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Three scientists, two American and one German, received this year’s Nobel Prize in Chemistry for circumventing a basic law of physics and enabling microscopes to peer at the tiniest structures within living cells.

The 2014 laureates, announced Wednesday by the Royal Swedish Academy of Sciences, are Eric Betzig, 54, of the Howard Hughes Medical Institute in Virginia; Stefan W. Hell, 51, of the Max Planck Institute for Biophysical Chemistry in Germany; and William E. Moerner, 61, of Stanford University in California.

For centuries, optical microscopes — those that magnify ordinary visible light — have allowed biologists to study organisms too small to be seen with the naked eye. But a fundamental law of optics known as the diffraction limit, first described in 1873, states that the resolution can never be better than half the wavelength of light being looked at.

For visible light, that limit is about 0.2 millionths of a meter, or one-127,000th of an inch. A human hair is 500 times as wide.

But a bacterium is not much larger than the size of the diffraction limit, and there was little hope of seeing details within the cell like the interaction of individual proteins.

Other technology like the electron microscope, which generates images from beams of electrons instead of particles of light, achieves higher resolution, but it has other limitations, like requiring the sample to be sliced thin and placed in a vacuum.

For biological research, that generally meant the subject of study had to be dead.

At first glance, circumventing the diffraction limit would seem a foolish pursuit, like trying to invent a perpetual motion machine or faster-than-light travel — doomed by fundamental limits on how the universe works.

Nonetheless, Hell, who was born in Romania, started working on the problem after finishing his doctorate at the University of Heidelberg in 1990. After failing to find financing in Germany to pursue his ideas, he obtained a research position at the University of Turku in Finland in 1993. A year later, he published his theoretical proposal for achieving sharper microscopic pictures.

Hell could not break the laws of physics, of course. But he realized they could work around the diffraction limit by lighting up some of the molecules.

Biologists were already using a technique called fluorescence microscopy — attaching glowing molecules to proteins or DNA and then following the movement of the glows, like watching the ebb and flow of city traffic at night via the streams of headlights. But that did not solve the diffraction limit. If fluorescent molecules came close to one another, all the biologists could see was one glowing blur.

Hell’s insight was that by using lasers, he could restrict the glow to a very small section. That way, for structures smaller than the diffraction limit, “You can tell them apart just by making sure that one of them is off when the other is on,” he said in an interview.

Other scientists could have just taken his proposal and made it work in the laboratory long before he did, he said, adding: “I was a sort of nobody in those days. I didn’t even have a lab, really. People could have taken it as a recipe, could have done it. But they didn’t do it. Why didn’t they do it? Because they thought it wouldn’t work that way.”

In 1997, he moved to the Max Planck Institute for Biophysical Chemistry, and in 1999, he successfully put his idea into practice, producing a clearer image of an E. coli bacterium. Hell said the top scientific journals, Science and Nature, rejected the paper before it was published in The Proceedings of the National Academy of Sciences.

About the same time, Moerner, then at the University of California, San Diego, was working with a green fluorescent protein that had first been found in a glowing jellyfish, an advance that brought three researchers the Nobel Prize in Chemistry in 2008. Moerner found a version of the protein that he could turn on or off by shining specific colors of light on it.

That advance proved crucial for Betzig, who in 1995 had published an idea for using fluorescent molecules of different colors to get around the diffraction limit. But Betzig, then a researcher at Bell Laboratories in New Jersey, was frustrated with the academic life. He quit Bell and joined his father’s machine tool company.

Years later, as he grew restless again and thought about returning to science, Betzig came across the green fluorescent protein. “And then it would become clear” how to put in effect his 1995 idea, he said.

Instead of using fluorescence of different colors, he could switch on a few of the molecules at a time. By combining separate images, Betzig was able to produce a sharper view.

The three laureates have employed their innovations to study biology at the smallest scales. Hell has studied how brain synapses work, Moerner has looked at proteins related to Huntington’s disease, and Betzig has tracked cell division inside embryos.

“Biology has turned into chemistry,” said Sven Lidin, the chairman of the Nobel Committee for Chemistry and a professor of inorganic chemistry at Lund University. “Chemistry has turned into biology.” (By training, all three laureates are physicists.)

The three scientists will share a prize of $1.1 million, to be awarded Dec. 10 in Stockholm.

Betzig said he had learned the news in a phone call in Munich, where he was attending a conference. He said his reaction was “I guess elation and fear — the fear being that my life is busy enough and happy enough, and it doesn’t need to be perturbed too much.”

The committee was not able to reach Moerner before making the announcement.

“I actually still haven’t a chance to talk to them,” Moerner said Wednesday morning from a hotel room in Brazil, where he is attending a scientific workshop. He said his wife called to tell him the news.

Hell said that when he received the phone call, he wondered if it might be a hoax. Then he recognized the voice of the caller, Staffan Normark, the permanent secretary of the academy. Another voice told him to stay on the line so that he could take questions from journalists.

“And then I realized, this is serious,” he said.