I read a short story in the early 1980s, probably from the 1960s or 1970s,
"Obviously Suicide", a short story by S. Fowler Wright, also the answer to this old question. Originally published in Suspense Magazine, Spring 1951, you probably read it in the anthology Fifty Short Science Fiction Tales edited by Isaac Asimov and Groff Conklin. The text of "Obviously Suicide" is available at the author's website www.sfw.org, as well as a slightly different version of the same story titled "The Last Man". The excerpts below are transcribed from Suspense Magazine.
that began with a scientist telling his wife that he and several colleagues had figured out how a combination of simple household chemicals and loop of hot wire could destroy the whole Earth (or maybe kill everyone on Earth).
"In about two seconds the Earth would dissolve in a blaze of fire," the research worker at the N. U. Laboratories told his wife. "There would be a burst of light and—one planet less in the universe. The amazing aspect is its very simplicity. It could be made in a backyard shed. All one needs is a combination of three substances, all easy to obtain, and then nothing more than a loop of heated wire."
"Wouldn't it be common prudence to get rid of these substances entirely?" she asked.
"Unfortunately, they are so widely distributed, and in such general use, that their complete destruction would be quite impossible."
The scientists take this discovery to somebody in the government, but the governmental response to the danger is inconclusive.
No, they don't bring it to the government, the thirty scientists who are in on it discuss it among themselves, as the protagonist tells his wife:
"Then it should surely be wiped out and forgotten as completely as possible from the minds of all of you who share such perilous knowledge."
"We have discussed that already, and shall do so again at a special meeting tomorrow. It may be decided in that way. But differences of opinion are natural among so many. At our first meeting, there were three who objected at once. No scientific fact, they argued, should be treated in such a way. . . . The trouble is that, though the calculations may be destroyed, the process and ingredients are too simple to be put out of mind—especially out of such minds as ours."
Eventually, in order to protect the people of Earth, the protagonist and his wife decide to murder everyone else who might know the secret.
Women are more practical and more ruthless than men. She had looked at the bed where a young child slept, and she thought of his sister, a year older, in the next room. Then she said: "If it were possible for the thirty to be destroyed before they could give their knowledge to other men, it would be the best thing that could happen now."
He said: "Oh, but my dear, think who they are! There's Professor Gribstein, and Dr. Thornton, and—"
"I never did like Dr. Thornton," she replied, as a woman would.
He did not give two thoughts to this criminal suggestion at the time, and it might never have re-entered his mind had there not been a discussion in the Council which became heated when it was clear that a substantial minority were indisposed to put the knowledge aside. One even suggested that they should make a public announcement of their discovery, so that they might become a Council of Thirty who would control a world that would crouch around them in abject fear. . . .
They kill them all without a hitch, and the scientist, tired out, heads to bed.
So, when the Council met again, it was done.
And no one suspected him in the least.
His one mistake was that he told Maude, thinking that she would approve, as indeed she did.
He said that the power was now in his hands alone, and he must consider the wisest course.
His wife looks once more at their sleeping infant, then kills her husband as well.
Maude thought of many things. Among these was the doubt of what, if or when he were dying, he might be tempted to do. She looked again at a sleeping child, and then did the practical thing.
It was a purlieu in which poisons were not hard to procure. She gave it to him in his morning coffee.