Question:
Total volume of atoms present in a face-centred cubic unit cell of a metal is (r is atomic radius):
Total volume of atoms present in a face-centred cubic unit cell of a metal is (r is atomic radius):
Updated On: Jul 5, 2022
- $\frac{20}{3}\pi r^{3}$
- $\frac{24}{3}\pi r^{3}$
- $\frac{12}{3}\pi r^{3}$
- $\frac{16}{3}\pi r^{3}$
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The Correct Option is D
Solution and Explanation
Total number of atoms in face centred cubic unit cell = 4
At comer $= 8\times\frac{1}{8} = 1$
On faces $= 6\times\frac{1}{2} = 3$
Total $= 4$
Total volume $= 4 \times \frac{4\pi r^{3}}{3}$
$= \frac{16}{3}\pi r^{3}$
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Concepts Used:
Solid State
Solids are substances that are featured by a definite shape, volume, and high density. In the solid-state, the composed particles are arranged in several manners. Solid-state, in simple terms, means "no moving parts." Thus solid-state electronic devices are the ones inclusive of solid components that don’t change their position. Solid is a state of matter where the composed particles are arranged close to each other. The composed particles can be either atoms, molecules, or ions.
Types of Solids:
Based on the nature of the order that is present in the arrangement of their constituent particles solids can be divided into two types;
- Amorphous solids behave the same as super cool liquids due to the arrangement of constituent particles in short-range order. They are isotropic and have a broad melting point (range is about greater than 5°C).
- Crystalline solids have a fixed shape and the constituent particles are arranged in a long-range order.