Question

Which of the following crystals has the unit cell such that \( a = b \neq c \) and \( \alpha = \beta = 90^\circ, \gamma = 120^\circ \)?

• A. Zinc blende
• B. Graphite
• C. Cinnabar
• D. Potassium dichromate

Hint:

Graphite has a hexagonal crystal structure with layered properties defined by its unique lattice parameters.

Answer 1

The Correct Option is B

To determine which of the given crystals has a unit cell characterized by \( a = b \neq c \) and \( \alpha = \beta = 90^\circ, \gamma = 120^\circ \), we need to understand the crystal systems and their respective lattice parameters:

1. Crystal System: The parameters provided indicate that the crystal belongs to the hexagonal crystal system. This system is defined by the lattice parameters \( a = b \neq c \) and angles \( \alpha = \beta = 90^\circ \), \( \gamma = 120^\circ \).
2. Options Analysis:
   • Zinc Blende: Zinc blende (ZnS) has a cubic crystal structure, where \( a = b = c \) and all angles \(\alpha = \beta = \gamma = 90^\circ\). This does not match the given parameters.
   • Graphite: Graphite has a layered structure that crystallizes in the hexagonal system, fitting the criteria of \( a = b \neq c \) and angles \( \alpha = \beta = 90^\circ, \gamma = 120^\circ \).
   • Cinnabar: Cinnabar (HgS) typically crystallizes in a trigonal/hexagonal form but often does not align with the pure hexagonal parameters given in this context.
   • Potassium Dichromate: This compound crystallizes in the orthorhombic system with three unequal axes at right angles to each other, which also does not match the given criteria.
3. Conclusion: Based on the analysis, the crystal with a unit cell where \( a = b \neq c \) and \( \alpha = \beta = 90^\circ, \gamma = 120^\circ \) is Graphite.

Thus, the correct answer is Graphite.