A metal can be crystallized in both BCC and FCC unit cells whose edge lengths are 2 pm and 4 pm respectively. Then ratio of densities of FCC and BCC unit cells is

Dear Student,
Please find below the solution to the asked query;
we know,
         $Density = \frac{Z\times M}{a^3\times N_0\times {10}^{-30}}$
where,
       Z = no of particles present per unit cell i.e. 4 for FCC
      a = edge length 
     M = molecular mass of the compound
    $N_0$ = Avogadros no
Density of metal in FCC
    $\rho = \frac{4\times M}{4^3\times N_0\times {10}^{-30}}$
Density of metal in BCC
$\rho = \frac{2\times M}{2^3\times N_0\times {10}^{-30}}$
​we can calculate ratio of densities of FCC & BCC
      $\frac{4\times M}{4^3\times N_0\times {10}^{-30}}$:$\frac{2\times M}{2^3\times N_0\times {10}^{-30}}$
$\frac{{\rho }_1}{{\rho }_2} = \frac{4\times 2^3}{4^3\times 2}$
we get ,
Density Ratio of FCC & BCC is 1:4.
Hope this information will clear your doubts about the topic.
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