Nuclear Synthesis And Carbon Formation

According to the Big Bang theory, the orthodox teaching of the origin of the universe, we owe our existence to a proto universe

10 cm across that was formed when the universe was about 10-32 sec in existence. This proto universe has expanded since to form Earth as we know it today about 15 billion years later. The proto universe was extremely hot (1027K), but the expansion of space has decreased its temperature to only 2.7 K now. During the early stage of quenching, the energy in the proto universe condensed into elementary particles that eventually coalesced to form protons and electrons. After 300,000 years of ongoing expansion, the temperature cooled enough (1000 K) to allow the formation of atoms. However, the cooling of the universe was so fast that only hydrogen atoms (93at.% or 79wt.%) and helium atoms (6at.% or 20 wt.%) could form in time.

Hydrogen and helium atoms are less stable than heavier atoms, so they have a tendency to fuse together. But, this fusion may only take place at the high temperature that existed when the universe was still in infancy. Although the ambient temperature of Earth is now been too cold, the center of a star is hot enough to continue the fusion of light atoms. Stars are formed by accumulating sufficient amount of light atoms that attract one another by gravity. As soon as pressure and temperature reach the right threshold level, nuclear synthesis by fusing light atoms into heavier ones will begin. Initially, like our Sun, hydrogen atoms will fuse together to form helium atoms. If the star is sufficiently massive (e.g. 3 times more massive than our Sun) helium atoms will also combine to form heavier atoms, and the trend will continue.

The binding energy of nuclei is the lowest for iron atoms (Fig. 1.5). Accordingly, nuclear synthesis may continue until iron atoms are formed. After that, any enlargement of nuclei will not release enough energy to sustain the reaction, but will absorb energy, such that the nuclear synthesis will halt.

At high temperature, nucleons have enough energy to move around and so tend to form the most stable nuclei possible. Hence, four hydrogen atoms will fuse into one helium atom (two hydrogen atoms become two neutrons that join the nucleus, at the same time, two protons and two electrons from the other two atoms will combine in the same atom). Subsequently, helium atoms may also fuse into beryllium atoms. Beryllium atoms may combine with helium atoms to form carbon atoms. Carbon atoms may fuse with helium atoms to form oxygen atoms, and the cycle can continue in this fashion.

Atomic Number - Proton Number = Electron Number

Figure 1.5. Iron (N = 26) has the lowest nuclear binding energy, so any atoms lighter than iron may combine (fusion) into larger atoms; but any atoms heavier than iron may disintegrate (fission) to form smaller atoms.

If the binding energy of nucleons monotonously increase with the addition of nucleons, then we would expect that the cosmic abundance of these elements to decrease with the atomic size (atomic number N, proton number or electron number). But the stability of nucleus size differ greatly with the number of protons present. Hence, the amounts of atoms formed are also highly variable. Although the general trend shows a decrease in the abundance of elements with increasing atomic size, but there are many exceptions. For example, although iron atoms are more than 10 times heavier than beryllium atoms, they are millions of times more abundant.

Beryllium nuclei formed by the impact of two helium nuclei is unusually unstable and has a half-life of only 10-17 sec. Hence, beryllium atoms are rarely found inside a star. However, beryllium atoms provide the source for making heavier atoms such as carbon and oxygen. These are the two of the most vital elements for us humans (e.g. our body may contain 12at.% or 23wt.% of carbon atoms, and we need to breath an air that contain about 20 wt.% oxygen). If there were no mechanism to boost the production of these essential elements, not only there would be no diamond stars, but also the universe would be lifeless.

In order to explain the ubiquitous presence of carbon and oxygen atoms in the universe, the English astrophysicist Fred Hoyle proposed in 1953 that carbon nuclei could resonant at a frequency 4% higher than beryllium nuclei, so when the latter is hit by helium nuclei, the combined energy will make carbon nuclei tick. According to this hypothesis, although beryllium nuclei are extremely unstable, the chance for these nuclei to transmute into carbon nuclei is exceedingly high. As a result, the abundance of carbon increases at the expense of beryllium.

Holye also proposed that the resonance frequency of oxygen nuclei is 1% less than that of carbon. Because of this, the collision of carbon and helium would not form oxygen readily. Hoyle's two predictions were confirmed latter by experimentation, a triumph because he backwardly reasoned the cause based on its effect. Thus, it is the subtle balance of the vibration frequencies between carbon and oxygen that result in how abundant these two critical elements are. By having the right balance of carbon and oxygen, the miracle of life is possible.

Carbon and oxygen atoms are much more abundant than any other heavy element. As a consequence, the four most abundant elements in the universe are H (93 at.%), He (6 at.%), O (0.06 at.%), and C (0.03 at.%) (Fig. 1.6). Among them, C is the only solid element. All the other heavy elements combined would account for only 0.1 at.% of the cosmic abundance, hence, carbon may actually account for 30% of all solid material in the universe. For example, the cosmic abundance of carbon is more than ten times that of silicon (a major semiconductor material and the essential constituent of rocks) or iron (a major industrial material and the core element of Earth). No wonder carbon is ubiquitous in space and therefore, diamond is everywhere in the cosmos.

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