Question

The effective radius of an iron atom is $1.42\mathring{A}$. It has FCC structure. Calculate its density (in g.cm${}^{-3}$) if it is given that the atomic mass of $Fe$ is $56$ amu.

• A. $2.47$
• B. $5.74$
• C. $8.24$
• D. None of the above

Answer 1

Answer: (B)

$5.74$

$d=\frac{zM}{N_A\times V}$
For FCC ,
$z=4$
$a=2\sqrt{2}r$
$⟹a=4.02\times {10}^{-8}$ cm
$d=\frac{4\times 56}{6.023\times {10}^{23}\times (4.02\times {10}^{-8}{)}^3}$
$d=\frac{4\times 56}{6.023\times 64.96\times {10}^{-1}}$
$d=5.74$ $gc{m}^{-3}$