Question

The edge length of a body-centre cubic unit cell is $390pm.$ If the radius of the cation is $150pm$, what is the radius of the anion?

• A. $147.7pm$
• B. $167.7pm$
• C. $187.7pm$
• D. $197.7pm$

Answer 1

The correct option is B $167.7pm$

In the bcc crytsal lattice, the atoms are present at corners of the cube and at the centres of the cube. Here, the corner atoms and the centre atoms are in contact along the body diagonal.

Here, the cation occupies the body centred position and the anion occupies the corners of the unit cell.


In a body - centred cubic unit cell,

$2(r^{+}+r^{-})=\sqrt{3}a$

$r^{+}+r^{-}=\frac{\sqrt{3}a}{2}$

$r^{-}=\frac{\sqrt{3}a}{2}-r^{+}$

Given:

$\text{Edge length,}a=390pm$
$r^{+}=150pm$

$r^{-}=\frac{\sqrt{3}\times 390}{2}-150$

$r^{-}=337.7-150=187.7pm$