Question

The parameters of Unit Cell in Hexagonal Crystal System is

• A. $a=b\ne c$ & $\alpha=\beta=\gamma=90^{\circ}$
• B. $a=b\ne c$ & $\alpha=\beta=90^{\circ},~\gamma=120^{\circ}$
• C. $a\ne b\ne c$ & $\alpha=\beta=\gamma=90^{\circ}$
• D. $a=b=c$ & $\alpha=\beta=\gamma\ne90^{\circ}$

Hint:

Memory Tip: In Hexagonal crystal system: \[ a=b\ne c \] and \[ \gamma=120^{\circ} \] This unique \(120^\circ\) angle is the identifying feature of hexagonal lattices.

Answer 1

The Correct Option is B

Concept:
Hexagonal crystal system has characteristic unit cell parameters.
Step 1:
In hexagonal system: \[ a=b\ne c \]
Step 2:
The interaxial angles are: \[ \alpha=\beta=90^{\circ} \] \[ \gamma=120^{\circ} \]
Step 3:

• Cubic: all sides equal
• Orthorhombic: unequal sides
• Rhombohedral: equal sides with unequal angles
Step 4:
Thus the correct parameters are: \[ \boxed{a=b\ne c,\quad \alpha=\beta=90^{\circ},\gamma=120^{\circ}} \] \[ \boxed{\text{Correct Option = (2)}} \]