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An element occuring in the bcc structure has $12.08 \times 10^{23}$ unit cells. The total number of atoms of the element in these cells will be
An element occuring in the bcc structure has $12.08 \times 10^{23}$ unit cells. The total number of atoms of the element in these cells will be
Updated On: Apr 26, 2024
- $24.16 \times 10^{23}$
- $36.18 \times 10^{23}$
- $6.04 \times 10^{23}$
- $12.08 \times 10^{23}$
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The Correct Option is A
Solution and Explanation
There are two atoms in a bcc unit cell. So, number of atoms in
$12.08 \times 10^{23}$ unit cells
$= 2 \times 12.08 \times 10^{23} = 24.16 \times 10^{23}$ atoms.
$12.08 \times 10^{23}$ unit cells
$= 2 \times 12.08 \times 10^{23} = 24.16 \times 10^{23}$ atoms.
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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.
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