Nuclear Chain Reactions — Overview & Applications

Maintaining a Chain Reaction

Power generated from nuclear fuel is very different from other fuel sources. Fossil fuels, oil, or natural gas must be combusted and constantly refueled to generate heat energy and perform work. But, once a nuclear reaction starts, if given proper conditions, it will not stop. This is the essence of the chain reaction.

In order to maintain a chain reaction, a few conditions must be met, all of which contribute to the probability of an event occurring. In this case, an event is nuclear fission. This is denoted by a term known as the Cross-section.

There are two methods to increase the probability of fission:

Moderation - neutrons are moderated by colliding them with a medium of particles to slow them down. Good examples of moderators are light water (H2O), heavy water (D2O), and graphite (C). If a moderator's mass is similar to that of a neutron, it will slow neutrons down more effectively. Slow neutrons are called thermal neutrons.

Enrichment - Natural uranium exists with a content of 99.3% U-238 and 0.7% U-235. Although U-235 has a high probability to fission at thermal neutron energies, its natural content is not enough to sustain a chain reaction. It must be enriched to around 3% to 5% for a chain reaction to begin and sustain itself.

Our Friend the Atom - Walt Disney Explains Chain Reactions

9-minute video summarizing the principle of a chain reaction using mousetraps

Sustaining a chain reaction is the key principle behind nuclear fission, for both electrical generation purposes, as well as nuclear weapons. While in both processes, a chain reaction occurs to accomplish some goal, it is impossible for a nuclear explosion to occur in a nuclear reactor. Walt Disney makes the comparison of energy-use towards the end of the video that may be easy to misinterpret.

(Video) The Uranium 235 Chain Reaction

By: PhysicsMadeFun

In this video, PhysicMadeFun, demonstrates the chain reaction of Uranium-235. Initially, U-235 absorbs a neutron to become U-236. But, U-236 is unstable. So, it undergoes fission to produce Krypton-92, Barium-141, and 3 more neutrons. What happens when the neutrons hit more U-235. The process repeats. More and more U-235 atoms undergo fission producing more and more neutrons. The exponential increase is a nuclear chain reaction!

We've been studying nuclear reactions. We've looked at both fusion and fission. In fusion, we slam two small nuclei together. It releases a ton of energy because of the binding energy and mass defect. But, it requires unfathomable temperatures. So, it's unpractical. In fission, we're taking advantage of unstable nuclei to generate energy. We bombard fissile atoms with neutrons. Sometimes, it absorbs the neutron. But, the extra neutron makes it unstable. So, it splits into multiple smaller elements and more neutrons. What would happen if the new neutrons hit other fissile atoms? They would also undergo fission! The process continues until there are no atoms left.

Nuclear Chain Reactions

A chain reaction is any chemical reaction where the products contribute to further chemical reactions. In nuclear chemistry, we apply it to fission reactions. The first step is initiation. Initiation is the formation of an intermediate. For a nuclear chain reaction, the intermediate is unstable. So, it will undergo fission. The next step is propagation. In propagation, the intermediate is continually regenerated. So, our reaction is self-sustaining. In fission, we create new neutrons. Those neutrons hit other fissile atoms. Those atoms undergo fission and produce more neutrons. Propagation continues until the intermediate can't form anymore. Finally, we have termination. We are no longer able to generate the intermediate. So, the reaction stops.

Let's look at the most common nuclear chain reaction. That's the fission of U-235. We start by hitting U-235 with a neutron.

${^{235}_{92}U} + {^{1}_{0}n} \rightarrow {^{236}_{92}U}$

U-236 is unstable and undergoes fission to produce krypton-92 and barium-141.

${^{236}_{92}U} \rightarrow {^{92}_{36}Kr} + {^{141}_{56}Ba}$

But, you'll notice that the atomic mass is unbalanced. Let's balance it!

$236-92-141=3$

$92-36-56=0$. The atomic number is already balanced!

How do we raise the atomic mass without changing the atomic number? We use neutrons! So, the reaction produces three neutrons. Let's write the complete balanced equation.

${^{235}_{92}U} + {^{1}_{0}n} \rightarrow {^{236}_{92}U} \rightarrow {^{92}_{36}Kr} + {^{141}_{56}Ba} + 3{^{1}_{0}n}$

Our initial fission reaction generated three neutrons. If the three neutrons hit other U-235 atoms, they'll also experience fission. Let's say three more U-235 atoms do undergo fission. So, they each emit three more neutrons. That's nine neutrons! Now, we can initiate nine reactions. During propagation, we're seeing an exponential increase!

The Neutron Multiplication Factor

In our U-235 example, we imagined that every neutron caused more fission. For nuclear chemists, that's the experimental best-case scenario. But in application, that's not always true. Let's imagine we're using U-235 in a reactor at a nuclear power plant. In a reactor, we don't have pure U-235. Instead, we have a mixture of three isotopes: U-238, U-235, and U-234. Let's consider U-234. What happens if it absorbs a neutron? It becomes U-235. So, it used up a neutron without producing more. