In which specific year and what date did the roman empire fall?

It was, of course, a gradual process. Specific dates are impossible, though many are given by various simplifiers. The end is sometimes placed at 4 September AD 476, when the last emperor of the Western Roman Empire, Romulus Augustus, was deposed, and not replaced. However, Diocletian, who retired in AD 305, was the last sole Emperor of an undivided Empire whose capital was the City of Rome. After the division of the Empire by Diocletian into East and West, each branch continued to style itself as "The Roman Empire." The Western Roman Empire declined and fell apart (see Decline of the Roman Empire) in the course of the 5th century. The Eastern Roman Empire, centered on Nova Roma (founded by Constantine I on the Greek city of Byzantion), which would later adopt Greek as its main language, known widely today as the Byzantine Empire, preserved Greco-Roman legal and cultural traditions along with Hellenic and Orthodox Christian elements for another millennium, until its eventual collapse with the conquest of Constantinople, as Constantine's city become known, at the hands of the Ottoman Empire in 1453. (The above from Wikipedia)