Question

Na and Mg crystallize in BCC and FCC types of crystals respectively. What will be the number of atoms of Na and Mg present in the unit cell of their respective crystal?

Answer 1

Hint: The FCC and BCC are the types of arrangement of atoms in the unit cell. BCC is the body-centered cubic type of crystal and FCC is the face-centered cubic type of crystal. The number of atoms in all the different types of crystals is fixed. It depends upon how the atoms are arranged in the unit cell.

Complete answer:
In BCC type crystals the atoms are arranged in a cube at each corner of the cube and also there is one atom present in the center of the cube.
In FCC-type crystals, eight atoms are present at the corners of the unit cell and one atom centered in each of the faces.
In the BCC lattice the number of atoms is $2$ and in the FCC lattice the number of atoms is $4$. Let us see how we get these numbers.
In the BCC lattice, $8$ atoms are present at $8$ corners of the BCC unit cell. Each atom contributes one eight to the unit cell, so the total contribution$ = 8 \times \dfrac{1}{8} = 1$. $1$ atom is present at the body center of the BCC unit cell. The atom will contribute fully to the unit cell. So total contribution$ = 1 \times \dfrac{1}{1} = 1$, thus the total number of atoms in one bcc unit cell $ = 1 + 1 = 2$
Therefore the number of atoms in the BCC lattice of Na $ = 2$
Now for FCC unit cell: there are $8$ atoms present at $8$ corners of BCC unit cells. Each atom contributes one eight to the unit cell, so the total contribution$ = 8 \times \dfrac{1}{8} = 1$. $6$ atoms are present at $6$ corners of the FCC unit cell. Each atom contributes one half to the unit cell. So the total contribution$ = 6 \times \dfrac{1}{2} = 3$. Thus total number of atoms in one FCC unit cell$ = 1 + 3 = 4$.
Therefore the number of atoms in FCC lattice of Mg $ = 4$

Note:
The BCC and FCC arrangements are used to describe the location of atoms, molecules, or ions and the empty spaces present in a lattice structure. The unit cell structures help in determining some of the properties of metals, such as FCC structures more likely to be ductile than BCC.