Question

Crystal system with the unit cell parameters \( a = b \neq c \) and \( \alpha = \beta = \gamma = 90^\circ \) is

• A. monoclinic
• B. orthorhombic
• C. tetragonal
• D. hexagonal

Hint:

In crystallography, the tetragonal system has two equal axes and one unequal axis, with all angles at 90°, which is the case for the given parameters.

Answer 1

The Correct Option is C

Step 1: Understanding the unit cell parameters.
The unit cell parameters are:
- \( a = b \neq c \), meaning two sides of the unit cell are equal, and the third side is different.
- \( \alpha = \beta = \gamma = 90^\circ \), meaning all angles between the sides are right angles.
Step 2: Identification of the crystal system.
- The monoclinic system has \( a \neq b \neq c \) and \( \alpha = \gamma = 90^\circ \), but \( \beta \neq 90^\circ \).
- The orthorhombic system has \( a \neq b \neq c \) and \( \alpha = \beta = \gamma = 90^\circ \).
- The tetragonal system has \( a = b \neq c \) and \( \alpha = \beta = \gamma = 90^\circ \), which is the correct fit for the given parameters.
- The hexagonal system has \( a = b \neq c \), but the angles are \( \alpha = \beta = 90^\circ \) and \( \gamma = 120^\circ \).
Step 3: Conclusion.
The correct system with these parameters is the tetragonal system.
Final Answer: \[ \boxed{\text{Tetragonal crystal system is the correct system.}} \]