Nuclear Reactions Study Guide

1.4 Nuclear Reactions (Chem.1.4)

Explore this Phenomenon

Stars produce large amounts of energy.

1. How do stars produce energy?
2. Can stars “run out” of their fuel?

Standard Chem.1.4

Construct an explanation about how fusion can form new elements with greater or lesser nuclear stability . Emphasize the nuclear binding energy, with the conceptual understanding that when fusion of elements results in a more stable nucleus, large quantities of energy are released, and when fusion results in a less stable nucleus, large quantities of energy are required. Examples could include the building up of elements in the universe starting with hydrogen to form heavier elements, the composition of stars, or supernovae producing heavy elements. (PS1.C, ESS1.A)

As you go through the section look for how fusion can form new elements with greater or lesser nuclear stability . What makes a nucleus stable or unstable?

Forces in the Nucleus

A carbon nucleus of ¹²C (for instance) contains 6 protons and 6 neutrons. The protons are all positively charged and repel each other: they nevertheless stick together, showing the  existence of another force—a nuclear attraction, the strong nuclear force, which overcomes electric repulsion at very close range. Hardly any effect of this force is observed outside the nucleus, so it must have a much stronger dependence on distance—it is a short range force. The same force is also found to pull neutrons together, or neutrons and protons.

Nuclear Fusion

In contrast to nuclear fission , which results in smaller isotopes being formed from larger ones, the goal of nuclear fusion is to produce larger materials from the collision of smaller atoms. The forcing of the smaller atoms together results in tighter packing and the release of energy . As seen in the Figure below , energy is released in the formation of the larger atom , helium (He) from the fusion of hydrogen-2 and hydrogen-3 as well as from the expulsion of a neutron.

Nuclear fusion reaction between deuterium and tritium.

This release of energy is what drives research on fusion reactors today. If such a reaction could be accomplished efficiently on Earth, it could provide a clean source of nuclear energy. Unlike fission reactions, nuclear fusion does not produce radioactive products that represent hazards to living systems.

Nuclear fusion reactions in the laboratory have been extraordinarily difficult to achieve. Extremely high temperatures (millions of degrees) are required. Methods must be developed to force the atoms together and hold them together long enough to react. The neutrons released during the fusion reactions can interact with atoms in the reactor and convert them to radioactive materials. There has been some success in the field of nuclear fusion reactions, but the journey to feasible fusion power is still a long and uncertain one.

The Curve of Binding Energy

In the main isotopes of light nuclei, such as carbon, nitrogen and oxygen, the number of neutrons and of protons is indeed equal. However, as one moves to heavier nuclei, the disruptive energy of electric repulsion increases, because electric forces have a long range and each proton is repelled by all other protons in the nucleus. In contrast, the strong nuclear attraction between those protons increases only moderately, since the force has a short range and affects mainly immediately neighboring protons.

The Binding Energy of Nuclei

The net binding energy of a nucleus is that of the nuclear attraction, minus the energy of the repulsive electric force. As nuclei get heavier than helium, their net binding energy per nucleon (deduced from the difference in mass between the nucleus and the sum of masses of component nucleons) grows more and more slowly, reaching its peak at iron. As nucleons are added, the total nuclear binding energy always increases—but the total energy of electric forces (positive protons repelling other protons) also increases, and past iron, the second increase outweighs the first. One may say 56 Fe is the most tightly bound nucleus.

To reduce the energy of the repulsive electric force, the weak interaction allows the number of neutrons to exceed that of protons—for instance, in the main isotope of iron, 26 protons, but 30 neutrons. Of course, isotopes also exist in which the number of neutrons differs, but if these are too far from stability, after some time nucleons convert to a more stable isotope by beta emission radioactivity—protons turn into neutrons by emitting a positron, the positive counterpart of the electron, or neutrons become protons by emitting electrons (neutrinos are also emitted in these processes).

Among the heaviest nuclei, containing 200 or more nucleons, electric forces may be so destabilizing that entire chunks of the nucleus get ejected, usually in combinations of 2 protons and 2 neutrons (alpha particles, actually fast helium nuclei), which are extremely stable.

The curve of binding energy (figure above) plots binding energy per nucleon against atomic mass. It has its main peak at iron and then slowly decreases again, and also a narrow isolated peak at helium, which as noted is very stable. The heaviest nuclei in nature, uranium 238 U, are unstable, but having a lifetime of 4.5 billion years, close to the age of the Earth, they are still relatively abundant; they (and other nuclei heavier than iron) may have formed in a supernova explosion preceding the formation of the solar system. The most common isotope of thorium, 232 Th, also undergoes α particle emission, and its half-life (time over which half a number of atoms decays) is even longer, by several times. In each of these, radioactive decay produces daughter isotopes, that are also unstable, starting a chain of decays that ends in some stable isotope of lead.

How are elements born?

A number of reactions take place in the sun that cannot be duplicated on Earth. Some of these reactions involve the formation of large elements from smaller ones. So far, we have only been able to observe the formation of very small elements here on Earth. The reaction sequence observed appears to be the following: Hydrogen-1 atoms collide to form the larger hydrogen isotopes, hydrogen-2 (deuterium) and hydrogen-3 (tritium). In the process, positrons and gamma rays are formed. The positrons will collide with any available electrons and annihilate, producing more gamma rays. In the process, tremendous amounts of energy are produced to keep us warm and continue supplying reactions.

The binding energy of helium is a significant energy source of the Sun and of most stars. The Sun has plenty of hydrogen, whose nucleus is a single proton, and energy is released when 4 protons combine into a helium nucleus, a process in which two of them are also converted to neutrons.

The conversion of protons into neutrons is the result of another nuclear force, known as the weak force. The weak force also has a short range, but is much weaker than the strong force. The weak force tries to make the number of neutrons and protons in the nucleus equal; these two particles are closely related and are sometimes collectively known as nucleons.

The protons combine to helium only if they have enough velocity to overcome each other's repulsion and get within range of the strong nuclear attraction, which means they must form a very hot gas. Hydrogen hot enough for combining to helium requires an enormous pressure to keep it confined, but suitable conditions exist in the central regions of the Sun (core), where such pressure is provided by the enormous weight of the layers above the core, created by the Sun's strong gravity. The process of combining protons to form helium is an example of nuclear fusion.

Elements past iron on the periodic table cannot be formed during the fusion happening during the life of a star. Elements past iron require a supernova to be formed. This is why there is a drop in abundance in elements after iron.

Putting It Together

Let us revisit this phenomenon:

Stars produce large amounts of energy.

1. Using your understanding of nuclear reactions, explain how stars produce energy.
2. How is the way that stars produce energy connected to nuclear binding energy?