Answer: The density of phosphorus is [tex]3.81g/cm^3[/tex]
Explanation:
To calculate the density of phosphorus, we use the equation:
[tex]\rho=\frac{Z\times M}{N_{A}\times a^{3}}[/tex]
where,
[tex]\rho[/tex] = density
Z = number of atom in unit cell = 1 (CCP)
M = atomic mass of phosphorus = 31 g/mol
[tex]N_{A}[/tex] = Avogadro's number = [tex]6.022\times 10^{23}[/tex]
a = edge length of unit cell = [tex]238pm=238\times 10^{-10}cm[/tex] (Conversion factor: [tex]1cm=10^{10}pm[/tex] )
Putting values in above equation, we get:
[tex]\rho=\frac{1\times 31}{6.022\times 10^{23}\times (238\times 10^{-10})^3}\\\\\rho=3.81g/cm^3[/tex]
Hence, the density of phosphorus is [tex]3.81g/cm^3[/tex]
