A hard but brittle solid is

MgO

The correct answer is Option (3) → MgO.

Let us look at each of the given options:

1. Dry Ice (Solid CO₂):

Dry ice is the solid form of carbon dioxide (CO₂). It sublimates at −78.5°C, meaning it changes directly from solid to gas without going through a liquid phase under normal atmospheric conditions.

Dry ice is not very hard and doesn’t exhibit brittleness in the same sense as a solid like MgO. It is more fragile and sublimates quickly, so it doesn’t fit the description of "hard and brittle."

2. Fe (Iron):

Iron is a transition metal known for its strength and malleability. It has a high melting point (around 1538°C) and is used in construction, tools, and machinery.

Iron is hard but not brittle. It is malleable anductile, meaning it can be shaped and drawn into wires without breaking. Brittleness refers to a material's tendency to fracture without significant deformation, which is not a property of iron under normal conditions.

3. MgO (Magnesium Oxide):

Magnesium oxide is an ionic compound composed of magnesium ions (Mg²⁺) and oxide ions (O²⁻). It forms a crystalline lattice where ions are held together by strong electrostatic forces.

MgO is hard because of the strong ionic bonds between the magnesium and oxygen atoms. This ionic structure makes it resistant to indentation or scratching.

Despite its hardness, MgO is brittle because of the nature of ionic solids. When stress is applied to an ionic lattice, the layers of ions shift. If like charges (e.g., two Mg²⁺ ions or two O²⁻ ions) are forced to align, the repulsive forces between them cause the material to fracture rather than deform. This is why MgO can shatter or break under stress, classifying it as brittle.

4. Graphite:

Graphite is an allotrope of carbon where carbon atoms are arranged in layers of hexagonal structures. These layers are held together by weak van der Waals forces.

Graphite is soft due to the weak interlayer forces, allowing the layers to slide over each other easily. This is why graphite is used as a lubricant and in pencils. It is not considered hard or brittle since it can be easily deformed without breaking.

Conclusion:

Magnesium oxide (MgO) fits the description of being a hard but brittle solid due to its ionic lattice structure, where the strong forces between ions make it hard, but the alignment of like charges under stress causes it to fracture easily, making it brittle.