**Binomial Nomenclature and its Purpose**

Binomial nomenclature is a system of naming living organisms developed by Carl Linnaeus. It assigns a unique scientific name to each species, consisting of two parts: the genus name and the species name. The purpose of binomial nomenclature is to provide a standardized and universal system for naming and classifying organisms, allowing scientists from different regions and languages to communicate effectively.

**Distinguishing Members of a Species**

The correct answer to the question is option B, "Members of a species." Binomial nomenclature is specifically designed to distinguish between members of different species. The species name in a scientific name represents a specific group of organisms that share common characteristics and are able to interbreed and produce fertile offspring. For example, in the scientific name for humans, Homo sapiens, "sapiens" is the species name, indicating that all individuals with this name belong to the same species.

**Differentiation at Different Taxonomic Levels**

While binomial nomenclature is effective in distinguishing between members of different species, it may not be as specific at higher taxonomic levels. Here is a breakdown of how binomial nomenclature differentiates organisms at various taxonomic levels:

1. **Species**: The species name differentiates members of a species from those of other species. For example, the species name distinguishes Homo sapiens from Homo neanderthalensis.

2. **Genus**: The genus name groups together similar species that share common characteristics. For example, all species within the genus Homo, such as Homo sapiens, Homo neanderthalensis, and Homo erectus, share certain traits.

3. **Family**: The family name further groups together related genera. For example, the family Hominidae includes the genera Homo, Pan (chimpanzees), Gorilla, and Pongo (orangutans).

4. **Order, Class, Phylum, Kingdom, and Domain**: The higher taxonomic levels continue to group together organisms with increasing levels of similarity. However, at these levels, binomial nomenclature alone may not be sufficient for distinguishing between members of different classes, orders, or phyla. Additional taxonomic ranks and criteria are used to differentiate organisms at these levels.

**Conclusion**

In summary, binomial nomenclature is a system of naming living organisms that effectively distinguishes between members of different species. However, at higher taxonomic levels, such as genus, family, order, class, phylum, kingdom, and domain, additional criteria are needed to differentiate between organisms.

Binomial nomenclature cannot distinguish between members of a spcecies because we know that it is the fundamental category of taxonomic classification.So,We cannot distinguish between the members of species.