Hans Bethe: where do the stars get their energy?

In 1938, Hans Bethe’s pioneering work answered a question that had been nagging scientists for years — that is, where do the stars get their energy?

This is for Monday, July 2 — a landmark date in 20th century science — the birthday in 1906 of Hans Albrecht Bethe.

Bethe served as the chief of the theoretical division for the Atomic Bomb Project. At the end of the Second World War, Bethe worked, along with Edward Teller, on the development of the hydrogen bomb. He was a member of the President’s Science Advisory Committee from 1956-1964, and in 1958 headed a presidential study of nuclear disarmament.

Bethe is known for discovering the energy source that powers the stars. He showed in 1938 that virtually all the energy produced by stars arises from nuclear fusion, in which the nuclei of hydrogen atoms are converted into helium.

This mechanism is now known as the carbon-nitrogen-oxygen cycle. It occurs in stars hotter and more massive than our sun, with core temperatures above 27 million degrees. Under these extreme temperatures, carbon, nitrogen, and oxygen nuclei collide with hydrogen nuclei. The carbon nucleus later reappears and a new helium nucleus is created. So, hydrogen is the fuel, helium the by-product, and carbon the catalyst — and a little leftover mass is turned into a lot of energy.

Bethe also showed that, for cooler stars like our sun, hydrogen nuclei directly fuse into helium. The sun converts 600 million tons of hydrogen into helium each second. This results in a loss in the sun’s mass of four million tons per second. The total mass of the sun is so great, though, that this loss is negligible — even over millions of years.

Author’s Notes

Brief Biography

Hans Albrecht Bethe was born in Alsace-Lorraine, while it was still a part of Germany. Today is a part of France. He was educated at the universities of Frankfurt and Munich. In 1933, when Hitler came to power, Bethe left Germany for England. There he determined how high-energy particles subjected to deflection by an electromagnetic field, emitted radiation. This was particularly important in cosmic ray research.

Bethe also one of the chief scientists engaged in the development of the atomic bomb. In postwar years, he became an active proponent of the peaceful exploitation of nuclear energy.

In 1961, Bethe was honored with the Fermi award for his role in the development and use of atomic energy. He received the Nobel Prize for physics in 1967 for his work on stellar fusion.

The Fusion Process

There are two ways stars burn hydrogen: the “proton-proton chain,” and the “carbon-nitrogen-oxygen cycle.” The proton-proton chain can account for hydrogen burning in stars with masses similar to the Sun’s but not in hotter, more massive stars. In the latter case, even though their internal temperatures are only a little higher than the Sun’s, their luminosities are also much higher, too high to be explained by the proton-proton chain. In massive stars, the more temperature-dependent carbon-nitrogen-oxygen cycle is invoked. The cycle requires the presence of small quantities of carbon produced in earlier generations of stars to catalyze with hydrogen to yield helium. The carbon-nitrogen-oxygen cycle is also known as the Bethe-Weizsacker cycle. Carl Weizsacker, working independently, came up with a similar energy mechanism in Germany. “Weizsacker is sometimes spelled “Weizsacher.”

In over 99 percent of the p-p chain reactions, two hydrogen nuclei protons combine to emit a positron and a neutrino, thus forming a deuterium nucleus. Deuterium then combines with another proton to yield a helium-3 nucleus and a photon. Some 95 percent of he-3 combines into helium-4, liberating two protons. Thus, each cycle converts four hydrogen nuclei into one he-4 nucleus with a release of energy. High-collision speeds plus quantum-mechanical tunneling are required to fuse nuclei, since they have to overcome the mutual repulsion arising from their positive charge.

In the Sun, hydrogen fusion can only take place within 150,000 kilometers of its core, where temperatures are greater than 10 million kelvins. Thus, nearly all the Sun’s energy is generated within a sphere whose radius is about one-fifth of the radius of the sun.