Question

When heated above ${916}^{o}C,$ iron changes its crystal structure from bcc to ccp structure without any change in the radius of atom. The ratio of density of the crystal before heating and after heating is :

• A. $1.089$
• B. $0.918$
• C. $0.725$
• D. $1.231$

Answer 1

Answer: (B)

$0.918$

I) for BCC , $Z=2$, $4r=a\sqrt{3}$, $M_A=56$ edge length=$a_1$

${\rho }_{BCC}=\frac{2\times 56}{N_A\times {a_1}^3}=\frac{112\times 3\sqrt{3}}{N_A\times 64r^3}=K\times 3\sqrt{3}$

II) for FCC, $Z=4$, $4r=a_2\sqrt{2}$, $M_A=56$ edge length=$a_2$

${\rho }_{FCC}=\frac{4\times 56}{N_A\times {a_2}^3}=\frac{2\times 112\times 2\sqrt{2}}{N_A\times {64r}^3}=\frac{224\times 2\sqrt{2}}{N_A\times {64r}^3}=K\times 4\sqrt{2}$

$\frac{{\rho }_{BCC}}{{\rho }_{FCC}}=\frac{3\sqrt{3}}{4\sqrt{2}}=0.918$