Nuclear Reactions

[ 2 Votes ]
Nucleur Physics Learning Material
Tutorial IDTitleTutorialVideo
20.4Nuclear Reactions

In this Physics tutorial, you will learn:

  • What are nuclear reactions? How do they occur?
  • What is energy of reaction?
  • What does the total mass of system before and after nuclear reaction indicate regarding the energy produced during the process?
  • What is the difference between nuclear reactions and radioactive decay processes?
  • What is nuclear fission? In which conditions does it occur?
  • How nuclear fission was discovered?
  • What is nuclear fusion? How it is different from nuclear fission?
  • What is the main example of nuclear fusion occurring naturally? What are the stages of this process?
  • What is neutron capture? Where does it differ from nuclear fusion?
  • What are radioactive families?
  • How can nuclear reactions occur spontaneously?
  • What are nuclear power plants? How do they work?
  • What is nuclear bomb? What is its principle of operation?
  • What are some practical applications of nuclear fusion reactions?
  • What does the penetration of nuclear radiation in matter causes in living and non-living things?
  • What are the advantages and disadvantages of nuclear energy use?


Have you ever heard about nuclear reactors? How do they work?

Do you think it is possible to merge two atomic nuclei at home conditions? What about to split an atomic nucleus in two smaller nuclei? Why?

What is nuclear energy used for? Give some examples.

In this article, we will discuss about nuclear reactions - a prerequisite to produce nuclear energy. We will explain various types of nuclear reactions as well as how nuclear energy (which is produced in abundance during nuclear reactions) is used in industry.

In addition - among many other things - we will explain the thermonuclear reactions, as a special category of nuclear reactions, as they have a wide range of use in daily life.

What are Nuclear Reactions?

The term "nuclear reactions" refers to a special category of matter-energy interaction that includes all processes in which two or more objects interact with each other through nuclear forces.

The particles involved in nuclear reactions include atomic nuclei and other particles either involved in the process or produced during them, as well as the corresponding radiation emitted. Nuclear reactions are apparently similar to chemical reactions (where we have to consider the amount of reactants and product based on the law of mass and energy conservation). Thus, in a nuclear reaction, a target (parent) nucleus is hit by another nuclear particle. As a result, a new (daughter) nucleus is obtained, where some energy (and nuclear particles) is/are released or absorbed, depending on the type of nuclear reaction. The hitting particle may be a proton, neutron, gamma ray or an entire atomic nucleus.

Schematically, a nuclear reaction is written as:

a + X → Y + b

where X is the target nucleus, a is the hitting particle, Y is the daughter (hit) nucleus and b is the particle/s produced during the reaction.

Another important quantity to be considered during a nuclear reaction is the energy of reaction, Q. It represents the energy released or absorbed during a nuclear reaction. Thus, based on mass-energy equivalence, when Q > 0, then the total mass of reaction products is smaller than the mass of target nuclei plus that of hitting particle. Likewise, when the total mass of system increases after the reaction, the energy is absorbed by the system (Q < 0).

Do not confuse nuclear reactions with radioactive decay processes. If we use an analogy with linear momentum, nuclear reactions are analogue to collisions (both elastic and inelastic) while decay processes are analogue to explosions, as the energy stored in atomic nuclei is activated when a radioactive decay takes place, similar to energy stored in chemical form that is activated during explosions.

Example 1

Beryllium-9 absorbs an alpha particle during a nuclear reaction, producing an unknown nucleus and a neutron. What is the unknown nucleus?

Solution 1

In the periodic table, we can see that Beryllium has Z = 4. Thus, giving that an alpha particle (42He) is absorbed by the Beryllium nucleus (energy is added to the system), and a neutron has Z = 0 and A = 1, this nuclear reaction is written schematically as follows.

94Be + 42He → AZX + 10n

Hence, we obtain two linear equations in one variable, one for protons Z and the other for nucleons A:

4 + 2 = Z + 0


9 + 4 = A + 1

Solving these two equations we obtain Z = 6 and A = 12. These values correspond to Carbon-12 element (126Ca). Therefore, the unknown atomic nucleus X is a Ca-12 nucleus.

