http://www.nikonchat.com/nikon-nikkor-35mm-dx/

What’s the optimum lens for portraiture photography?
I have heard that its good to use a lens with more than 100mm for portraiture. But won’t that need a large studio?
How about Nikkor AF-S DX 35mm f/1.8? I am currently having a nikon d3000.
I don’t have space to do buy longer mm lens, but if I have to avoid distortion using 35mm, will it be effective if i shoot from far, but crop the photo later?
Yes, 85-105 is the “classic” range for a portrait lens on a 35mm camera. You are using a D3000, which has a “cropped sensor,” though, so you have to consider that. With the 1.5X “crop factor,” you should look for a lens between about 50mm and 70mm. Two come to mind. Well, three.
The 50mm lens is really great for portraits on a D3000. If you don’t mind NOT having auto-focus, you can use the 50mm f/1.4D lens. It costs about $330. If you want auto-focus with your camera, you need the 50mm f/1.4G AF-S lens, which costs about $100 more. You could consider other makers, but I am not familiar enough to say which ones are good or bad.
Another way to go is to get the 60mm f/2.8G AF-S macro (Micro-Nikkor) lens. Just because it allows macro photography doesn’t mean you can’t use it as any other 60mm lens. It’s not cheap, though, at over $500.
The 35mm is a good “normal” lens, but it might make you work too close to your subjects for their comfort and for a good point of view. If you are too close, their features look a bit distorted.
The best choice for you is probably the 50mm f/1.4G AF-S lens.
Someone will undoubtedly recommend the 85mm lens, but with your 1.5X factor (which they have ignored), it is rather long for portrait work unless you have a large studio to work in so you can back up quite a bit from your subject. Okay, you should only have to be about 10-12 feet from your subject for a head shot (15 feet for a torso), but add 5 feet behind them for the background and 5 or more feet behind you so you can have room to work and you are looking at a room 20-25 feet long.