Question:

Which of the following is correct?

  • Crystal system - Cubic Axial Distance - $a \neq b=c$ Axial angles $-\alpha=\beta \neq \gamma$ Examples -$Cu, KCl$
  • Crystal system - Monoclinic Axial Distance - $\alpha \neq b=c$ Axial angles - $\alpha \neq \beta=\gamma$ $=90^{\circ}$ Examples - $p b C r O_{2}, p b C r O_{4}$
  • Crystal system - Rhombohedral Axial Distance $-a=b=c$ Axial angles - $\alpha=\beta=\gamma \neq 90^{\circ}$ Examples - $CaCO _{3}$, Hgs
  • Crystal system - Triclinic Axial Distance - $a = b = c$ Axial angles $-\alpha \neq \beta=\gamma \neq 90^{\circ}$ Examples - $K _{2}\, Cr _{2} \,O _{7}\, CuSO _{4} \,5 H _{2} O$
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The Correct Option is C

Solution and Explanation

[a] For cubic $a=b=c$ and $a=\beta=\gamma=90^{\circ}$ So, it is wrong. [b] For monoclinic $a \neq b \neq c$ and $\alpha=\gamma=90^{\circ}$ and $\beta \neq 90^{\circ}$ $\therefore$ is wrong. [c] For triclinic $a \neq b \neq c$ and $\alpha \neq \beta \neq \gamma \neq 90^{\circ} $ $\therefore$ It iswrong. [d] For rhombohedral crystal system $a=b=c$ and $\alpha=\beta=\gamma \neq 90^{\circ}$.
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Concepts Used:

Unit Cells

The smallest portion of a crystal lattice which repeats in different directions to form the entire lattice is known as Unit cell.

The characteristics of a unit cell are:

  • The dimensions are measured along the three edges, a, b and c. These edges can form different angles, they may be mutually perpendicular or may not.
  • The angles held by the edges are α (between b and c) β (between a and c) and γ (between a and b).

Therefore, a unit cell is characterised by six parameters such as a, b, c and α, β, γ.

Types of Unit Cell:

Numerous unit cells together make a crystal lattice. Constituent particles like atoms, molecules are also present. Each lattice point is occupied by one such particle.

  1. Primitive Unit Cells: In a primitive unit cell constituent particles are present only on the corner positions of a unit cell.
  2. Centred Unit Cells: A centred unit cell contains one or more constituent particles which are present at positions besides the corners.
    1. Body-Centered Unit Cell: Such a unit cell contains one constituent particle (atom, molecule or ion) at its body-centre as well as its every corners.
    2. Face Centered Unit Cell: Such a unit cell contains one constituent particle present at the centre of each face, as well as its corners.
    3. End-Centred Unit Cells: In such a unit cell, one constituent particle is present at the centre of any two opposite faces, as well as its corners.