The Federal Aviation Administration yesterday officially plugged in a new backup computer at the Washington Air Route Traffic Control Center in hopes of relieving the momentary chaos that results when the main computer breaks down and controllers scurry to old radar screens to find their airplanes.

The center, in the Virginia countryside just east of Leesburg, is responsible for handling planes crossing 140,000 square miles of the eastern United States, including D.C., Maryland and Virginia. More than 1.6 million aircraft looked to the center for air traffic control service last year.

The new computer is part of a $22-million system the FAA is installing at 20 centers around the nation. It will replace the current back-up system, the old sweep-hand radar screen. That system lacked such valuable information as the altitudes of airplanes being controlled and is extremely confusing for controllers accustomed to uncluttered computerized radar displays.

A number of tense air traffic control situations have occurred during computer breakdowns. In November 1979, for example, Air Florida and Delta jetliners carrying a total of 208 people came within 200 to 300 feet of each other high over North Carolina because one of the planes had been "lost" when the computer broke down for six minutes.

Eugene Cote, a controller at Leesburg, called the new system "100 percent better" than the old radar screen. "It's a much clearer presentation," he said, "and it makes transition [from the main computer] much easier."

The FAA said that there were 6,283 "interruptions" in air traffic control computers in 1980, and that 144 of them occurred at Leesburg. If the interruption lasts longer than a minute, it is called "an outage," and is regarded as serious. There were 696 outages last year, including 24 at Leesburg.

Each controller at Leesburg is responsible for a block of airspace and monitors it on a large TV-type screen. The computer shows him the airplanes in his sector of responsibility. Each airplane on the screen is accompanied by a block of type that tells the controller the radio call sign of the plane, its assigned altitude, its actual altitude, its ground speed and its computer code.

The old radar screen does few of those nice things. It tells a controller where all of the airplanes are from the ground up, instead of telling him only about the ones in his sector. Thus, he has much information he does not need. The radar screen contains none of the helpful data identifying the plane or giving its altitude and speed; the controller has to guess from his experience with the radar screen. The problem is, fewer and fewer controllers on active duty have substantial experience with the old radar screen.

The new back-up system, while not as exotic as the main computer, has three features that should make it an improvement. It displays only the airplanes a given controller needs to worry about; it tells the controller at what altitude the plane is flying, and it provides a code by which the controller can quickly identify the plane.

Leesburg controllers have been testing the new equipment since October, but yesterday was the first day it was officially accepted for duty. The new system, called DARC (for Direct Access Radar Channel), was built for the FAA by Raytheon.