Would a 35mm f/1.8 Nikon Lens be good for headshots?

Ill be using it on a d3000.

The D3000 by Nikon is a half frame (DX format) camera… For 35mm I recommend at the very least a 105mm lens. Half frame 35mm lens is equal to about 53mm lens on a 35mm or full frame (FX format) camera, There are two reasons why you need more than a 35mm lens on a half frame camera. First you don't want to be in your subject's face. I try to be at least 5-7 feet away when doing a head and shoulders shot, and therefore use at least 120mm. The other reason is that at nearly wide open aperatres will help throw the background out of focus when using a longer lens… Often I shoot at even 200mm for head and shoulder shots. You should consider something around 100mm in focal length for DX format cameras… Perhaps a little less, say 80mm.

Joseph Nowak

No. You'd get lousy working distance and wideangle distortion on the facial features

Nope. 50mm.

Or a constant aperture f2.8 zoom.

A 35mm lens on the nikon d3000 (which has a crop factor of 1.5, according to the internet) would become a 52mm lens. This is fine for headshots (although a 50mm would be better).

In the days of 35mm film cameras, 85mm was the 'classic' portrait lens. 50mm was 'normal' lens. Both were/are good for headshots, but the 85 is better (which is why on your camera, the 50mm would be better, since that becomes a 75mm lens; i.e. 50 x 1.5 = 75mm, which is fairly close to 85mm)