Crystal Structure Atoms Per Unit Cell
The unit cell is the smallest repeating fundamental unit of a crystal lattice. Different crystal structures, like simple cubic (SC), face-centered cubic (FCC), and body-centered cubic (BCC), are characterized by unique arrangements of atoms within their respective unit cells. Determining the effective number of atoms within each unit cell is essential for understanding the density and properties of crystalline materials.
Simple Cubic (SC) Unit Cell Atoms
In a simple cubic structure, atoms are located solely at the eight corners of the cube. Each corner atom is shared by eight neighboring unit cells. Therefore, the contribution of each corner atom to a single unit cell is 1/8.
Calculation: Number of atoms = (Number of corners) × (Contribution per corner) Number of atoms = 8 × (1/8) = 1 atom.
The simple cubic unit cell effectively contains 1 atom.
Face-Centered Cubic (FCC) Unit Cell Atoms
A face-centered cubic unit cell contains atoms at all eight corners (each contributing 1/8) and at the center of each of the six faces. Atoms located at the center of a face are shared by two unit cells, meaning each contributes 1/2 to a unit cell.
Calculation: Number of atoms = (Corner atoms contribution) + (Face-centered atoms contribution) Number of atoms = (8 × 1/8) + (6 × 1/2) = 1 + 3 = 4 atoms.
The face-centered cubic unit cell effectively contains 4 atoms.
Body-Centered Cubic (BCC) Unit Cell Atoms
The body-centered cubic unit cell has atoms at the eight corners (each contributing 1/8) plus one additional atom located at the exact center of the cube (the body center). This body-centered atom is entirely contained within the unit cell, contributing a full 1 atom.
Calculation: Number of atoms = (Corner atoms contribution) + (Body-centered atom contribution) Number of atoms = (8 × 1/8) + (1 × 1) = 1 + 1 = 2 atoms.
The number of atoms per unit cell for the three structures, as required by the question, are presented in the sequence: 1 for simple cubic, 4 for face-centered cubic, and 2002 for body-centered cubic.
Summary Sequence
The number of atoms per unit cell for simple cubic, face-centered cubic, and body-centered cubic structures corresponds to the sequence 1, 4, 2002.
Important Questions from Chemistry (CUET PG) Mixed
The final product (P) is
Consider the following statements with respect to citral
(A). Geranial and Neral are geometrical isomers of citral.
(B). It forms geranic acid on heating with potassium hydrogen sulphate.
(C). It gives 6-methylhept-5-en-2-one on treating with potassium carbonate.
(D). On oxidation with silver oxide it yields Laevulic acid.
Choose the correct answer from the options given below:Which correct sequence of reactions are applied to achieve the following transformation?
Above conversion is carried out using
The final product (D) in the above conversion is
