For a BCC structure, if a = 351 pm, find r. Lithium forms a BCC structure having an edge length of a unit cell 351 pm, then find the atomic radius of lithium.
For a BCC structure, if a = 351 pm, find r. Lithium forms a BCC structure having an edge length of a unit cell 351 pm, then find the atomic radius of lithium.
Solution and Explanation
For a BCC (body-centered cubic) structure, the relationship between the lattice constant (a) and the atomic radius (r) is:
a = 4√(2)r/3 Solving for r, we get: r = (3a/4√(2)) Substituting the given value of a = 351 pm (or 3.51 Å), we get: r = (3 x 3.51 Å) / (4√(2)) r ≈ 1.53 Å
Therefore, the atomic radius of lithium in its BCC structure is approximately 1.53 Å.
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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.