Question

If the effective radius of iron (Fe) atom is $141.4$ pm which has rock salt type structure, then its density (in g cm${}^{-3}$) will be:

[$Fe=56$ amu]

• A. $5.81$
• B. $2.63$
• C. $1.08$
• D. None of the above

Answer 1

The correct option is A $5.81$

In rock salt type structure its form fcc type unit cell where edge legth, $a=2\sqrt{2}r$

$⟹a\approx 400\text{pm}$

Density, $d=\frac{zM}{N_A\times (a{)}^3}$

For FCC structure, $z=4$

Now,

Density, $d=\frac{4\times 56}{6.02\times {10}^{23}\times (400\times {10}^{-10}{)}^3}$

Density, $d=5.81{\text{g cm}}^{-3}$

Hence, the correct option is $\text{A}.$