Jury selection began here today in the $11.5 million personal injury trial in the celebrated case of young Karen Silkwood. The trial may have broad impact on the nation's nuclear power industry.

Silkwood was the Kerr-McGee nuclear worker contaminated with plutonium during labor union difficulties shortly before her death in what some people say was a suspicious auto wreck in 1974.

The trial is the nation's first involving radioative contamination outside a nuclear facility. If the six-person jury now being selected finds in favor of Silkwood's relatives, it could establish a benchmark unfavorable to the nuclear industry for determining legal liabilities.

But perhaps more importantly, the widely publicized trial comes at a time of growing public and official criticism of the nationhs nuclear industry, with almost daily adverse reports on radiation whether connected to nuclear power or not.

"It's anti-nuclear," Alison Freeman of the "Karen Silkwood Public Education Fund" says of the trial.But the Silkwood case, she notes, is also wrapped in feminism, civil rights and trade unionism -- causes that have attracted organizations to the the fund in addition to a multitude of individuals.

The civil rights and organized labor aspects of the Silkwood suit have been thrown out of court so far and are on appeal.

In a sense, Silkwood's relatives are in the Vatican suing the Pope: Kerr: McGee, with $2.1 billion in annual sales, is a pillar of Oklahoma's economy and politics. Its co-founder was the late U.S. senator Robert Kerr; it employs almost 2,000 people here and contributes to local charities.

The company is a diverse energy conglomerate -- oil, natural gas, coal and uranium. It owns more uranium reserves than anyone else in the United States and is a major processor and supplier of uranium for commercial nuclear reactors.

One federal judge was excused from the case because of his ties to the late senator, and a sec ond judge was excused after making unflattering remarks about the Silkwood attorneys. The case will be heard by U.S. District Court Judge Frank Theis of Wichita.

In a trial that may last six weeks, attorneys for the Silkwood estate hope to show that she was contami nated by minute amounts of plutonium from Kerr-McGee's Cimarron plant that ended up in her refrigerator and other places in her apartmet.

At the time, according to Kerr-McGee, Silkwood was employed to check plutonium pellets for use in the fuel rods of a fast breeder reactor in Richland, Wash. She was also negotiating health and safety issues with Keww-McGee as a bargainer for the Oil, Chemical and Atomic Workers Union.

On Nov. 5, 1974, Silkwood reported that a routine check for plutonium exposure showed her to be contaminated. She reported eing contamenated also on the 6th and 7th. That's when Kerr-McGee and Atomic Energy Commission officials checked her apartment and later said they found bare traces of plutonium.

On Nov. 13, as she drove to meet with a union official and a New York Times reporter, allegedly with documents showing sleazy safety practices at Kerr-McGee, Karen Silkwood's car went off the road and hit a culvert, and she was killed.

No such documents were found in the car, and a private investigator reported a suspicious dent indicating that maybe another auto ran her off the road.

While Silkwood's death is not an issue in this trial, the Silkwood lawyers say that, no matter how the plutonium got into her apartment, Kerr-McGee is responsible and thus must bear the burden for any injuries and anguish Silkwood experienced in the last days of her life.

Kerr-McGee's lawyers say Silkwood, 24, was herself negligent -- hinting that she took the plutonium home. Indeed, an Atomic Energy Commission investigation, one of 17 of Kerr McGee since the events of that November, concluded that a radioactive urine specimen from Silkwood contained plutonium placed in it after the urine had been passed.

The suit claims Silkwood suffered anguish over her exposure to the plutonium, what with all the fears that the cancer-causing element can give rise to. She was on tranquilizers at the time of her death, but Kerr-McGee says they were prescribed before her exposure.

Any anguish, the company said, was the result of other events in her life, not her exposure to plutonium.

The Silkwood lawyers hope to convince the jury that nuclear power is oveall more hazarbous to the public than beneficial, and that Kerr-McGee was so sloppy that no matter how the plutonium got to Silkwood's apartment, Kerr-McGee was negligent.

The company claims it was not negligent and operated within federal safely standards. If the jury finds for Silkwood's estate, nuclear facilities might not be able to cite federal safety standards as a defense against negligence.

Moreover, if the inherent hazards of radioactive materials are found to be absolute no matter what precautions are taken, the Silkwood case could set a precedent for how much a nuclear facility must pay in damages.