Scientific Pursuits

Scientific Pursuits is the sixth main quest $$ It is also an Xbox 360/PC achievement and a PlayStation 3 Trophy.

Detailed walkthrough
This quest can be started by talking to Dr. Madison Li in the Rivet City science lab, with or without completing the Galaxy News Radio quest. Also, it can be started by picking up the notes in Jefferson Memorial regarding Project Purity, or by entering Vault 112 itself.

It is highly likely that one has already visited Rivet City, likely as part of the Wasteland Survival Guide or in the course of visiting the southern Metro stations to reach areas like Museum of History or the National Archives. In this case, reaching Dr. Li is trivial.

The easiest - as in, quickest with the least combat - way to get to Rivet City is to go back via the map marker in your Pip-Boy 3000 to Super-Duper Mart.
 * From there, follow the river (Potomac) south on the west bank, passing Wilhelm's Wharf, down to the Key Bridge at the Citadel.
 * One can either avoid a few Super Mutants by swimming over at the Jefferson Memorial, or one can cross the Memorial Bridge and head south after a brief battle.
 * When the Jefferson Memorial is in sight, head east. Near the Anacostia Crossing Station metro entrance one will notice a metal construct next to the aircraft carrier; climb it and use the intercom to get the bridge connected.

One can also cross the D.C. urban area, dodging in and out of metro stations, or follow the east bank of the Potomac.

Depending on one's earlier missions - The Power of the Atom in particular - the Lone Wanderer may run into Talon Company or Regulators.

Talk to Doctor Li about Dad and Project Purity
Dr. Li knows the Lone Wanderer's father, James. She offers details on Project Purity and tells them where James ran off to: the Jefferson Memorial. If one has been to this location and visited the underground tunnel, the game will allow the Lone Wanderer to tell her that he is not there; she will instead insist that they go back as his notes were left there.

Look for Dad in Project Purity's Control Room
Enter the Memorial through the metal door labeled "Gift Shop", it is on the right front side with a metal frame around it and a set of lights next to it. Be warned that there are a number of super mutants inside. Head to the Rotunda by following the signs.

Once in the Rotunda, walk up to the auxiliary filtration unit near the entryway and pick up the Project Purity journals resting here. One of the tapes, #10, will indicate that James has left for Vault 112 already. The location will be added to the Pip-Boy map; there are several other points of interest in the area, which makes it relatively simple to fast travel to.

Gain access to Vault 112
Vault 112 is located hidden underground of Smith Casey's garage which is due west of Evergreen Mills. Once inside, head past the front desk and into the back room, which is infested with radroaches and mole rats. One will find a switch located on the wall to their left that operates a large hole in the floor. Activate the switch and the door will open. Proceed down the stairway, down the next set of stairs, and to the bottom.

One cannot miss the Vault 112 doorway. Activate the door using the panel and one can walk in. When first walking in, one will need to speak to a security bot and receive a Vault 112 jumpsuit. Next walk down into the tranquility lab and find the only unoccupied operational tranquility lounger where one will complete the quest. Smith Casey's garage can be accessed straight after the player leaves Vault 101, therefore advancing through a large section of the game's main quest-line.

Achievement
It is possible to skip major portions of this quest, for example by speaking directly to Dr. Li in Rivet City before visiting Three Dog, or by visiting the Jefferson Memorial directly. In these cases, this achievement will still be rewarded at the same time that the Tranquility Lane achievement is received.

In the Xbox and PS3 versions, if one has already entered the Jefferson Memorial (especially the rotunda) before talking to Dr. Li in Rivet City, the achievement/trophy will not be unlocked until the Lone Wanderer materializes at Tranquility Lane. Thus this achievement/trophy cannot be obtained out of sequence, with regards to the main quest achievements. In order to rectify this, the player character can load a saved game at a point where Jefferson Memorial has not been explored and work through the main quest again.

It is possible to bypass this quest altogether, along with all preceding quests, by heading to Smith Casey's Garage directly from Vault 101 and starting Tranquility Lane: this will make the Scientific Pursuits achievement impossible to earn on that playthrough.

Bugs

 * If the Broken Steel add-on is installed when this mission is started, a glitch may occur on Galaxy News Radio where Three Dog will occasionally talk about Project Purity being activated, which may give serious plot spoilers to the player.
 * The mission marker that should point to Smith Casey's garage may be placed at the entrance to Evergreen Mills.
 * When told to equip the Vault 112 jumpsuit, equipping the Vault 77 jumpsuit will continue the quest. However, in order to get inside the simulation, one must equip the Vault 112 jumpsuit. Currently unknown if this happens with other consoles, or with other suits.