Just to chime in on my experience with a WD 1TB Green drive:
Though it's a differant model than the OP had, I bought two WD 1TB Green drives the day I bought my Mac Pro back in June.
One drive still works perfectly to this day, the other began to die about a month after purchase. It would just disappear from finder and upon rebooting the computer, it would show up again for maybe 10 minutes, than be gone again. A few weeks later, it just died completly. I replaced it with a drive that the OP has and it works perfectly.
It's very much possible to get a bad one regardless of brand and they can be bad from the start.
You should bring it back while you can still exchange it. I will have to return mine to WD under the warranty but I probably will just throw it away because I'm too lazy to go through all the hassle of shipping it out.