Question

The planar density for BCC (110) plane in terms of 1/R2 , where R is the atomic radius, is

Answer 1

Given info : The planar density for BCC (110) plane in terms of 1/R²

To find : planar density.

Solution : for Body centered cubic lattice (110) [ shown in figure ]

Panar density = (number of atoms located on the plane)/(area of plane)

Area of plane = √2a²

Here a = edge length

We know, for BCC , 4R = √3a

so, area of plane = √2 × (4R/√3)² = 16√2R²/3

Number of atoms in the plane = (1/8 + 1/8 + 1/8 + 1/8) = 1/2

now planar density = (1/2)/(16√2R²/3)

= 3/32√2R²

therefore planar density of BCC(110) is 3/32√2R²