex]\( N_A = 6.022 \times 10^{23} \)[/tex]
Substituting into the formula, we get:
[tex]\[
\text{RAM} = \left( \frac{1.05 \times 10^{-3} \, \text{g}}{1.58 \times 10^{19}} \right) \times 6.022 \times 10^{23}
\][/tex]
5. Calculate the value inside the parentheses first:
[tex]\[
\frac{1.05 \times 10^{-3} \, \text{g}}{1.58 \times 10^{19}} \approx 6.65 \times 10^{-23} \, \text{g/atom}
\][/tex]
6. Multiply by Avogadro's number:
[tex]\[
\text{RAM} = 6.65 \times 10^{-23} \, \text{g/atom} \times 6.022 \times 10^{23} \, \text{atoms/mol}
\][/tex]
7. Simplify to find the RAM:
[tex]\[
\text{RAM} \approx 40.019620253164554 \, \text{g/mol}
\][/tex]
Thus, the relative atomic mass of element A is approximately [tex]\(40.02 \, \text{g/mol}\)[/tex].
