Silicon has a density of 2.23g/cm3 and atomic mass of 28.09g/mol calculate the number of atom in 1cm3 of silicon
This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Calculate the mass of silicon in $1\text{ cm}^3$.
The density of silicon is given as $2.23\ \frac{\text{g}}{\text{cm}^3}$.
Mass = Density $\times$ Volume
$$ \text{Mass} = 2.23\ \frac{\text{g}}{\text{cm}^3} \times 1\text{ cm}^3 = 2.23\text{ g} $$
Step 2: Calculate the number of moles of silicon in $1\text{ cm}^3$.
The atomic mass of silicon is $28.09\ \frac{\text{g}}{\text{mol}}$.
Number of moles = $\frac{\text{Mass}}{\text{Atomic Mass}}$
$$ \text{Number of moles} = \frac{2.23\text{ g}}{28.09\ \frac{\text{g}}{\text{mol}}} \approx 0.07938\text{ mol} $$
Step 3: Calculate the number of atoms in $1\text{ cm}^3$ of silicon.
Use Avogadro's number, which is $6.022 \times 10^{23}\ \frac{\text{atoms}}{\text{mol}}$.
Number of atoms = Number of moles $\times$ Avogadro's number
$$ \text{Number of atoms} = 0.07938\text{ mol} \times 6.022 \times 10^{23}\ \frac{\text{atoms}}{\text{mol}} $$
$$ \text{Number of atoms} \approx 4.781 \times 10^{22}\text{ atoms} $$
The number of atoms in $1\text{ cm}^3$ of silicon is:
$$ \boxed{4.781 \times 10^{22}\text{ atoms}} $$
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