Thermonuclear Fusion in the Sun and Other Stars

Thermonuclear Fusion in the Sun and Other Stars

The Sun radiates energy at the rate of 3.9 X 1026 Wand has been doing so for several billion years. Where does all this energy come from? Chemical burning is ruled out; if the Sun had been made of coal and oxygen-in the right proportions for combustion-it would have lasted for only ab out 1000 y. Another possibility is that the Suns slowly shrinking, under the action of its own gravitational forces. By transferring gravitational potential l energy to thermal energy, the Sun might maintain its temperature and continue to radiate. Calculation shows, however, that this mechanism  also fails; it produces a solar lifetime that is too short by a factor of at least500. That leaves only thermonuclear fusion. The Sun, as you will see, bums not coal but hydrogen, and in a nuclear furnace, not an atomic or chemical one.  The fusion reaction in the Sun is a multistep process in which hydrogen is burned into helium, hydrogen being the “fuel” and helium the “ashes.”  shows the proton-proton (p-p) cycle by which this occurs.  The POpcycle starts with the collision of two protons eH + IH) to form a deuteron (2H), with the simultaneous creation of a positron (e “) and a neutrino (II). The positon very quickly encounters a free electron (e”) in the Sun and both particles  annihilate (see Section 22-6), their mass energy appearing as two gamma-ray photos (y).A pair of such events is shown in the top row of . These events are actually extremely rare. In fact, only once in about 1026 proton-proton collisions is a deuteron formed; in the vast majority of cases, the two protons simply rebound  elastically from each other. It is the slowness of this “bottleneck” process that regulates the rate of energy production and keeps the Sun from exploding. In spite of this slowness, there are so very many protons in the huge and dense volume of the  Sun’s core that deuterium is produced in just this way at the rate of 1012 kg/so

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Once a deuteron has been produced, it quickly collides with another proton and forms a 3He nucleus, as the middle row of . Two such 3He nuclei may eventually (within lOs y; there is plenty of time) find each other, fondling an alpha particle (4He) and two protons, as the bottom row in the figure shows.  overall, we see from that the pop cycle amounts to the combination of four protons and two electrons to found an alpha particle, two neutrinos, and six gamma-ray photons. That is,

4 IH + 2e- – 4He + 2J1+ 6y.

Let us now add two electrons to each side of Eq, 44-10, obtaining

(4 IH + 4e-) – (4He + 2e-) + 2J1+ 6y.

The quantities in the two sets of parentheses then represent atoms (not bare nuclei) of hydrogen and of helium. That allows us to compute the energy release in the overall reaction of Eq. 44-10 (and Eq. 44-11) as

Q = -Am c2
= -[4.002603 u – (4)(1.007825 u)][931.5 Mev/u]
= 26.7 MeV

in which 4.002 603 u is the mass of a helium atom and 1.007 825 u is the mass of a hydrogen atom. Neutrinos have at most a negligible small mass, and gamma-ray photons have no mass; thus, they do not enter into the calculation of the disintegration energy. This same value of Q follows (as it must) from adding up the Q values for the separate steps of the proton-proton cycle in . Thus

Q = (2)(0.42 MeV) + (2)(1.02 MeV) +. (2)(5.49 MeV) + 12.86 MeV
= 26.7 MeV.’

About 0.5 MeV of this energy is carried out of the Sun by the two neutrinos indicated in Eqs. 44- 10 and 44-11: the rest (= 26.2 MeV) is deposited in the core of the Sun as thermal energy. That thermal energy is then gradually transported to the Sun’s surface where it is radiated away from the Sun as electromagnetic waves, including
visible light. .   he burning of hydrogen in the Sun’s core is alchemy on a grand scale in the sense that one element is turned into another. The medieval alchemists, however, were more interested in changing lead into gold than in changing hydrogen into  helium. In a sense, they were on the right track, except that their furnaces were not hot enough. Instead of being at a temperature of, say, 600 K, the ovens should have been at least as hot as 108 K. Hydrogen burning has been. going on in the Sun for about 5 X 109 y, and calculations show that there is enough hydrogen left to keep the Sun going for about the same length of time into the future. In 5 billion years. however, the Sun’s  which by that time will be largely helium, will begin to cool and the Sun will start to collapse under its own gravity. This will raise the core temperature and cause the outer envelope to expand, turning the Sun into what is called a red giant. If the core temperature increases to about 108 K again, energy can be produced through fusion one more-this time by burning helium to make carbon. As a star   evolves further and becomes still hotter, other elements can be formed by other fusion reactions. However, elements more massive than those near the peak of the
binding energy curve of  cannot be produced by further fusion processes. Elements with mass numbers beyond the peak of that curve are thought to be formed by neutron capture during cataclysmic stellar explosions that we call supernovas . In such an event the outer shell of the star is blown outward into space, where it mixes with-and becomes part of-the tenuous medium that fills ‘the space between the stars. It is from this medium, continually enriched by debris  rom stellar explosions, that new stars form, by condensation under the influence of the gravitational force.  he abundance on Earth of elements heavier than hydrogen and helium suggests that our solar system has condensed out of interstellar material that contained the remnants of such explosions. Thus, all the elements around us-including those in our own bodies-were; manufactured in the interiors of stars that no longer exist. As one scientist put it: “In truth, we are the children of the stars.”

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