The fall of Jerusalem and of the subsequent destruction of the Temple,
occurred in the year 586 B.C
The date of the fall of Jerusalem was uncertain until 1956, when D.J. Wiseman deciphered tablet B.M. 21946. This translation made possible to calculate and finally establish 597 B.C. as the year of the first occupation of Jerusalem by King Nebuchadnezzar, who established Zedekiah. For the confirmation of this statement, here are some passages from Wiseman's book.
In Jeremiah, chapter 39, verses 1 and 2, we read: "In the ninth year of Zedekiah king of Judah, in the tenth month, Nebuchadrezzar king of Babylon and all his army came against Jerusalem and besieged it; in the eleventh year of Zedekiah, in the fourth month, on the ninth day of the month, a breach was made in the city… all the princes of the king of Babylon came and sat in the middle gate…"
If Zedekiah was enthroned in 597 B.C. and in the eleventh year of his administration, Nebuchadnezzar captured the town for the second time because of his rebellion, as Jeremiah says, we find out that subtracting 11 years to the 597, the destruction of Jerusalem and its Temple happened in year 586 B.C.
By this we understand that the 70 years of Jerusalem's desolation started in 586, with the destruction of Yahuh's Temple, and lasted until year 516, when the new Temple was established. Whitley also agrees with this in his work Vetus Testamentum vol. IV page 60 to 62.
Chronicle containing the battle of Karkemis in 605 and Jerusalem's capture in 597 B.C. (B.M 21946)
Tablet B.M. 21946, lines 11, 12,13.