Elements A and B have fcc and bcc structures respectively with a unit cell edge length of 3 ~A ^0 for both elements. The no. of atoms in 210 gm of A is equal to 594 gm of B . If density of A is 7 ~g ~cm ⁻³ , what is the density of B ?

Step-by-step solution

210 ~g of A contains ( N _ A M _ A 210 ) no. of atoms A and 594 ~g of B contains ( N _ A M _ A 594 ) no. of atoms B . [ M _ A . and M _ b are the atomic weights of A and B , respectively]. Now, N _ A M _ A 210= N _ A M _ B 594 or M_B M_A = 594 210 Effective no. of A atoms in fcc =4 and that of B atoms in bcc =2 d _ A = M _ A 4 ~N _ A a ^3 and d _ B = M _ B 2 ~N _ A a ^3 ; d _ A =7 ~g / cm ^3 d _ B d _ A = M _ B 2 M _ A 4 ; d _ B =7 594 210 2=9.9 ~g / cm ^3