Question

how many nearest and next nearest neighbours respectively each potassium has in BCC lattice

Answer 1

In bcc lattice the corner atoms are called as the nearest neighbours and also a bcc structure has 8 corners atoms, so the pottassium atom will have 8 nearest neighbours.

Second nearest neighbors are the neighbors of the first neighbors. So for BCC let's consider the atom at the body centre, for this atom the atom at the corner are nearest and for the atoms at the corners the atom at body centres of other cubes are nearest. Little imagination(there are 6 body centred atoms surrounding the atom we are considering) and counting gives the answer as six.