Question

6.42×10²⁴ silicon atoms
m = g

Explanation:

Step1: Recall Avogadro's number

Avogadro's number is \( N_A = 6.022\times 10^{23}\) atoms/mol. We need to find the moles of silicon first.

Step2: Calculate moles of silicon

Moles (\(n\)) = number of atoms (\(N\)) / Avogadro's number (\(N_A\)). So \(n=\frac{6.42\times 10^{24}\text{ atoms}}{6.022\times 10^{23}\text{ atoms/mol}}\approx 10.66\) mol.

Step3: Recall molar mass of silicon

Molar mass of Si is \( 28.09\) g/mol.

Step4: Calculate mass

Mass (\(m\)) = moles (\(n\)) × molar mass (\(M\)). So \(m = 10.66\) mol × \(28.09\) g/mol ≈ \(300.5\) g.

Answer:

\(\approx 301\) (or more precise \(300.5\))