Question

How many nearest and next nearest neighbors respectively does potassium have in b.c.c lattice?
A) $8$ , $8$
B) $8$ , $6$
C) $6$ , $8$
D) $8$ , $2$

Answer 1

Hint: We realize that a unit is that the littlest portrayal of an entire precious stone. During a unit, a molecule's coordination number is the quantity of iotas it's contacting. The coordination number of face-focused cubic (FCC) is twelve and contains four molecules for every unit. The coordination of body-focused cubic (bcc) is eight and contains two molecules for every unit.

Complete step by step answer:
We have to remember that the body centered cubic unit cell has the iotas at each of the eight corners of a shape in addition to one particle in the focal point of the 3D square. Every one of the corner iotas is the edge of another shape so the corners molecules are shared by 8 unit cells.
The no of atoms\[ = \left( {\dfrac{{{\text{Number of atom shared per unit cell}}}}{{{\text{Number of corners}}}}} \right) + \dfrac{{{\text{Number of atom per unit cell}}}}{{{\text{Number of center atom}}}}\]
In body centered crystal lattice the particles present at the corners are called as the nearest neighbors and moreover a bcc structure has 8 corners atoms, so the potassium particle will have 8 nearest neighbors.

Second closest neighbors are the neighbors of the principal neighbors. So for BCC we should consider the particle at the body place, for this molecule the iota at the corner are closest and for the iotas at the corners the iota at body focuses of different 3D squares are closest. Little imagination (there are 6 body focused molecules encompassing the iota we are thinking about) and considering offers the response six.

Therefore, the option B is correct.

Note: We must remember that the radius of atom in bcc is given by,
Radius of atom in bcc(r)$ = \dfrac{{\sqrt {3a} }}{4}pm$
Where a is the edge length of the atom
The second closest neighbor is at the separation of a.Consequently for the middle particle (It will apply for the wide range of various too). First closest neighbor is eight (molecules at corner)and The Second closest neighbor is six.