Question

Pyrite, $Fe{S}_2$ crystallises in a cubic unit cell with a cell edge of 0.54 nm. The density of pyrite is $5.02g/c{m}^3$. How many $F{e}^{2+}$ and $S_2^{2-}$ ions are present in a single unit cell?
(S = 32, Fe =56u)

• A. $1F{e}^{2+}$ and $1S_2^{2-}$
• B. $2F{e}^{2+}$ and $2S_2^{2-}$
• C. $4F{e}^{2+}$ and $4S_2^{2-}$
• D. $6F{e}^{2+}$ and $6S_2^{2-}$

Answer 1

The correct option is C $4F{e}^{2+}$ and $4S_2^{2-}$

$d=\frac{ZM}{a^3{N}_A}$

$M=2\times 32+56=120$

$5.02=\frac{Z\times 120}{6.023\times {10}^{23}\times (5.4\times {10}^{-8}{)}^3}$

$Z=4i.e.,4F{e}^{2+}$ and $4S_2^{2-}$ ions are present in a single unit cell.