Question

A cubic unit cell contains manganese ions at the corners and fluoride ions at the centre of each edge.

Calculate the edge length (in $\mathring{A}$) of the unit cell if the radius of $M{n}^{2+}$ ions is $0.65\mathring{A}$ and that of $F^{-}$ ion is $1.36\mathring{A}$.

• A. $4.0$
• B. $4.8$
• C. $6.2$
• D. $2.4$

Answer 1

Answer: (A)

$4.0$

Given that:
$r^{+}=0.65\mathring{A}$
$r^{-}=1.36\mathring{A}$

For such structure,
Along the edge,

$2r^{+}+2r^{-}=a$
$2r^{+}+2r^{-}=2\times 0.65+2\times 1.36$
$a\approx 4\mathring{A}$
Hence, the correct option is A.