Answer: The density of the given element is [tex]3.07g/cm^3[/tex]
Explanation:
To calculate the edge length, we use the relation between the radius and edge length for BCC lattice:
[tex]R=\frac{\sqrt{3}a}{4}[/tex]
where,
R = radius of the lattice = 0.17 nm
a = edge length = ?
Putting values in above equation, we get:
[tex]0.17=\frac{\sqrt{3}\times a}{4}\\\\a=\frac{0.17\times 4}{\sqrt{3}}=0.393nm[/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 = 2 (BCC)
M = atomic mass of metal = 56.08 g/mol
[tex]N_{A}[/tex] = Avogadro's number = [tex]6.022\times 10^{23}[/tex]
a = edge length of unit cell = [tex]0.393nm=3.93\times 10^{-8}cm[/tex] (Conversion factor: [tex]1cm=10^{7}nm[/tex] )
Putting values in above equation, we get:
[tex]\rho=\frac{2\times 56.08}{6.022\times 10^{23}\times (3.93\times 10^{-8})^3}\\\\\rho=3.07g/cm^3[/tex]
Hence, the density of the given element is [tex]3.07g/cm^3[/tex]
