Nuclear Reaction

Nuclear reaction diagram

Below is a diagram of possibly the most infamous nuclear reactions in history. The splitting of the atom, specifically uranium-235. The nuclear bomb that was dropped over Hiroshima in World War 2. A neutron collides with the atomic nucleus, causing the uranium to split into Barium-139, Krypton-95, 2 neutrons, and releasing 200 MeV of energy.

Fig. 1. Nuclear fission reaction of Uranium-235, releasing particles and energy, Wikimedia Commons CC-BY-SA-3.0

Types of nuclear reactions

There are three types of nuclear reactions, nuclear fission, nuclear fusion, and radioactive decay.

Nuclear fission reactions

In a nuclear fission reaction, a parent nucleus is split to produce two daughter nuclei. The difference in mass before and after the reaction is converted directly into energy. It requires a neutron to collide with the heavy nucleus for the splitting to occur. After the neutron collides with the nucleus, it causes the nucleus to become unstable. The nucleus then splits into two daughter nuclei, that are usually similar in size, and releases two or three neutrons in the process along with large amounts of energy in the form of gamma rays. The smaller daughter nuclei are usually also unstable and may release alpha or beta particles via radioactive decay to attain stability. Part of the energy that is released in this nuclear reaction is in the form of the kinetic energy of the daughter nuclei.

Fig. 2. An example diagram of Nuclear Fission. Wikimedia Commons

In the diagram above you can see that the nuclear fission of the example nucleus above produces 3 new neutrons, which in turn are absorbed by 3 more atomic nuclei. Those nuclei will split too, emitting 9 new neutrons in total! This is called a nuclear chain reaction and is how we are able to split more than one nucleus at a time to generate more energy.

The term critical mass is a term used to define the minimum amount of fissile material needed to sustain a nuclear chain reaction. The critical mass is different for every fissile material, it depends on the density, temperature, and even the shape of the material will affect the critical mass.

Nuclear fusion reactions

If two light nuclei merge, they can form one heavier nucleus and release energy in the process. This is known as nuclear fusion. The interaction requires a significant amount of energy to occur. For fusion to occur you need to overcome the repelling force between two positively charged atomic nuclei. The two nuclei must be close enough that the nuclear force will be strong enough to induce nuclear fusion. An environment with extremely high temperature and pressure is needed to accomplish this, like that found inside a star.

Fig. 3. The force repelling two positively charged nuclei that must be overcome for nuclear fusion, Wikimedia Commons CC-BY-2.5

Nuclear decays reactions

Radioactive decay is a random process by which unstable atoms (with an excess of particles and/or energy) emit radiation to achieve stability. An excess of neutrons and protons in the nucleus can cause this instability, which leads to the emission of alpha particles, beta particles, high-energy photons (gamma radiation), or neutrons. An atom undergoes decay processes until it reaches a stable form where no more radiation emission occurs.

Nuclear reaction equations

A nuclear equation is written in the style of a chemical reaction equation. This makes it clear a nuclear reaction has an initial state and an end state. The example word equation below is for a nuclear decay reaction.

\[\text{unstable isotope}\xrightarrow{\text{nuclear decay reaction}} \text{more stable isotope}+\text{radiation}\]

Einstein's equation

To figure out exactly how much energy is released in nuclear reactions we must refer to the most famous equation in all of physics. Einstein's equation! Which helps us understand how mass can be converted into energy.

\[E=(\Delta m)c^2\]

where \(E\) is energy, \(\Delta m\) is mass defect, and \(c\) is the speed of light.

To calculate the energy released from a nuclear fission reaction you must determine the difference in mass between the parent nucleus and the daughter nuclei. (A periodic table can help you with this). Einstein's equation shows you can then multiply this mass difference by the speed of light squared to reveal the mass that has been converted into energy in the reaction.

Binding energy equation

The mass of an individual nucleus is lower than the mass of its constituent protons and neutrons. A specific amount of energy would be required to split an atomic nucleus into separate protons and neutrons, this is equal to the binding energy. Alternatively, by fusing protons and neutrons together, a quantity of energy is released during the nuclear reaction, equal to the binding energy. The formula to calculate the binding energy within any individual atomic nucleus is as follows:

\[E_b=(Zm_p+Nm_n-M)c^2\]

Where \(B\) is the binding energy we are solving for, \(Z\) and \(N\) are the number of protons and neutrons respectively, \(m_p\) and \(m_n\) are the masses of an individual proton and neutron, \(M\) is the resulting nucleus’ total mass, and \(c\) is the speed of light.

Nuclear reaction examples

There are many different examples of nuclear reactions that occur naturally or are artificially induced by humankind for our own purposes.

Nuclear fission example

We must first recall that the symbol for any neutral atom \(X\) is written in the following way:

\[^A_Z X\]

where the atomic number \(Z\) represents the number of protons in the nucleus of this atom and the mass number \(A\) represents the number of protons and neutrons in the nucleus.

Now, let us consider the example of splitting uranium-235 into barium-139 and krypton-95. We can write an equation for the reaction to represent the balance of the reactants and products. This is called a nuclear equation and the equation for the example described looks as follows. The mass and atomic numbers on both sides of a nuclear equation must balance for the nuclear reaction to occur. Note that this equation contains a rightward-facing arrow rather than the equality symbol

\[^1_0\text{n}+^{235}_{92}\text{U}\rightarrow ^{139}_{56}\text{Ba}+^{95}_{36}\text{Kr}+2^1_0 \text{n}\]

The reactants are on the left side of this arrow and the products are on the right. The atomic numbers and mass numbers on either side of this equation balance, which means that fission can indeed occur in this manner. The example below shows how another nuclear equation can be written.

Nuclear fusion example

Fig. 4. A diagram showing the fusion of two isotopes of hydrogen; deuterium and tritium that fuse to form helium. A neutron is released in the process along with a significant amount of energy, Wikimedia Commons CC BY-SA 3.0

Let us consider the figure above and attempt to write and balance the nuclear equation for the reaction.

Radioactive decay and carbon dating

Carbon plays a vital role in the functioning of organic beings. Carbon-12 is the most abundant, stable isotope of carbon, which we usually find in every organic structure. On Earth, we also find an unstable isotope (carbon-14), which is continuously formed in the atmosphere due to the radiation from outer space.

Carbon-14 has a half-life of 5730 years. So half the Carbon-14 isotopes in a sample would have radioactively decayed after 5730 years. Living organisms contain a lot of carbon and so do their fossils. By measuring the ratio of Carbon-14 (which decays over time) and Carbon-12 (which does not) in a sample, then we can estimate its age. For instance, If fossil A has only half the amount of Carbon-14 compared to fossil B, then we know that fossil A is approximately 5730 years older than fossil B.