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11.10 Nuclear Reactions in the Sun

Hermann von Helmholtz showed in 1871 that the energy output of the Sun would equal that released by the burning of 7000 kilograms of coal every hour on every square meter of the Sun's surface. Helmholtz realized that no ordinary chemical reaction can produce energy at this rate. Thus, the Sun is not "burning" in the normal sense of a chemical reaction.

 

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Hermann von Helmholtz. Click here for original source URL.

 


Helmholtz could not have known that the Sun is a powerful fusion reactor because nuclear physics was not yet understood. Nuclear reactions inside the Sun, as in all stars, do two important things: they generate energy, and they gradually change the Sun's composition because they build up increasingly heavy nuclei. The temperature inside the Sun is so high that electrons have all been stripped from their atomic nuclei. This physical state is called a plasma. The electrons are also far less massive than the nuclei and carry far less energy. We therefore only need to consider the interactions between nuclei.

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Schematic of the proton-proton chain nuclear fusion reaction. Click here for original source URL.

The principal nuclear reactions inside the Sun convert hydrogen into helium in three stages. Because this chain of reactions starts with two hydrogen nuclei — that is, two single protons — it is called the proton-proton chain. In step 1, two protons collide and fuse, forming deuterium, which is designated 2H or D. Two additional particles are released: a positron and a neutrino. The positron is the antiparticle of the electron, identical except for having a positive charge. It is designated e+. The positron quickly interacts with an electron, disappearing to produce radiation. The neutrino is a ghostly particle, with no charge and a negligible mass. It is designated by the Greek letter ν. The neutrino interacts extremely weakly with matter; a neutrino from the Sun could pass through thousands of miles of steel without being stopped. Therefore it acts as if other particles are not there, escaping the Sun's core traveling at nearly the speed of light. 

The first step of the fusion process in the Sun mates two protons. In step 2, the hydrogen nucleus hits another proton and fuses into a form of helium known as helium-3, designated 3He. More radiation is released. In step 3, two of the 3He nuclei collide and fuse into the most common form of helium, helium-4, designated 4He. This third step leaves two extra protons behind, which are available to participate in step 1 again. In each step, the reaction releases energy in the form of photons, and its end result is that the Sun creates helium out of the lighter element hydrogen. 

The total amount of mass left at the end of the three-step chain is slightly less than the mass of the initial hydrogen atoms. During the fusion, a small amount of mass is converted to a large amount of energy  and we use a very famous equation to calculate the energy E = mc2. In the Sun's fusion sequence, about 0.007 kilograms of matter is converted into energy for each kilogram of hydrogen processed. In other words, the efficiency of mass-energy conversion is 0.7% and the amount of energy released is 0.007mc2. The synthesis of a single helium nucleus creates 4.5 × 10-12 Joules of radiant energy. The entire Sun radiates 4 × 1026 Joules each second. This corresponds to 400 trillion trillion Watts — which equals a lot of light bulbs! Remember, though, that this energy is created in the Sun's core. Although neutrinos escape the Sun immediately (and reach the Earth in 8 minutes), the photons created in nuclear reactions scatter off of atomic nuclei on their way out of the Sun and, even though they still travel at the speed of light, their path traveled becomes much longer than the radius of the Sun. They start out as gamma rays in the Sun's core and lose energy as they bounce their way outward. The result is that they take about 50,000 years to reach the photosphere. At that point they have become visible photons and they travel to us across the vacuum of space in just 8 minutes. So if something strange happened to the fusion reaction in the Sun it would take 50,000 years for us to know about it! Don't worry — the Sun will fuse hydrogen steadily for another 4 billion years.

Every second, the Sun converts 4 million tons of hydrogen into energy in its core and radiates it toward its surface! Yet, the reservoir of hydrogen in the Sun is so large that, even using its fuel at the rate of one tall skyscraper's worth per second, there has been no detectable change in the Sun's output in recorded history. According to recent calculations, the Sun won't run out of hydrogen for about 4 billion years. The consumption of hydrogen inside the Sun tells us that stars are not permanent, but must evolve and run out of fuel. Note that astronomer and physicists are sometimes sloppy and use the colloquial term "burning" to describe the Sun's energy production. It is not chemical burning, however, it is the quite different process of nuclear fusion.

The discovery of fusion as the power source of the Sun is a good example of how science works. We can see how scientists piece together information into a coherent physical description of a remote object. The starting point is our knowledge of the distance to the Sun. This combined with a measure of how much radiation reaches the Earth's surface gives the Sun's energy output. Since the Earth only intercepts 1 billionth of the Sun's light, and 1370 Watts reach each square meter of the Earth's surface, the Sun must be a truly impressive energy source. It is easy to show that no chemical energy source the size of the Sun can produce the required output for more than a few thousand years. Since we have records of fossils and geological activity older than that, the evidence points to a new energy source: the fusion of atomic nuclei. Sure enough, we learn from spectroscopy that the Sun is made mostly of hydrogen and helium, the nuclear fuel and its byproduct.