In an atmosphere marked by idle chatter, backslapping, a few fidgeting children and many more fidgeting adults, President-elect Jimmy Carter and Vice President-elect Walter F. Mondale yesterday officially were declared the winners of the 1976 election.

The declaration came at a joint session of the House and Senate, whose members met on the House floor to witness the opening and counting of ballots cast Dec. 13 by 538 electors in their state capitals.

The results: Carter and Mondale each received 297 electoral botes; Sen. Bob Dole of Kansa, the Republican vice presidental candidate, got 241; President Ford finished fourth with 240.

Ford lost one vote because Mike Padden, 30, a Seattle lawyer pledged to the President and Dole, cast his ballot for former California Gov. Ronald Reagan in the meeting of Washington state electors.

Though Ford had carried the state by 60,409 votes, Padden refused to vote for him because of what he called Ford's failure to take a strong stand against abortion.

There had been some rumors of an effort to reject Padden's vote and record it for Ford in the final tabulation yesterday, but no such move materialized.

In fact, there seemed to be an overwhelming desire on the part of all concerned to end this final step in the electoral process as quickly as possible.

Traditionally, for example, the secretary of the Senate has opened the envelope containing the state's electoral vote certificate and then handed it to the House parliamentarian. The parliamentarian would then give the certificate to the Vice President, who is the president of the Senate and the presiding officer over the tabulation proceedings.

After reading the certificate, the Vice president would then hand it to one of four tellers - two from the Senate, two from the House, chosen evenly along party lines. After all the tellers had reviewed the certificate, one of them would then announce: "Mr. President, the certificate of the electoral vote of the state - appear to be regular in form and authentic and it appears therefrom that "(he reads the vote)."

Yesterday, for the sake of form, Vice President. Rockefeller went through the complete procedure for only one state, Alabama, whose electoral votes were the first to be counted. Rockefeller then moved to shorten the proceedings by taking himself out of the routing of the state certificates.

The motion was unanimously approved by the House and Senate members, who filled about half of the 448 seats available in the House.

The ceremony began promptly at 1 p.m. and ended 34 minutes later.

Throughout it all there was the constant chatter of legislators - many of whom walked around, meeting and greeting and shaking hands. On one side of the floor, Daniel Patrick Moynihan, newly elected Democratic senator from New York, spoke enthusiastically with an unidentified listener, frequently punctuating his conversation with brisk hand movements.

When the vote of the New York electors was announed, in favor of Carter-Mondale, Moynihan applauded.

On the other side of the floor, Dole, dressed in a blue business suit and wearing a compatible red tie, greeted colleagues. He laughed, and his colleagues guffawed, when Rockefeller inadvertently announced at the end of the proceedings: "Sen. Dole of the state of Michigan has received for the vice presidency of the United States 241 votes."

For a moment, Rockefeller's goof seemed fitting evidence of Dole's often-stated belief that Vice Presidents are soon forgotten and vice presidential candidates who lose are forgotten even more quickly.

Rockefeller, however, quickly corrected himself to say, "Sen. Dole of the state of Kansas."

On the House floor were several children, whose friskiness apparently disturbed some House and Senate aides.

"What are they doing down there?" asked one irate aide, viewing the scene from the House press gallery.

"I think they can be there if they're over nine [years old]," another aide said.

"Wonder why they came?" asked the first aide. "This [the ceremony] is a useless exercise in futility."