Question

Statement: Iron has a body-centred cubic lattice structure. The edge length of the unit cell is found to be 286 pm. The radius of the iron atom is 123.84 pm.

If the given statement is true enter 1, else enter 0.

Answer 1

Atoms along the body diagonal (bd) touch each other. Thus, the body diagonal has a length that is four times the radius of the atom, R.

$bd=4R$

The relationship between a and R can be worked out by the Pythagorean theorem:

${\left(4R\right)}^2=3a^2$

Thus,

$4R=\sqrt{3}a$

$a=286$ pm

Hence, $R=\frac{\sqrt{3}}{4}\times 186=123.84$ pm

Hence, the given statement is $\text{true}$ and the correct entry is $1$