The edge length of unit cell of a metal having molecular weight 75 ~g / mol is 5 Å which crystallizes in cubic lattice. If the density is 2 ~g / cc then find the radius of metal atom, (N_A=6 10²³ ) . Give the answer in pm.

Step-by-step solution

For cubic lattice, = Z A N_A V or Z= N_A V A Given that, aligned & A=75 ~g / mol & V=(5 Å)^3= (5 10⁻⁸ )^3 ~cm ^3 & =125 10⁻²⁴ ~cm ^3 & N_ A =6.02 10²³ & =2 gm / cc & Z= 2 6.02 10²³ 125 10⁻²⁴ 75 2 & aligned The value of Z represents that element must have body centred cubic (bcc) structure. For bcc structure atomic radius (r)= 3 4 a= 3 4 5=2.165 Å =216.5 pm