Project Purity

 is a water purification project that began before the beginning of Fallout 3. It was originally supported by the Brotherhood of Steel, although they soon abandoned the project due to dwindling manpower. In Rivet City, Doctor Li will tell the PC that his father, James, left Vault 101 to travel to Rivet City to start the project up again. Dr. Li refused and James moved on. Project Purity is what motivates your father to eventually leave the Vault in search of a GECK in the hope of completing the project.

After finding James, it is revealed Project Purity was rekindled at the Jefferson Memorial, but the location was captured by super mutants. After enlisting the assistance up Doctor Li and her staff from Rivet City, the location will have to be cleared before the project finally resume progress. However, the Enclave invades and seizes the Jefferson Memorial, and attempts to persuade James to cede control to the Enclave. James refuses, and kills both himself and the Enclave soldiers with lethal doses of radiation. The player is forced to escort the remaining staff to the relative safety of the Citadel, contending with Feral Ghouls and even more Enclave soldiers.

Quotes

 * The plan was to build a facility that could purify all the water in the Tidal Basin at once. No radiation, no muck, just clear water. - Doctor Li

Related quests
The project is tied to Following in His Footsteps, and possibly tied to The Waters of Life, as well as the Jefferson Memorial location.