Nuclear Fission

Nuclear fission represents a process in which a parent nucleus splits in two daughter nuclei when it "catches" a neutron. Look at here the necessity of presence of a neutron from outside the parent nucleus, without which it would be impossible to obtain a fission. This is where nuclear fission differs from radioactive decay (two original particles here produce two new particles, unlike nuclear decay, in which one original particle produces two new particles).

The figure below shows schematically how a nuclear fission process takes place.

Physics Tutorials: This image provides visual information for the physics tutorial Nuclear Reactions

The most typical nuclear reaction of fission is when a Uranium-235 nucleus splits into two daughter nuclei (Barium-141 and Krypton-92) after catching a slow (thermal) neutron - a process in which three new neutrons are released according the following scheme:

10n + 92235U → 14156Ba + 9236Kr + 3 ∙ 10n

A large amount of energy is released in such reactions as there is a large difference between binding energy of parent nucleus (U-235) and the sum of binding energies of daughter nuclei (Ba-141 and Kr-92). The daughter nuclei obtained through nuclear fission have a high kinetic energy but since they are electrically (positively) charged, lose this kinetic energy in the form of heat by interacting with matter through ionization.

Other natural elements that may experience nuclear fission include Plutonium-239 (Pt-239), Uranium-233 (U-233) and Thorium-232 (Th-232).

How the Discovery of Nuclear Fission did Occur?

The discovery of nuclear fission was a pure casual process. All this started with the discovery of neutron by James Chadwick in 1932. A few years later, Enrico Fermi discovered the fact that various elements might become radioactive by hitting them with neutrons. This discovery puzzled two German scientists, Otto Hahn and Fritz Strassmann, who attempted to obtain heavier nuclei than uranium by bombarding uranium nuclei with neutrons. Thus, instead of heavier nuclei, they obtained some unidentified particles, which after a careful observation in laboratory, were identified as Barium-141 nuclei (one of products). The two scientists were so much surprised by such a discovery that they hesitated to publish their results for a long time. However, this draw the attention of Lise Meitner - an Austrian scientist who had previously worked with Hahn. Thus, after emigrating in Sweden, she deepened further the study of this process and as a result, she realized that Barium-141 and the other products obtained through this process derive from the splitting (fission) of Uranium-235 nuclei. Meitner and her nephew Otto Frisch continued their experiments and discovered that if a uranium nucleus is hit by a neutron, a high amount of energy is released - a process that also produces at least two free neutrons for every single neutron absorbed by the parent nucleus, in an avalanche-like process. Such a discovery was the first step towards the construction of nuclear reactors - a very important source of energy in the modern world.

Nuclear Fusion

Nuclear fusion is a process in which two parent nuclei merge to form a daughter nucleus. This is a typical case where the "target" and the "shell" are both atomic nuclei. The figure below shows an example of nuclear fission process where light atomic nuclei (hydrogen isotopes and helium) are involved.

Physics Tutorials: This image provides visual information for the physics tutorial Nuclear Reactions

A sufficient amount of kinetic energy in needed to overcome the electric force caused by the unbalanced charge in the two parent nuclei (both of them are positively charged). If the effect of (repelling) electric force is soothed, the two parent nuclei get closer and start interacting with each other through nuclear forces. This necessary kinetic energy is provided to parent nuclei by speeding them up in modern nuclear accelerators (this is why such processes cannot be realized at home conditions).

You may wonder why in the example of nuclear fusion provided in the above figure we have shown very light nuclei such as hydrogen isotopes given that the previous process (nuclear fission) occurs only in heavy nuclei. This is because fusion requires an external source of kinetic energy to speed up the parent nuclei. Despite improvements in technology, today is still impossible to build such powerful accelerators to give heavy nuclei enough kinetic energy to achieve nuclear fusion, i.e. to provide the parent nuclei enough kinetic energy to overcome electric forces and make the nuclei merge. Therefore, despite theoretically we can use whatever chemical element as source of nuclei in the process of nuclear fusion, practically this is still impossible.

On the other hand, in nuclear fission the parent nucleus must be heavy, as elements with many nucleons are less stable and therefore, not too much energy is needed to split them, unlike light nuclei that require a very high amount of energy to make them split in two parts.

The nuclear fusion reaction shown in the figure above, is symbolically written as:

21H + 31H → 42He + 10n

where (21H) is the deuterium nucleus and (31H) is the tritium one.

