The bible says about dating
This land is noteworthy in the Bible because it was here that the exiles were taken captive after the destruction of Jerusalem. The civilization of Babylonia and Assyria: Its remains, language, history, religion, commerce, law, art, and literature.
Table 1 presents the traditional chronology of early Mesopotamia from the Hassunah period to the end of the First Dynasty of Babylon when Hammurabi lived.
One should notice that some of these dynasties overlap considerably.
Thus, from circa 2000 to 1750 (1650 at the extreme), we have the one and only period during which extensive power alliances were common in Mesopotamia and with its neighbors (Kitchen 2003, p. Kitchen explains it well why so many modern scholars date Abraham to the Isin-Larsa period.
However, the search for the Mesopotamian background for Abraham does not stop there.
For many years, Abraham was believed to have lived at the same time as Hammurabi, king of Babylon.