Question

The atomic radius of strontium (Sr) is $215 pm$ and it crystallises with a cubic closest packing. Edge length of the cube is:
A.$430 pm$
B.$608.2 pm$
C.$496.53 pm$
D.None of these.

Answer 1

Hint: The structure of strontium (Sr) is like FCC. And the relation between edge length and atomic radius in FCC is as $\sqrt 2 a = 4r$ because in FCC unit cell atoms are present at corner and at the face centres of the cube.

Complete step by step solution:
Unit of crystal: It is defined as the repeating unit in the crystal. They are of three types: (I) primitive cubic unit cell, (II) Body-centered cubic unit cell (III) Face-centered cubic unit cell.
Primitive cubic unit cell: In this unit cell, atoms are present only at the corners of the cube. We know that there are eight corners in a cube. So one atom is shared by right corners. So the contribution of an atom in one corner is $\dfrac{1}{8}$. The number of atoms present in a primitive cubic unit cell is one.
Body-centered cubic unit cell: In this unit cell, atoms are present at the centre and corners of the cube. We know that there is only one centre in a cube. So one atom is completely present there. And one atom is contributing to the eight corners. So the total number of atoms present in a Body-centered cubic unit cell is $2$.
Face-centered cubic unit cell: In this unit cell, atoms are present at corners and at the face centres of the cube. There are a total six faces in a cube. So one atom contributes to two face centres i.e. contribution is one atom is half. And one atom contributing to all eight corners of the cube. So there are four atoms present in the face-centered cubic unit cell.
The structure of strontium (Sr) is like FCC. And the relation between edge length and atomic radius in FCC is as $\sqrt 2 a = 4r$ because in FCC unit cell atoms are present at corner and at the face centres of the cube. Here in the question we are given with atomic radius and we have to find the edge length.
Here $r = 215 pm$ so $a = \dfrac{{4 \times 215}}{{\sqrt 2 }} = 608.2 pm$.

Hence, option B is correct.

Note: Density: It is defined as the mass per volume. Hence density of unit cell is mass of unit cell divided by volume of unit cell. The mass of a unit cell is equal to the product of the number of atoms in a unit cell and mass of each unit cell.