In ΔABG, b2 = a2 + a2
∴ b2 = 2a2;
In, ΔAGD,
C2 = a2 + b2 = a2 + 2a2
∴ C = \(\sqrt3a\)
Radius of the atom = r.
Length of the body diagonal C = 4r
\(\sqrt3a\) = 4r; a = \(\frac{4r}{\sqrt3}\)
Edge length of the cube = a = \(\frac{4r}{\sqrt3}\)
Volume of the cubic unit cell = a3 = \((\frac{4r}{\sqrt3})^3\)
Volume of one particle (sphere) = \(\frac{4}{3}\)πr3
The number of particles per unit cell of a BCC = 2
Total volume occupied by two spheres = 2 × \(\frac{4}{3}\)πr3
Packing efficiency = \(\frac{\textit{Total volume occupied by the two spheres}}{\textit{Volume of a cubic unit cell}}\) x 100
