IT ISN'T YOUR everyday 17 year old that sets an entire department of government on its ear and throws the administration's public relations apparatus into a super- swivet.

Boat-rockers Washington has seen, but Ariela Gross of Princeton, N.J., is in a class by herself. During a week of intense pressure she stayed the course and made her point. A preternaturally composed teen-age with dark blond hair and hazel eyes, she was editor of her school paper, led its track team and excelled in her studies. She was chosen as a Presidential Scholar.

To the unutterable consternation of the Reagan White House, she turned out to have an obssession about the nuclear freeze. On being told of her scholarship, the first thing she did was to write her fellow-winners inviting them to join her in presenting a freeze petition to the president. When the Department of Education heard about it -- no subject riles the chief more than the freeze -- the panic button was pressed.

Gary Stember, executive director of the commission on Presidential Scholars, called Ariela's mother and warned her that Ariela "would risk being labeled a radical" and might lose her $1,000 prize. Mrs. Gross, a professor of statistics, warned Stember that threatening her daughter would only make her more determined. Stember was subsequently reprimanded for heavy-handednes.

When Ariela arrived at Georgetown Sunday night for a week of briefings, "everyone had been polarized -- "it was a situation like I was wearing the scarlet letter," she said. At the picnic supper, education department spokesmen who kept making the point that the scholars were "not here on account of your political views," got standing ovations.

Although some of her peers had expressed admiration for her courage, potential petition-signers melted away. She called home and reported to her mother that she was "dejected" at the rejection. Mrs. Gross came down, "not to stop her" but to help.

"They were always muttering just in front of me or in back of me, saying things like, 'Oh, I think she's just doing it because she thinks she is smart because she comes from Princeton,' " she said.

"I don't think most of them disagreed with me, but there was a kind of mass intimidation that made it difficult for them to be on my side."

On Tuesday, to remind herself of what it was all about, she went to the anti-MX rally. She met its organizer, Ed Markey of Massachusetts, who shares her idea that politics is opportunities taken. Markey put her on the program, and when she was introduced as "a young woman of courage and conviction," she sailed up to the microphone as if born to it. To loud applause from the audience, she said, "My generation will not be intimidated."

That was hardly the case at the time. Only 14 of her fellow-scholars of 141 signed the petition. She said later she was thinking of Princeton, where 70 per cent signed, and of Harvard, where she is headed in the fall.

By Wednesday, the plan to have the president present the medallions was changed. Secretary Bell would substitute, plainly to spare the president the onus of being handed a dissenting letter by a super-achiever of the academic excellence he is now almost daily saluting.

To the sweating education department officials, Ariela promised that she would deliver her document to the president's surrogate, and would not mar the ceremonies in any way.

The scholars discussed, then dropped the idea of handing the president a written apology for Ariela's conduct on the grounds that it would be as "disruptive" as the petition.

One scholar said to her, "Don't you understand as Presidential Scholars we give up some of our rights?"

But when Ariela's name was called, and all eyes in the broiling sun turned in her direction, she walked calmly up to the platform, shook hands with Bell -- and handed him nothing.

That is because someone on the first team at the White House decided it was better to end the mortification abruptly and have the president engage in a fatherly chat with the dissenter. She was escorted to the White House, and presented to cabinet secretary Craig Fuller who conducted the final bargaining. Would she present her petition to the president -- not to Secretary Bell in public? Since that was what she had wanted all along, Ariela agreed.

In the Oval Office, Ariela and the president had a 20-minute summit. Later, she observed that she found it "even more terrifying" to hear the president's views on nuclear war in person than on TV.

From the back row, Ariela's teacher at Princeton High, Ronald Gendaszeh, mused, "I don't know if I would have Ariela's guts."

Her mother, a jolly, ample woman, cast a fond look at her daughter, who was lost in a thicket of microphones and cameras.

"I'm so proud of her," she said. "She has the strength of character that comes with conviction."