Question

A cubic unit cell contains manganese ions at the corners and fluorides ions at the center of each edge. Calculate the density of the compound. (Given that atomic mass $Mn=55$amu and F is $19$amu).

Answer 1

${Z_{Mn}}^{+3}=8\times \frac{1}{8}=1$ Let the edge length be $a\mathring{A}$

${Z_F}^{-}=12\times \frac{1}{4}=3$

Formula:- $Mn{F}_3$ $M_A=112$, $Z=1$ formula unit of $Mn{F}_3$

$\rho =\frac{Z\times M_A}{N_A\times a^3}\Rightarrow \rho =\frac{1\times 112}{6.02\times {10}^{23}\times a^3\times {10}^{-24}}$

$=\frac{186}{a^3}$ $g/c{m}^3$