Yes it will...the 24/2.8 AIS is also one of the sharpest and closest focusing Nikkors ever made including the new lenses...that lens in excellent condition is probably worth at least a couple of hundred bucks...
In fact any and every Nikon lens made since 1959 with the exception of the invasive fisheyes will work on your camera...that is what makes the D3000 and 5000, 3100 and 5100, and D40 and the such so cool...they will mount all NIkkors not just AI and newer...