Thus, like in fission, in nuclear fusion we also obtain free neutrons during the process. Nuclear fusion occurs very often in nature. An example in this regard is the Sun, in which a large number of proton-proton fusion-type reactions take place, according the scheme shown in the table below.

Physics Tutorials: This image provides visual information for the physics tutorial Nuclear Reactions

As you see, with the production of Helium-4 nuclei (Helium-4 is known as a noble gas, as it does not interact with other chemical elements) the process starts from the beginning with 2 new protons, i.e. this process is cyclic. This means when all hydrogen nuclei actually present in the Sun convert to helium, the Sun's life will come to an end (but this will occur several billions of year from now) as no nuclear reactions will occur anymore, hence no energy will be released. In fact, the Sun produces this type of nuclear energy since 5 billion years ago through continuous nuclear fusion-type reactions.

As you see from the table, from a chain of nuclear reactions derived by a double proton-proton fusion, a considerable amount of energy (26.72 billion electronvolts) is generated.

Neutron Capture

Neutron capture is another type of nuclear reaction, during which radioactive nuclei are produced. These radioactive nuclei meet three conditions:

  1. Atomic Number Z of nuclei involved does not change
  2. Atomic Mass A of nuclei involved increases by 1 unit
  3. Number of neutrons in the nuclei involved increases by 1 unit

Here are a few examples of neutron capture reactions occurring more frequently:

21H + 10n → 31H + γ
94Be + 10n → 104Be + γ
147N + 10n → 157N + γ


As you see, nuclear fission and neutron capture reactions begin in the same way, by absorbing a neutron. The difference between these two processes consists in the fact that while after the merging process in fission the excited nucleus is unstable and eventually it splits in two parts to release the excess of energy, in neutron capture the new nucleus is merely radioactive and it gets rid from the excess of energy by emitting gamma radiation.

Nuclear Reaction Occurring Spontaneously. Radioactive Families

In such reactions, heavy nuclei throw spontaneously one or more particles and as a result, they lose the excess of energy by transforming into lighter nuclei. A typical example of this category of nuclear reactions include situations related to radioactive decay. Thus, the natural uranium U-238 converts to actinium Ac-234 by means of an alpha decay, according the scheme:

23892U → 23490Ac + 42He + energy

On the other hand, the actinium (daughter) nucleus is excited as well, so it releases another alpha particle to get rid of this excess of energy according the nuclear reaction

23490Ac → 23088Ra + 42He + energy

and so on. This process continues until a stable nucleus is obtained. The nuclei that participate in a certain chain of nuclear reaction as the one shown above form a radioactive family.

Example 2

A neutron hits an oxygen O-16 nucleus and as a result, a deuterium H-2 nucleus is obtained. What is the other nucleus produced in this nuclear reaction?

Solution 2

This nuclear reaction occurs according the following scheme:

168O + 10n → AZX + 21H

In this way, we obtain two linear equations:

16 + 1 = A + 2


8 + 0 = Z + 1

Hence, by solving both of them, we obtain A = 15 and Z = 7. The element having such values corresponds to a nitrogen isotope, (157N ).

More on Nuclear Fission. Nuclear Energy and Its Use

Earlier, we saw that some heavy nuclei split in two lighter nuclei after the capture of a slow neutron. This occurs because the parent nuclei acquire more energy than needed and as a result, they becomes excited. This is not a stable state, so the parent nuclei split to release this surplus of energy. During this process, at least two neutrons are also released for each single process. They have a high kinetic energy produced because the energy contained in the parent nucleus is higher than the total energy of daughter nuclei. This kinetic energy eventually turns into heat during particles deceleration when encountering a dense material on their way. In this way, nuclear reactions are used for obtaining heat energy, which eventually converts into other forms of energy such as electricity in nuclear power plants, thermal and chemical energy in nuclear bombs etc.

Obviously, there is a very large number of uranium nuclei participating in the process, so the energy obtained is very large. Therefore, the reaction must be controllable, otherwise it gets out of control and severe accidents may occur because of explosions arising when the energy delivered is higher than needed. The avalanche effect we explained earlier occurring when one neutron gives two new neutrons, two neutrons give four other neutrons and so on, must therefore be controllable to avoid troubles. The following conditions must meet in order to make this process take place safely:

  1. The fast neutrons must not go far from the region in which there are the divisible uranium nuclei;
  2. The fast neutrons must slow down as much as to be easy capturable by uranium nuclei; and
  3. Even when they are in the region containing uranium nuclei, neutrons must avoid being captured by nuclei other than uranium.

