Question

Which unit cell has two sides of equal length, a third side of different length, and all angles equal to 90 degrees?

• A. Tetragonal
• B. Orthorhombic
• C. Hexagonal
• D. Cubic

Hint:

Tetragonal = two equal sides + one different + all 90° angles. It’s like stretching a cube along one axis!

Answer 1

The Correct Option is A

A unit cell is the smallest repeating unit in a crystal lattice that defines the structure’s symmetry and dimensions. Each crystal system is classified based on the length of the edges (\(a, b, c\)) and the angles (\(\alpha, \beta, \gamma\)) between them.
Tetragonal Unit Cell:

• Has the following characteristics: \[ a = b \neq c \quad \text{and} \quad \alpha = \beta = \gamma = 90^\circ \]
• This means two edges (say length \(a\) and \(b\)) are of equal length, while the third (\(c\)) is different.
• All angles between edges are right angles (90 degrees).
• Examples of materials with tetragonal crystal structure include white tin and zirconia.

Why the Other Options Are Incorrect:

• (B) Orthorhombic: All three sides are of different lengths and all angles are 90°.
• (C) Hexagonal: Has two equal sides, one different, but angles are \(90^\circ, 90^\circ, 120^\circ\), not all 90°.
• (D) Cubic: All sides are equal and all angles are 90°.

Hence, the unit cell with two equal sides, one different side, and all 90° angles is Tetragonal.