Question

Compute the atomic density (the number of atoms per cm3 ... rather than the mass density g/cm3) for a perfect crystal of silicon at room temperature, given that the room temperature density and atomic weight of silicon are 2.33 g/cm3 and 28.09 g/mol, respectively.

Answer 1

Answer:

        $\large\boxed{\large\boxed{5.00\times 10^{22}atoms/cm^3}}$

Explanation:

You can convert the density into atomic density using the atomic weight and Avogadro's number

A dimensional analysis is very helpful:

           $\dfrac{g}{cm^3}\times \dfrac{mol}{g}\times \dfrac{atoms}{mol}=\dfrac{atoms}{cm^3}$

Follow the chain: g cancels with g, mol cancels with mol; at the end, what remains is atoms/cm³, which is what you want.

Use that with your data:

         $\dfrac{2.33g}{cm^3}\times \dfrac{1mol}{28.09g}\times \dfrac{6.022\times 10^{23}atoms}{mol}=\approx 5.00\times10^{22}atoms/cm^3$