Test: Crystal Lattices and Unit Cells - Chemistry MCQ

Given,
Edge length (a) = 500 pm = 500 x 10^-12 m
Atomic mass (M) = 110 g/mole = 110 x 10^-3 kg/mole
Avogadro’s number (N_A) = 6.022 x 10²³/mole
z = 4 atoms/cell
The density, d of a metal is given as d= 
On substitution, d =5846 kg/m³.

A unit cell is characterized by six parameters i.e. the three common edge lengths a, b, c and three angles between the edges that are α, β, γ. These are referred to as inter-axial lengths and angles, respectively. The position of a unit cell can be determined by fractional coordinates along the cell edges.

Atomic mass of Al = 27g/mole (contains 6.022 x 10²³ Al atoms)
Since it exhibits FCC, there are 4 Al atoms/unit cell.
If 27g Al contains 6.022 x 10²³ Al atoms then 54g Al contains 1.2044 x 10²⁴atoms.
Thus, if 1 unit cell contains 4 Al atoms then number of unit cells containing 1.2044 x 10²⁴ atoms=(1.2044 x 1024 x 1)/4 = 3.011× 10²³ unit cells.

The number of tetrahedral voids form is equal to twice the number of atoms of element X. Number of atoms of Y is 3/4th the number of tetrahedral voids i.e. 3/2 times the number of atoms of X. Therefore, the ratio of numbers of atoms of X and Y are 2:3, hence X2Y3.

The given figure represents an orthorhombic unit cell. Experimentally, it is determined that for orthorhombic unit cells a ≠ b ≠ c. All sides are unequal. It results from extension of cube along two pairs of orthogonal sides by two distinct factors.

For a crystal lattice, if there are N close-packed spheres the number of tetrahedral voids are 2N and number octahedral voids are N. For N=6, number of tetrahedral voids = 2 × 6 = 12.

Coordination number of a unit cell is defined as the number of atoms/ions that surround the central atom/ion. In the case of BCC, the central particle is surrounded by 8 particles hence, 8.

Unit cell is the smallest entity of a crystal lattice which, when repeated in space (3 dimensions) generates the entire crystal lattice. Lattice comprises of the unit cells which hold all the particles in a particular arrangement in 3 dimensions. Crystal is a piece of homogenous solid and Bravais indices are used to define planes in crystal lattices in the hexagonal system.

Each point of the particle’s position is referred to as ‘lattice point’ or ‘lattice site’. Every lattice point represents one constituent particle which may be an atom, ion or molecule.

For body-centered unit cells, the relation between radius of a particle ‘r’ and edge length of unit cell ‘a’ is given as 
On substituting the values we get r =  x 333 pm = 144.19 pm is the radius of the metal atom.

Since particles are assumed to be spheres and volume of one sphere is total volume of all particles in BCC =  since a BCC has 2 particles per cell.

The description is of a BCC. For BCC, each atom at the corner is shared by 8 unit cells. One atom at the center wholly belongs to the corresponding unit cell.
Therefore, total number of atoms of A present= 1/8 x 8=1
Total number of atoms of B present=1
Therefore, A:B=1:1 implying the formula of the compound is AB.

Crystalline solids possess anisotropic nature within their structure. Anisotropy is the directional dependence of a property. Meaning, a property within the crystal structure will have different values when measured in different directions. Snowflake is a crystalline solid whereas the rest are amorphous solids.

Simple cubic lattice results from 3D close packing from 2D square-packed layers. When one 2D layer is placed on top of the other, the corresponding spheres of the second layer are exactly on top of the first one. Since both have the same, exact arrangement it is AAA type.

According to classification of unit cells, a primitive unit cell is one which has all constituent particles located at its corners. BCC has one particle present at the center including the corners. FCC has an individual cell shared between the faces of adjacent cells. End centered cells have cells present at centers of two opposite faces.