Answer:
[tex]1.536 g/cm^3[/tex] is the density of solid calcium.
Explanation:
Formula used :
[tex]\rho=\frac{Z\times M}{N_{A}\times a^{3}}[/tex]
where,
[tex]\rho[/tex] = density
Z = number of atom in unit cell
M = atomic mass
[tex](N_{A})[/tex] = Avogadro's number
a = edge length of unit cell
We have:
r = 197 pm = [tex]197\times 10^{-12} m = 197\times 10^{-12}\times 100 cm[/tex]
[tex]r=197\times 10^{-10} m[/tex]
[tex]a=r\times 2\sqrt{2}[/tex]
[tex]a=197\times 10^{-10} m\times 2\sqrt{2}=557.200\times 10^{-10} cm[/tex]
M = 40 g/mol
Z = 4
On substituting all the given values , we will get the value of 'a'.
[tex]\rho =\frac{4\times 40 g/mol}{6.022\times 10^{23} mol^{-1}\times (557.200\times 10^{-10} cm)^{3}}[/tex]
[tex]\rho =1.536 g/cm^3[/tex]
[tex]1.536 g/cm^3[/tex] is the density of solid calcium.
