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Which lenses will work with which cameras can be figured out by looking at the abbreviations that make up the name of each lens.
Some Nikon camera bodies don't have a built in focus motor, and these bodies will need to use lenses that incorporate a built in focus motor. If the lens has AF-S as an abbreviation, then it has a built in motor. If it is simply called AF, then it does not incorporate a focus motor.
Nikon camera bodies that have a focus motor built in are: D70, D70s, D80, D90, D100, D200, D300, D300s, D600, D700, D800/D800E, D7000, D7100 D1-series, D2-series, D3-series and D4 models. These cameras can utilise both the AF and AF-S lenses.
Most consumer Nikon DSLRs are designed without inbuilt focus motors to make them lighter and smaller than their professional counterparts. But this doesn't mean that you can't use an AF lens on your camera. You'll be able to use the lens, but with limited functionality. For example, you'll have to manually focus the lens, using the electronic rangefinder, visible in the lower left portion on the viewfinder, to confirm that your subject is in focus.