Answer: The density of metal X is [tex]7.19g/cm^3[/tex]
Explanation:
We are given:
Atomic radius of metal X = [tex]1.20\times 10^2pm=120pm[/tex]
To calculate the edge length, we use the relation between the radius and edge length for FCC lattice:
[tex]a=2\sqrt{2}R[/tex]
Putting values in above equation, we get:
[tex]a=2\sqrt{2}\times 20=339.4pm[/tex]
To calculate the density of metal, 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 = 4 (FCC)
M = atomic mass of metal = 42.3 g/mol
[tex]N_{A}[/tex] = Avogadro's number = [tex]6.022\times 10^{23}[/tex]
a = edge length of unit cell = [tex]339.4pm=339.4\times 10^{-10}cm[/tex] (Conversion factor: [tex]1cm=10^{10}pm[/tex] )
Putting values in above equation, we get:
[tex]\rho=\frac{4\times 42.3}{6.022\times 10^{23}\times (339.4\times 10^{-10})^3}\\\\\rho=7.19g/cm^3[/tex]
Hence, the density of metal X is [tex]7.19g/cm^3[/tex]
