Will this lens fit on my Nikon?

Read the back of the manual. All Nikon manuals list which series of Nikon lenses they are compatible with. For the record that lens there is an AI Nikkor lens.
... For the record that lens there is an AI Nikkor lens.

Well, it's an AI-S rather than an AI, but there is no functional difference between AI and AI-S lenses on the D40 and D40x. For reference, AI-S lenses have the smallest aperture (highest F-number) in red rather than white on the small aperture scale right at the back of the lens.

The D40 and D40x have the widest range of lens compatibility of the current product line, as far as I know. They also have the lowest range of functional compatibility - ie many lenses will fit, but autofocus or metering will be lost.

Okay this may not be the right thing to say here but have you considered buying the auto focus version? It won't auto focus with your camera but it isn't that much more and if you ever upgrade it will auto focus. Just a thought. Plus I'm pretty sure it will meter.
dude, it won't work with your AF, it has to be AF-S. . .but it's compatible, you'll have to manually focus. . .this is the only prime that currently works with our D40(x), the Sigma 30mm HSM f/1.4
I'm aware that it won't autofocus, but its $40 cheaper than the new AF version that wouldn't autofocus anyway.

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