The Carter administration has targeted the tiny island of Palmyra, 1,000 miles southwest of Hawaii, as the Pacific's first dumping ground for radioactive wastes.

The island's selection and the uproar it is expected to cause through much of the Pacific illustrate the cruel dilemma in which President Carter finds himself as he champions nuclear power.

Before he can sell the United States and other countries on getting more electricity from the atom to lessen the demand for oil, the president must find a way to dispose of the poisonous wastes civilian nuclear reactors produce.

Although some countries reprocess these radioactive wastes into fuel that can be used again, Carter opposes this option because it frees plutonium, which can be used to make atomic bombs. India, it is widely believed, made its bomb from the plutonium waste of its Canadian-supplied nuclear reactor, which produces electricity.

Rather than see the Indian example repeated all around the world, thus putting the bomb in the hands of some reckless leaders, Carter has opted for storing the radioactive waste in a safe place, if his experts can fine one.

While the United States considers everything from salt domes to granite caves for storing its radioactive wastes, it is trying to prod Pacific countries into storage rather than reprocessing by offering to supply the dump.

Enter Palmyra.

After highly secret explorations, the administration has tentatively decided that the uninhabited 500-acre atoll would make the best Pacific dump.

State Department officials note that the atoll, rising 6 to 10 feet above sea level, has a good harbor, enough land for airstrips and buildings, no severe weather and "long-term geologic stability."

Once part of the kingdom of Hawaii, it is now privately owned by the Fullerd-Leo family of Honolulu. The government could buy it for $16 million to $18 million, officials estimate.

Thomas R. Pickering, assistant secretary of state in the bureau of ocean and international environmental and scientific affairs, stressed at a secret Senate hearing that although Palmyra's selection is not final, it would be much better than Midway Island or Wake Island, which were also studied.

If present plans go forward, said Pickering, Palmyra could become the Pacific's first radioactive dump as early as "mid-1986."

A recently cleared transcript of the June 5 closed hearing by the Senate Energy and Natural Resources Committee show that several senators expect a tidal wave of protests, especially if past secrecy about such radioactive storage continues.

Pickering agreed that "there is a great sensitivity among many island nations in the Pacific basin, as well as around the world, regarding any possible contamination, no matter how small the risk, of a part of the Pacific with radioactive material.

However, Pickering said, in making the administration's case for a dumping site, "We have a serious concern about the pileup of spent fuel in the Pacific area. If this spent fuel forces reprocessing as an answer to the question of waste management, it will provide a lot of plutonium to a lot of countries that don't have a need for it. It opens the question of the proliferation of nuclear weapons in a serious way."

Radioactives wastes would be stored on Palmyra for only 30 years, and then moved to some other undetermined dump for fear the concrete-covered canisters would not stay impregnable on the island much longer than that.

Under the current plan, Japan, which sends its radioactive wastes to Britain and France for reprocessing, would ship some of them to Palmyra.

The smaller amounts to be produced by South Korea, Taiwan and the Philippines would be stored on Palmyra. The United States eventually might store some of its nuclear wastes on Palmyra, too, Pickering said.

At the moment, State and the Energy Department envision using only 100 of Palmyra's 500 acres as the dump. From 100 tons to 300 tons of radioactive wastes could be stored on each of the 100 acres, for a total load of between 10,000 and 30,000 tons.

The wastes would be sealed in steel containers coated with concrete. The canisters would be sent to Palmyra by ships and stored in other concrete containers constructed on the island.

"The major purpose, said Pickering of the Palmyra plan, "is to reduce pressure for additional reprocessing."

Senators listening to the testimony, the cleared transcript shows, expressed the kinds of fears about the plan that are expected from concerned groups in the Pacific.

"What happens," asked Sen. J. Bennet Johnston (D-La.) "if a ship sinks carrying spent fuel to the island?"

"The same thing, I would imagine," responded Pickering, "that would happen if ships sink carrying spent fuel from Japan to the United Kingdom or France, as is currently done . . .

"The fuel would be lost and would be subject to whatever protection the cask provides, which I understand is very considerable," he said.

Marvin Moss, associate director of energy research for the Energy Department said that if the casks were not recovered from the ocean bottom, "I think one would have the makings of certainly a severe accident there."

"What is a severe accident?" Johnston persisted.

"Large quantities of radioactivity released into the floors of the ocean," Moss replied.