A hard but brittle solid is

The correct answer is Option (3) → MgO

Crystalline solids are classed by the particles they contain and the forces that hold them together, and these forces decide hardness:

• Ionic solids (NaCl, MgO): ions held by strong electrostatic forces; hard but brittle, high melting points, insulators in the solid state.

• Metallic solids (Fe, Cu): positive ions in a sea of electrons; hard but malleable and ductile, good conductors.

• Covalent network solids (diamond, \( \ce{SiO2} \)): very hard; graphite is an exception, being soft and a conductor.

• Molecular solids (dry ice, ice, \( \ce{I2} \)): weak intermolecular forces; soft, low melting.

Ionic solids are brittle because a small shift of one layer of ions brings ions of the same charge face to face; they repel and the crystal cracks. MgO, an ionic solid of \( \ce{Mg^{2+}} \) and \( \ce{O^{2-}} \) ions, is therefore hard but brittle.

Why the other options are incorrect

• Option (1) Dry ice — Incorrect. Solid \( \ce{CO2} \) is a non-polar molecular solid held by weak dispersion forces, so it is soft and sublimes at low temperature.

• Option (2) Fe — Incorrect. Iron is a metallic solid; it is hard, but the sea of electrons lets layers slide, so it is malleable and ductile, not brittle.

• Option (4) Graphite — Incorrect. Graphite is a covalent solid made of layers held by weak forces; the layers slide over one another, so it is soft and slippery.

Note: This question is from the pre-rationalised NCERT book (2022-23). The topic is not there in the latest NCERT book (2026-27), and it is also out of the CUET 2026 syllabus.

NCERT (Pre-rationalised edition, 2022-23):
Classification of Crystalline Solids – …