Question

The number of close neighbors in a body-centered cubic lattice of identical sphere is:
A.4
B.12
C.6
D.8

Answer 1

Hint:
 The smallest repeating array of atoms in a crystal is called a unit cell. A third common packing arrangement in metals, the body centered cubic unit cell has atoms at each of eight corners of a cube plus one atom in the center of the cube.

Complete step by step answer:
-The number of close neighbors in a body centered cubic lattice of identical spheres is 8.
In a body centered cubic lattice, spheres are present at 8 corners of the cube and the body centre. The sphere at the body centre is surrounded by eight spheres present at 8 corners.
- Therefore,It has lattice points at the eight corners of the unit cell plus an additional point at the center of the cell.
-It has unit cell vectors a=b=c and interaxial angles α+β+ϒ = 90˚.
-The simplest crystal structures are those in which there is only a single atom at each lattice point. In the bcc structures the spheres fill 68% of the volume.
-It is remarkable that for the bcc structure the next-nearest neighbours are only slightly further away which makes it possible for those to participate in bonds as well.

Hence, option D is correct.

Note:
 The bcc unit cell has a packing factor of 0.68. Some of the materials that have a bcc structure include lithium, sodium, potassium, chromium, barium, vanadium and tungsten. Metals which have a bcc structure are usually harder and less malleable than closely-packed metals such as gold.