Iron crystallizes in several modifications. At about 910^ C , the body centred cubic -form undergoes a transition to the face centred cubic -form. Assuming that the distance between nearest neighbours is same in the two forms at the transition temperature. Calculate the ratio of density of -iron to that of iron at the transition temperature.

Step-by-step solution

In bcc structure ( form) of iron 4 r= 3 a n =2 atoms per unti cell from (one atom from 8 corners, one atom from the body centre) So, ( -form )= n M_m a^3 N₀ = 2 M_m ( 4 3 r )^3 N₀ ....(i) In fcc structue ( r form) of iron 4 r= 2 a a=2 2 r n =4 atoms per unit cell ( form )= 4 M_m (2 2 r)^3 N₀ ...(ii) Dividing Eq. (ii) by Eq. (i) (y form ) ( form ) = 2 ( 4 3 r )^3 (2 2 r)^3 4 =1.0887