There is a certain probability that the neutrons produced in the first stage of nuclear fission become effective "shells" to be used in new fission processes. If at least one new neutron is ensured from such a process, then it continues without the need for other neutrons coming from an external source.

If the number N2 of new neutrons produced during the nuclear fission is smaller than the number N1 of shell neutrons coming from the source to hit the uranium nuclei, then the process is not sustainable and it fades with time. In other words, if

N2/N1 <1

then the process is not sustainable.

If the number N2 of new neutrons produced during the nuclear fission is equal the number N1 of shell neutrons coming from the source to hit the uranium nuclei, the system is known as critical and the process continues at a constant and controllable rate. In other words, if

N2/N1 = 1

then the process is sustainable and it takes place at constant rate.

If the number N2 of new neutrons produced during the nuclear fission is greater than the number N1 of shell neutrons coming from the source to hit the uranium nuclei, the system is known as supercritical and the process continues at an increasing and not controllable rate. In other words, if

N2/N1 >1

then the process is not controllable despite the system is sustainable.

Controllable processes are better as we always are aware of the parameters involved in the process. This makes possible using the energy produced during the process in a practical way because the process can be stopped at any instant in case of needs fulfillment. A controllable and sustainable process of nuclear fission is known as chain process as explained earlier. The first controllable chain nuclear process was realized by Enrico Fermi in 1942.

There are a number of factors affecting the progress of a chain nuclear reaction such as temperature, type of reaction, as well as the amount of matter involved in the process. The geometrical shape of environment in which the reaction occurs also plays a role in this regard. However, the most relevant factor is the minimum mass of matter involved in the nuclear reaction, below which the reaction cannot occur. This minimum mass is known as the critical mass of nuclear reaction. Operating with values very close to critical mass is very important when nuclear reaction is involved, as this makes possible stopping the process very easily in case of anomalies. In addition, the self-activation of an uncontrollable (spontaneous) chain nuclear reaction is less likely to occur when working with such minimum amounts of nuclear material.

Nuclear Power Plants and Energy Production

The main mechanism of nuclear power plants is nuclear reactor, formerly known as an atomic pile, which is a device used to initiate and control a fission nuclear chain reaction or nuclear fusion reactions.

A fission nuclear reactor consists on a fissile nuclear material enclosed within a protective (and insulating) case and equipped with mechanisms that regulate the fission rate as well as a heat exchange mechanism to remove the excessive heat produced during the operating process. The nuclear material used in such reactors is either uranium or plutonium whose percentage of fissile material has been increased artificially to ensure a higher efficiency. In this case, we say that we the nuclear material has experienced an enrichment process. For example, the percentage of enriched uranium (U-235) isotopes which make only 0.7% of natural uranium (U-238) is increased artificially to ensure a better fission process, as U-235 is more fissile than U-238.

Giving that the neutrons obtained through fission process are fast (they have a high kinetic energy), we have two options to decrease the risk for anomalies in the process:

  1. Relying on the low fissile ability of fast neutrons in order to produce only a small number of neutrons (in fast reactors)
  2. Making them slower by using a moderator to increase the probability of neutrons capture (in thermal reactors).
Physics Tutorials: This image provides visual information for the physics tutorial Nuclear Reactions

In thermal reactors, we must add substances that slow down quickly the neutrons produced during fission. Low atomic number elements are perfect for this goal. Some of these materials include graphite, beryllium, heavy water (H3O), etc. They either surround or mix with the fissile material. Thermal energy produced during this process heats some (uncontaminated) water producing steam, which is then used to rotate any turbine after flowing very fast through narrow tubes in order to generate electricity.

Nuclear Bombs

Nuclear bombs also use the fission process but unlike in nuclear reactors, the process here is in supercritical state, i.e. the nuclear reactions are quite non-controllable. This means the chain process rate is in continuous acceleration and the energy delivered remains practically in the region in which the fission takes place. This brings a very high increase in temperature. The products obtained through fission are radioactive and they acquire high kinetic energy. Gamma radiation obtained through fission process after the explosion has a very high energy and intensity. This brings a powerful explosion, during which the fission products spread out at very high speed in all directions. The energy released caused high deformations in everything in the surrounding area while gamma radiation and radiation caused by radioactivity spread out in much wider regions, causing health issues in living organisms.

