Question

Iron exhibits bcc structure at room temperature. Above 900°C, it transforms to fcc structure. The ratio of density of iron at room temperature to that at 900°C (assuming molar mass and atomic radii of iron remains constant with temperature) is ______.

पर्याय

• `(3 sqrt 3)/(4 sqrt 2)`

• `(4 sqrt 3)/(3 sqrt 2)`

• `sqrt 3/sqrt 2`

• `1/2`

Answer 1

Iron exhibits bcc structure at room temperature. Above 900°C, it transforms to fcc structure. The ratio of density of iron at room temperature to that at 900°C (assuming molar mass and atomic radii of iron remains constant with temperature) is `bbunderline((3 sqrt 3)/(4 sqrt 2))`.

Explanation:

In fcc atoms along face diagram touch each other, i.e., `sqrt 2 a = 4 r`    ...(i)

In fcc atoms along body diagram touch each other, i.e., `sqrt 3 a = 4 r`    ...(ii)

∴ a = `(4 r)/sqrt 2`    ...[From (i)]

∴ a = `(4 r)/sqrt 3`    ...[From (ii)]

∴ `d_"bcc"/d_"fcc" = ((Z_"bcc" xx M)/(N_A * a^3))/((Z_"fcc" xx M)/(N_A * a^3))`

= `(N_A((4 r)/sqrt 2)^3/(4 xx M))/(N_A((4 r)/sqrt 2)^3`

= `(3 sqrt 3)/(4 sqrt 2)`