Allotropy is the property of certain elements to exist in two or more different forms. These different forms of an element are called allotropes. Each allotrope of an element has distinct physical and chemical properties. The phenomenon of allotropy occurs due to variations in the arrangement of atoms or molecules in the solid state.

Allotropy is commonly observed in many elements, including carbon, oxygen, sulfur, and phosphorus. These elements can exist in different allotropes under different conditions of temperature and pressure. Some examples of allotropes are diamond and graphite for carbon, and oxygen and ozone for oxygen.

**1. Carbon:**
- Diamond: In diamond, each carbon atom is bonded to four other carbon atoms in a tetrahedral arrangement. This gives diamond its exceptional hardness and high thermal conductivity.
- Graphite: In graphite, carbon atoms are arranged in layers of hexagonal rings that are stacked on top of each other. The layers are held together by weak van der Waals forces, allowing them to slide past each other easily. This gives graphite its slippery and lubricating properties.

**2. Oxygen:**
- Oxygen: In its most stable form, oxygen exists as a diatomic molecule (O2), where two oxygen atoms are bonded together. This is the form of oxygen present in our atmosphere and is essential for supporting life.
- Ozone: Ozone (O3) is another allotrope of oxygen. It is formed when oxygen molecules are exposed to ultraviolet (UV) radiation or electrical discharges. Ozone is a powerful oxidizing agent and is found in the Earth's ozone layer, where it protects us from harmful UV rays.

**3. Sulfur:**
- Rhombic Sulfur: Rhombic sulfur is the most stable form of sulfur at room temperature and pressure. It consists of S8 rings arranged in a puckered crystal lattice. Rhombic sulfur is yellow in color and has a crystalline structure.
- Monoclinic Sulfur: Monoclinic sulfur is formed when rhombic sulfur is heated above 96°C. It has a different crystal structure and appears as long, needle-like crystals. Monoclinic sulfur is a red solid and is less stable than rhombic sulfur.

**4. Phosphorus:**
- White Phosphorus: White phosphorus is a waxy, translucent solid that glows in the dark. It consists of P4 tetrahedra arranged in a cubic crystal lattice. White phosphorus is highly reactive and ignites spontaneously in air.
- Red Phosphorus: Red phosphorus is formed by heating white phosphorus in the absence of air. It has a different crystal structure and appears as a dark red powder. Red phosphorus is much less reactive than white phosphorus and is used in safety matches and flame retardants.

In conclusion, allotropy is the property of certain elements to exist in two or more different forms with distinct physical and chemical properties. This property allows elements to exhibit a wide range of behaviors and applications in various fields.