# 1.18.   An element with molar mass  $\inline 2.7\times 10^{-2}kg\; mol^{-1}$  forms a cubic unit cell with edge length $\inline 405\; pm$. If its density is $\inline 2.7\times 103\; kg\; m^{-3},$ what is the nature of the cubic unit cell?

We know that :

$Density\ of\ unit\ cell = \frac{z.M}{a^3.N_A}$

We are given :        $Density = 2.7\times10^3\ Kg\ m^{-3}$

and                        $Molar\ mass = 2.7\times10^{-2}\ Kg\ mol^{-1}$

and                      $Edge\ length = 405 pm =4.05\times10^{-10}\ m$

So we need to find z (no. of atoms present in unit cell) by putting all values in formula of density.

We get,                          $z \approx 4$.

It is known that face centred cubic also has 4 atoms in its unit cell, So given cubic unit cell is face centred.

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