The courtroom fell silent as an FBI technician began to play a tape recording of the arrest last Oct. 9 of Washington defense lawyer William A. Borders Jr. at the Marriott Twin Bridges motel in Arlington.

The jurors, each wearing yellow plastic earphones, listened to the sounds of Borders walking to his car with an FBI undercover agent who was carrying $125,000 in cash in a red leather suit bag. Airplanes could be heard roaring over their heads, followed by the familiar sound of seat belt chimes and the car radio. Suddenly came the ominous whine of sirens.

"We're busted," Borders said on the tape to the agent.

"I'm afraid so," the agent replied.

Borders, slumped in his chair at the defense table, abruptly removed his earphones when the tape was done. He glanced quickly behind him at the rows of spectators who have attended his trial, turned back to the front of the courtroom and rubbed his forehead.

Along with the seven men and five women of the jury, Borders has listened intently this week to 15 secretly recorded conversations, including the dramatic tape of his arrest, that form the core of the government's bribery and conspiracy case against him.

Prosecutors played one tape after another in U.S. District Court here in their effort to prove that Borders, acting as a middleman, conspired with U.S. District Judge Alcee L. Hastings of Miami, his longtime friend, to take a $150,000 payoff from Frank Romano and his brother, Thomas.

The Romanos were tried and convicted of racketeering and fraud charges in Hastings' courtroom in December 1980. In return for the payoff, the prosecution charges, Hastings ordered the release of $845,000 forfeited by the Romanos and planned to reduce the three-year prison sentences he imposed on them.

Borders, a member of the D.C. commission that helps select local judges and former president of a national association of black lawyers, is being tried separately from Hastings, a prominent civil rights lawyer appointed to the federal bench by President Jimmy Carter in 1979. He is the first black federal judge in Florida.

Although Hastings is absent from this trial, he has been a central figure in it. The government has been compelled to lay out much of its case against him in its attempt to prove its charge that Borders conspired with Hastings to solicit bribe money.

In defending Borders against that conspiracy charge, defense lawyer John A. Shorter Jr. appeared to try to disassociate Borders from any actions that Hastings took during the period of the alleged bribery scheme.

In effect, Shorter has had to present a defense for Hastings in his effort to prove that Borders could not have been involved in a criminal conspiracy with Hastings.

Shorter, relying on his cross-examination of FBI undercover agent Paul Rico, who was posing as Frank Romano, has also tried to suggest to the jury that Borders, rather than trying to obtain a bribe for Hastings, may have been playing the role of a con man, trying to get money from the man Borders thought was Frank Romano by pretending he had influence with Hastings.

Borders is not expected to take the witness stand in his own defense.

Justice Department lawyers Reid Weingarten and Robert I. Richter began the presentation of prosecution evidence last week with the heart of their case--three tape recordings of meetings between Borders and the man he thought was Frank Romano.

In the first meeting, Borders was introduced to the undercover agent posing as Romano by an informant and former client of Borders who had told the FBI that Hastings was soliciting bribes from defendants who had appeared in his courtroom and that Borders was acting as a middleman. At the second meeting, Borders allegedly accepted $25,000 from the agent. At the third, Borders was arrested. The prosecution followed with tapes of 12 telephone conversations, secretly intercepted after a court-authorized wiretap was placed on Borders' home and law office telephones. More than 2,000 calls came in and out of those two locations during the eight days that the wiretap was in place; only 21 were monitored by the FBI because they related to the criminal investigation, and 12 were played for the jury this week.

One of those recordings--a telephone call from Hastings to Borders--links the federal judge to the bribery scheme, the government contends.

Two events are crucial to the government's conspiracy allegation. Both involve alleged promises that Borders made to the FBI undercover agent about actions that would be taken by Hastings as part of the alleged bribery scheme. One involved Hastings' appearance at a Miami restaurant and the other his order directing that the $845,000 be sent back to the Romano brothers.

When the FBI undercover agent Rico first met with Borders on Sept. 12, he indicated he wanted a sign that Borders could influence Hastings.

". . . I think you made the suggestion that we name a place . . ." the agent said on the tape.

"Okay. No sweat," Borders replied on the tape.

". . . and a time . . ." the agent said.

"Okay," Borders said.

". . . and that, ah, the jud, your, ah . . ." the agent said.

"That somebody could have dinner there," Borders said.

According to the tape recordings, the two men settled on the posh Fontainebleau Hilton Hotel in Miami, for 8 p.m. on Sept. 16. According to the government's evidence, Hastings and a female companion had dinner there that night.

The other event that is key to the conspiracy charge against Hastings is the far more complicated issue of the return of the $845,000 that had been forfeited by the Romanos. A long portion of Richter's opening statement for the government was spent explaining the legal issues in the Romano case to the jury, which then had to digest extensive testimony, loaded with legal jargon, from a prosecutor and a law clerk involved in the case.

In May 1981, five months after the Romanos were convicted of 21 counts of racketeering, tax and mail fraud, Hastings ordered them to forfeit to the government $1.2 million that he determined was the illegal profit of their criminal enterprise. Such forfeitures are included in federal anti-racketeering laws.

According to government testimony, an appeals court decision in a similar case a month later made it clear that Hastings would have to return $845,000 in cash to the Romanos because, while obtained illegally, it had not been reinvested in their criminal enterprises.

Another hearing was held the following July.

The government prosecutor in the Romano case, James Deichert, testified that Hastings said at that hearing that he intended to uphold his previous order, despite the appeals court decision. Hastings' law clerk at the time, Jeffrey Miller, testified he thought Hastings had not made up his mind. Miller, who was drafting a decision for Hastings, also testified that after he apprised Hastings of another similar appeals court decision in August, Hastings told him "Well, give them (the Romanos) their money back."

The actual preparation of the opinion languished for months, said Miller, who blamed some of the delay on an unrelated, but complex, finance case that was assigned to Hastings on an emergency basis.

Then, on Oct. 5, in what Miller described as an "unusual" demand, Hastings came into his office and told him to complete the Romano order that day. That same afternoon Hastings called Borders in his Washington law office.

According to the tape of that conversation, Hastings said, "I've drafted all those, ah, ah, letters for him . . . and everything's okay."

In cross-examination of Deichert, defense lawyer Shorter tried to suggest that Hastings either had not read the appeals court decision, or at least was confused about it, when he indicated in the July hearing that he intended to uphold his earlier order that the Romanos forfeit their property. When questioning law clerk Miller, Shorter tried to show that Hastings had no choice, based on the appeals court decision, but to return the property to the Romanos.

Shorter also raised the issue that any lawyer who read the appeals court decisions--including Borders--could see that Hastings would have to return the property. Shorter, attempting to bolster his theory that Borders had conned the undercover agent who was posing as Romano, tried to show that Borders didn't need to conspire with Hastings to know that the forefeiture order would have to be reversed.

Judge Edward T. Gignoux of Portland, Me., who is presiding over the case by special designation of the chief justice, has said he expects the trial to end early this week.