Question

A metal 'M' is crystallised in F.C.C lattice. The number of unit cells in it having $2.4 \times {10^{ - 24}}$ atoms.
A.$6.023 \times {10^{23}}$
B.$\dfrac{{6.023 \times {{10}^{23}}}}{2}$
C.$2 \times 6.023 \times {10^{23}}$
D.$4 \times 6.023 \times {10^{23}}$

Answer 1

Hint:
Face-centered cubic lattice (fcc or cubic-F), like all the lattices, has lattice points at the eight corners of the unit cell plus additional points at the centers of each face unit cell. It has unit cell vectors $\,a{\text{ }} = b{\text{ }} = c\,$ and interaxial angles $\,\alpha = \beta = \gamma = 90^\circ .\,$ The number of atoms in a unit cell is equal to four.

Complete step by step answer:
Unit Cell is the smallest part (portion) of a particular crystal lattice. It is referred to as the simplest repeating unit in a crystal structure. The entire lattice is created by the repetition of the unit cell in different directions.
We know,
One unit cell contains four atoms.
Then on applying unitary method, we can say that
$ \Rightarrow $One atom is present in $\dfrac{1}{4}$ unit cell
$ \Rightarrow $$2.4 \times {10^{ - 24}}$atoms will be present in
$
   = \dfrac{1}{4} \times 2.4 \times {10^{24}} \\
   = 6 \times {10^{23}}atoms \\
 $
So the correct answer is option A.

Note:The simplest crystal structures are those ones in which there is only a single atom at each lattice point. In the FCC structures the spheres fill seventy four percent of the volume. There are $26$ metals in total that have the FCC lattice.
-The structures of all crystals would be classified according to the symmetry of the unit cells. There are collectively seven groups, collectively called Crystal Systems: Tricinic, Monoclinic, Orthorhombic, Tetragonal, Trigonal, Hexagonal, and Cubic are the names.
-Metals which possess face-centered cubic structure include copper, aluminum, silver, and gold.