Notice that the verse also mentions the destruction of the heavens, not just the earth. (Nuclear fission is not that destructive-- no weapon that humanity has is sufficient to destroy the entire universe.)
By cross-referencing with other scripture, it is apparent that the day of the Lord is the end of the world where the universe as it is now will cease to exist and the only thing left will be the throne of God, before which every person who has ever lived will be judged. There are verses that share a similar concept (Isaiah 51:6, 2 Peter 3:7, and Revelation 20:11)