Question

A metal crystallizes in a face-centered cubic lattice. The radius of the atom is 0.126 nm. The density of the element is 1.92 g/cm³. What is this metal?

Answer 1

In fcc no of atoms=4

density=1.92g/cm$^3$

radius=0.126nm= 0.126*10$^-9$

we know that

r= $\tfrac{a}{2(2)^1/2}$

a= 0.126$10^-9$ *2.8

a=0.31*$10^-9$

now

d=$\tfrac{ZM}{a^3N_A}$

1.92=$\tfrac{4M}{0.0302*10^-27*6*10^23}$

M=0.0869*10$^-4$ g\mol