You're very clear and specific, frighteningly so. Your teacher told you to screw a 10.5V mercury arc bulb into a 120V socket! You're lucky that it didn't explode, releasing mercury vapor. Don't ever, ever, do that again and tell your teacher never to do anything that stupid again.
These sorts of bulbs won't work except on the proper voltage. They aren't like incandescent bulbs which just get dim and orange-ish if they get slightly too little voltage. There's no chance a 10.5 V arc bulb could work at 2 V and little chance it would work at 9 V.
You might start preparing for this project by reading this nice article on germicidal bulbs: http://en.wikipedia.org/wiki/Germicidal_lamp
. It describes the principles of operation and some of the major safety issues.
Your guess that using dc voltage is a problem is correct. Although these mercury arc bulbs can run on dc, there are significant problems both in maintaining a steady current and in avoiding damage to the bulb. You can read a discussion on this site:http://en.wikipedia.org/wiki/Fluorescent_lamp#Electrical_aspects_of_operation
. Although it is about fluorescent bulbs, they're just modified mercury arc bulbs with very similar electrical properties.
As far as the electrical operation goes, you probably would want to get one of the bulbs (about the same price as the one that was destroyed) that work in the same plug-in fixtures as some small fluorescent lamps. Getting a fluorescent lamp and swapping bulbs would then take care of the electrical issues. However, there major safety concerns with the UV light itself. Risks include blindness and melanoma, a deadly skin cancer. I wouldn't trust that particular teacher to guide you through those risks.
(published on 02/16/12)