Fix the mine's air purifier

Talk to Zaius inside the house outside the Broken Hills mine's entrance. He will tell you the mine needs parts for the mine purifier and asks you to go to New Reno to pick it up. You can either take the reward for money, or, you can decline, and recieve a combat shotgun when you finish the quest.

The mine purifier can not be fixed without the right parts so make sure you do this quest before the Who Killed Richard Wright quest in New Reno.

Talk to Renesco the Rocketman in New Reno. Tell him Zaius' password. If you don't, you'll need to fork over $200 for the parts. ($100 with a Barter or Speech check)

Return to Zaius and he will ask you to enter the mine to fix the purifier. The mine is filled with radon gas, which will damage you and your party for about 5 points of damage every few steps. If you or any of your followers have power armor equipped, it will negate the damage. Use the parts on the clanking machine in the back (but watch out for the Deathclaw!) for 1000 XP.

Return to Zaius and he will give you a City-Killer combat shotgun (or $500 if you asked for a reward earlier).