**Explanation:**

The Langmuir adsorption isotherm is a mathematical model that describes the adsorption of a gas molecule onto a solid surface. It was derived by Irving Langmuir in 1916 and is based on several assumptions. The correct assumption leading to the Langmuir adsorption isotherm is option A, which states that the adsorption sites are equivalent in their ability to adsorb the particles.

**Adsorption Sites are Equivalent:**

The assumption that the adsorption sites are equivalent means that all the surface sites on the solid material have the same affinity or ability to adsorb gas molecules. In other words, each adsorption site on the surface has the same energy and probability of capturing and retaining gas molecules. This assumption simplifies the mathematical model and allows for a straightforward interpretation of the experimental data.

**Homogeneous Surface:**

When the adsorption sites are equivalent, it implies that the surface of the solid material is homogeneous, with no variation in the strength or activity of the adsorption sites. This assumption is reasonable for surfaces that have been well-prepared and have a uniform composition and structure.

**Monolayer Adsorption:**

The Langmuir adsorption isotherm assumes that the adsorption occurs in a monolayer, meaning that only one layer of gas molecules is adsorbed onto the surface. This assumption is valid when the gas pressure is not too high and the surface coverage is relatively low. In a monolayer adsorption, each adsorption site is occupied by a single gas molecule.

**No Interaction Between Adsorbed Molecules:**

Another assumption of the Langmuir adsorption isotherm is that there is no interaction between the adsorbed molecules. This means that the adsorbed molecules do not interact with each other to form multilayers or clusters. Each adsorbed molecule is independent and does not influence the adsorption of other molecules.

By assuming that the adsorption sites are equivalent, the Langmuir adsorption isotherm provides a simple and elegant mathematical description of the relationship between the gas pressure and the surface coverage. It allows for the determination of key parameters such as the adsorption equilibrium constant and the maximum surface coverage.