A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is $'a'$, the closest approach between two atoms in metallic crystal will be :
- $\sqrt{2} a $
- $\frac{a}{\sqrt{2}}$
- $2a$
- $2\sqrt{2} a$
The Correct Option is B
Solution and Explanation
By $\Delta ABC$,
$2a^{2} = 16r^{2}$
$\Rightarrow r^{2} = \frac{1}{8} a^{2}$
$\Rightarrow r = \frac{1}{2 \sqrt{2}} a$
Distance of closest approach $ = 2r = \frac{a}{\sqrt{2}}$
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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.