Physics Tutorials: This image provides visual information for the physics tutorial Nuclear Reactions

Example 3

A powerful electric generator uses thermal energy obtained by pressurized water of a nuclear reactor as input energy source. If the power delivered by turbine is 1500 MW, thermal power at rector core is 4000 MW and the heat energy delivered by a single fission is 200 MeV, calculate:

  1. Efficiency of generator
  2. Reaction rate at reactor core in fissions per unit time

Solution 3

  1. We have Poutput = 1500 MW and Pinput = 4000 MW. Thus, we obtain for the efficiency e of generator:
    e = Poutput/Pinput × 100%
    = 1500 MW/4000 MW × 100%
    = 37.5%
  2. Energy delivered in the form of heat by a single reaction is Q = 200 MeV = (2 × 102 · 106 eV) · (1.6 × 10-19 J/eV) = 3.2 × 10-11 J. Hence, the rate R of reaction (giving that 4000 MW = 4 × 103 · 106 W = 4 × 109 W) is
    R = Winput/Q
    = 4 × 109 W/3.2 × 10-11 J
    = 1.25 × 1020 fissions/second

Thermonuclear Reactions and their Use in Technology

As explained earlier, fusion - as a merging process that occurs between two light nuclei - is a process that results in release of energy, as the sum of energies contained in every single nucleus involved in this process is greater than the energy of the daughter nucleus after fusion. However, these reactions cannot occur spontaneously; nuclei involved in a fusion process need a high amount of kinetic energy (we know that heat is related to the average kinetic energy of particles involved in a process). On the other hand, heat is directly proportional to temperature of objects or particles, so the temperature during a fusion process must be very high. That's why such reactions are known as thermonuclear reactions, as they cannot occur in low or normal temperature.

An example of thermonuclear reaction is the hydrogen bomb, in which the kinetic energy of light nuclei that merge with each other is ensured by means of high temperature produced by an adjacent nuclear bomb that explodes in advance.

Thermonuclear reaction processes are regarded as powerful producers of energy. From all possible fusion reactions, the reaction between deuterium (H-2) and tritium (H-3) has resulted as the most productive so far. The only drawback in this process is that it is very complicated, i.e. it is very difficult to create the suitable conditions for the reaction to take place.

Since the mass of individual nuclei when taken together is greater that the mass of merged nucleus, there is a release of energy in the environment during the fusion process as the extra mass converts to energy. As explained earlier, fusion is very common in bright stars, including the Sun. This process results in the release of high amounts of energy in the form of EM radiation (and heat obviously, but heat itself is IR radiation).

There is a considerable amount of deuterium available on Earth. It is estimated that nearly 1/5000 of all hydrogen atoms in oceans are deuterium isotopes. In total, there are 1018 kilograms of deuterium on Earth, practically an inexhaustible source of this material considering the actual demands for energy. However, the drawback consists on ensuring the necessary tritium, because it is a radioactive material that has a relatively long half-life (about 10 years). Hence, the tritium natural reserves are not sufficient and therefore, it must be produced though industrial methods in some way. The following reaction is commonly used for this purpose:

63Li + 10n → 42He + 31H

Application in Practice of Nuclear Fusion Reactions

In the following paragraphs of this article, we will provide some examples of application in practice of nuclear fusion reactions.

a. Hydrogen bomb

This bomb consists of two main parts: nuclear bomb, which produces the neutrons needed for the transformation of lithium into tritium and at the same time, it brings the system at high temperature, as needed for enabling the fusion reaction. This is the primary bomb. There is also a second part (secondary bomb), which consists of a mixture of lithium and deuterium. Neutrons produce tritium and helium according the above reaction. The figure below shows a scheme of hydrogen (thermonuclear) bomb.

