Question:
The number of atoms contained in a fcc unit cell of a monoatomic substance is
The number of atoms contained in a fcc unit cell of a monoatomic substance is
Updated On: Jul 18, 2024
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The Correct Option is C
Solution and Explanation
Face centred cubic is also called cubic close packed arrangement. It has points at all the comers as well as at the centre of each of the six faces. In this arrangement, there is one atom at each of the eight comers.
The number of atoms present at comers per unit cell $=8\times \frac{1}{8}=1.$
The number of atoms present at faces per unit cell$=6\times\frac{1}{2}=3$
$\therefore$ Total number of atoms in ccp or fee arrangement =1+3 = 4
The no. of atoms is a unit cell may be calculated by the the formula
$Z = \frac{n_{c}}{8} + \frac{n_{b}}{1}+ \frac{n_{f}}{2} + \frac{n_{e}}{4} $
Where nc = no. of atom at the corner
$n_b$ = no. of atoms at body centre
$n_f$ = no. of atoms at face centre
$n_e$ = no. of atoms at edge centre.
An Fcc crystal contains
$ = \frac{8}{8} + \frac{6}{2} = 4 $ atoms in a unit cell.
The number of atoms present at comers per unit cell $=8\times \frac{1}{8}=1.$
The number of atoms present at faces per unit cell$=6\times\frac{1}{2}=3$
$\therefore$ Total number of atoms in ccp or fee arrangement =1+3 = 4
The no. of atoms is a unit cell may be calculated by the the formula
$Z = \frac{n_{c}}{8} + \frac{n_{b}}{1}+ \frac{n_{f}}{2} + \frac{n_{e}}{4} $
Where nc = no. of atom at the corner
$n_b$ = no. of atoms at body centre
$n_f$ = no. of atoms at face centre
$n_e$ = no. of atoms at edge centre.
An Fcc crystal contains
$ = \frac{8}{8} + \frac{6}{2} = 4 $ atoms in a unit cell.
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Concepts Used:
Unit Cells
The smallest portion of a crystal lattice which repeats in different directions to form the entire lattice is known as Unit cell.
The characteristics of a unit cell are:
- The dimensions are measured along the three edges, a, b and c. These edges can form different angles, they may be mutually perpendicular or may not.
- The angles held by the edges are α (between b and c) β (between a and c) and γ (between a and b).
Therefore, a unit cell is characterised by six parameters such as a, b, c and α, β, γ.
Types of Unit Cell:
Numerous unit cells together make a crystal lattice. Constituent particles like atoms, molecules are also present. Each lattice point is occupied by one such particle.
- Primitive Unit Cells: In a primitive unit cell constituent particles are present only on the corner positions of a unit cell.
- Centred Unit Cells: A centred unit cell contains one or more constituent particles which are present at positions besides the corners.
- Body-Centered Unit Cell: Such a unit cell contains one constituent particle (atom, molecule or ion) at its body-centre as well as its every corners.
- Face Centered Unit Cell: Such a unit cell contains one constituent particle present at the centre of each face, as well as its corners.
- End-Centred Unit Cells: In such a unit cell, one constituent particle is present at the centre of any two opposite faces, as well as its corners.