A crystal with $a = b = c$ and $\alpha = \beta = \gamma \neq 90^\circ$ belongs to which crystal system?

## CORE INFORMATION\n✓ **Answer**: C\n## CONCEPT FRAMEWORK\n **Primary Concept**: Crystal Systems and their characteristics\n **Related Topics**: Crystallography, Unit cells, Bravais lattices\n **Prerequisites**: Understanding of crystallographic axes and angles.\n## SOLUTION PATHWAY\n**Given Information**:\n $a = b = c$ (all lattice parameters are equal)\n $\alpha = \beta = \gamma \neq 90^\circ$ (all interaxial angles are equal and not 90 degrees)\n**Method & Steps**:\n 1. Identify the crystal system based on the given lattice parameters and angles.\n Reasoning: We need to compare the given parameters with the defining characteristics of each crystal system.\n Formula/Rule: There is no specific formula, but a table summarizing the characteristics of each crystal system is used.\n 2. Compare with the characteristics of each crystal system.\n Working: \n * Cubic: $a = b = c$, $\alpha = \beta = \gamma = 90^\circ$\n * Tetragonal: $a = b \neq c$, $\alpha = \beta = \gamma = 90^\circ$\n * Rhombohedral (Trigonal): $a = b = c$, $\alpha = \beta = \gamma \neq 90^\circ$\n * Orthorhombic: $a \neq b \neq c$, $\alpha = \beta = \gamma = 90^\circ$\n Key Point: The key difference lies in the interaxial angles. Only the rhombohedral system has equal lattice parameters and interaxial angles not equal to 90 degrees.\n 3. Determine the crystal system.\n Result: Rhombohedral\n Verification: The given parameters perfectly match the definition of a rhombohedral crystal system.\n ## OPTION ANALYSIS\nA :x: Cubic system requires $\alpha = \beta = \gamma = 90^\circ$.\nB :x: Tetragonal system requires $a = b \neq c$ and $\alpha = \beta = \gamma = 90^\circ$.\nC ✓: Rhombohedral system has $a = b = c$ and $\alpha = \beta = \gamma \neq 90^\circ$.\nD :x: Orthorhombic system requires $a \neq b \neq c$ and $\alpha = \beta = \gamma = 90^\circ$.\n ## LEARNING AIDS\n **Common Mistakes**:\n 1.Confusing rhombohedral with cubic: Remember the difference in interaxial angles.\n 2.Misinterpreting the notation: Carefully examine the values of a, b, c, α, β, γ.\n **Quick Tips**:\n 1.Create a table summarizing the characteristics of each crystal system for quick reference.\n 2.Focus on the relationship between lattice parameters (a, b, c) and interaxial angles (α, β, γ).

The correct Option is "Rhombohedral"

NEET Chemistry The Solid State MCQs

Prepare for NEET Chemistry The Solid State with MCQs & PYQs on NEET.GUIDE. Access free practice, previous year questions, and expert insights into crystal lattice and packing.

NEET Questions / Chemistry / The Solid State