Question

What is void? Tungsten crystallizes into a BCC unit. If the edge length of this unit structure is $300pm$ then what will be the radius of the tungsten atom.

Answer 1

Hint: By using the relationship between radius and edge length for BCC structure which is equal to \[\sqrt 3 a = 4r\] we can find out the radius of the tungsten atom.

Complete answer:
The vacant spaces obtained between two constituent particles when arranged in close packed structure are called voids. These are triangular in shape. There are two types of voids: a) Tetrahedral voids b) Octahedral voids.
Tetrahedral voids are formed when a second layer similar to the first one in a two dimensional close packed structure is placed above it such that the spheres of the second layer are placed in the depression of the first layer. These are so called because a tetrahedron is formed when the centres of four spheres are joined. Octahedral voids are formed when the triangular voids of the second layer are above the triangular voids of the first layer, provided these voids do not overlap. One of them has the apex of the triangle pointing upwards and the other downwards. such voids are surrounded by six spheres and are called octahedral voids.
Putting the value of a which is equal to $300pm$ in the formula \[\sqrt 3 a = 4r\] we get, $r = \dfrac{{\sqrt 3 a}}{4} = \dfrac{{\sqrt 3 \times 300}}{4}$
$ \Rightarrow r = \dfrac {{1.732 \times 300}}{4} $
$ \Rightarrow r = 129.9pm$
Thus the radius of the tungsten atom is $129.9pm$.

Note:If N is the number of close packed spheres then, number of octahedral voids will be N and number of tetrahedral voids will be twice that of octahedral voids.