Physics Tutorials: This image provides visual information for the physics tutorial Nuclear Reactions

Despite the hydrogen bomb being clean in itself (although it causes harm in living organisms and structural damage in the surrounding objects due to high explosive power), there is some radioactive pollution caused by the incorporated nuclear bomb that provides the initial ignition (nuclear bombs use uranium as primary source of energy).

b. Neutron bomb

This bomb makes use of fast neutrons emitted during a fusion reaction. The energy of these neutrons is able to seriously harm living organisms and cause their death. Neutron bombs are not environment pollutants as they are not radioactive. Likewise, neutron bombs do not cause harm to building structures.

c. Neutron Generators

In some cases, the technology used in neutron bombs can be used to generate new neutrons needed for nuclear reactions. However, to avoid radioactive pollution, an electric field is used instead of radioactive material to accelerate the nuclei in order to obtain fast neutrons. This electric field is obtained by creating a potential difference of several hundreds of kilovolts. After gaining enough speed, the nuclei hit a target enriched with tritium. At this point, nuclear fusion takes place - a process which results in generation of fast neutrons that can eventually be used for various purposes.

d. Energy production

As explained earlier, energy is another product of nuclear reactions besides the changes in the structure of matter involved in the process. This energy turns into heat during the deceleration of fast neutrons. The high temperature achieved during this process brings a continuity in the process resulting in a sustainable source of energy.

This technology however, bears two issues: (1) how to keep the deuterium and tritium enclosed in fixed containers in such high temperatures by avoiding explosion, and (2) how to extract the extra energy form there, in order to convert it into other forms of energy. In other words, how to keep under control a thermonuclear reaction? This is still an unaddressed issue despite the huge advancements in technology. If scientist are able to find a way to overcome these drawbacks in the future, then the issue of energy production will be definitively addressed.

Currently, we use a small portion of thermonuclear energy produced naturally in the Sun. The good news in this regard is that we are too far to be affected by the harmful effects of such non-controllable thermonuclear fusion processes.

Penetration of Nuclear Radiation in Matter and the Harm Caused by Radiation

Penetration of nuclear radiation in matter is a normal phenomenon because such radiation is produced in closed environments. After all, matter is composed by various atoms and molecules and it is a normal thing that radiation interacts with them - a process which in some cases changes the structure of matter itself.

Sometimes (in ionization radiation), a ionization process takes place in matter. This is the process in which a neutral atom initially neutral, splits (experiences fission) in two oppositely charged ions. Such ionization process may be very powerful, resulting in the generation of a large number of such pairs of ions. They participate actively in chemical reactions, bringing changes in the structure of matter.

When neutrons participate in the process, it becomes more complicated as besides the energy delivered by elastic collisions, neutrons are added in this process by participating in nuclear reactions as well. In this way, new chemical elements may arise. Since they are radioactive, matter experiences radical transformations. Therefore, neutrons are more influential when they pass through matter than when moving in space.

The effects of radiation in matter have their advantages and disadvantages. When the effects produced by nuclear radiation are undesirable, this process causes a lot of harm (for example during the non-controllable explosions). This represents a disadvantage of such reactions. On the other hand, the high amount of energy obtained through nuclear processes represents an advantage of radiation interaction with matter.

However, when discussing about harms caused by nuclear radiation, the focus is on harms caused in living organisms, as this may result in irreparable damage caused in living cells.

As for damages caused by nuclear radiation in non-biological materials, we may mention the structural damages in materials such as polymers, which under the effect of gamma radiation change their structure. This however may be used in our advantage, such as in the case of thermo-insulating materials obtained through the process of radiation incident on matter.

Whats next?

Enjoy the "Nuclear Reactions" physics tutorial? People who liked the "Nuclear Reactions" tutorial found the following resources useful:

  1. Physics tutorial Feedback. Helps other - Leave a rating for this tutorial (see below)
  2. Nucleur Physics Revision Notes: Nuclear Reactions. Print the notes so you can revise the key points covered in the physics tutorial for Nuclear Reactions
  3. Nucleur Physics Practice Questions: Nuclear Reactions. Test and improve your knowledge of Nuclear Reactions with example questins and answers
  4. Check your calculations for Nucleur Physics questions with our excellent Nucleur Physics calculators which contain full equations and calculations clearly displayed line by line. See the Nucleur Physics Calculators by iCalculator™ below.
  5. Continuing learning nucleur physics - read our next physics tutorial: Atomic Nucleus and Its Structural Properties

Help others Learning Physics just like you

[ 2 Votes ]

Related Physics Calculators by iCalculator

Physics Calculators

You may also find the following Physics calculators useful.