The crystal system of a compound with unit cell dimensions \(\mathrm{a}=0.387, \mathrm{~b}=0.387\) and \(\mathrm{c}=0.504 \mathrm{~nm}\) and \(\alpha=\beta=90^{\circ}\) and \(\gamma=120^{\circ}\) is: (a) Cubic (b) Hexagonal (c) Rhombohedral (d) Orthorhombic

Understanding the unit cell dimensions is fundamental to the study of crystal systems in chemistry. A unit cell is the smallest building block of a crystal, which repeats in three-dimensional space to create the overall structure of the crystal. These unit cells are defined by their lattice parameters: the lengths of the cell edges (a, b, and c) and the angles (\(\alpha\), \(\beta\), and \(\gamma\)) between them.

• The lengths a, b, and c represent the distances between the lattice points along the edges of the cell.
• The angles \(\alpha\) (alpha), \(\beta\) (beta), and \(\gamma\) (gamma) are measured between the edges of the unit cell.

It is critical, when solving problems related to crystal systems, to compare the given unit cell dimensions to the characteristic dimensions of known crystal systems. For instance, in the exercise at hand, by identifying that the lengths a and b are equal and distinct from length c, and by examining the specific angles between them, students can deduce the crystal system in question.

The hexagonal crystal system is one of the seven lattice systems in crystallography. It is characterized by unit cells that have a unique set of dimensions and angles:

• Two identical axes (a and b) at 120 degrees to each other.
• A third axis (c) that is perpendicular to the a and b axes and of a different length.
• The angles \(\alpha = \beta = 90^\circ\) and \(\gamma = 120^\circ\).

When visualizing a hexagonal crystal system, it’s helpful to think of a hexagon shape in two dimensions, with the third c axis protruding perpendicularly, creating a prism-like form. The equal a and b dimensions and distinct c length, along with the specified angles, distinguish it from other crystal systems. For example, the compound in the provided exercise matches these hexagonal criteria exactly, affirming that it indeed belongs to the hexagonal crystal system.

For students preparing for competitive exams like the National Eligibility cum Entrance Test (NEET), a solid grasp of crystallography is essential. Crystallography, the science of studying crystal structures and properties, plays a major role in understanding various concepts in chemistry and material science. NEET aspirants need to be well-versed in core topics, including recognizing different crystal systems and determining the types of unit cells within a crystal structure.

To excel in crystallography-related questions on the NEET, one must:

• Memorize the characteristic dimensions and angles of the seven crystal systems.
• Understand how to relate a compound's unit cell parameters to its particular crystal system.
• Apply this knowledge to solve problems, much like the one featured in this exercise.

Data such as unit cell dimensions, edge lengths, and interaxial angles provided in problems should be methodically analyzed to conclude the crystal system, which is a common type of question in exams like the NEET. By mastering these concepts, students will be able to approach such questions with confidence and precision.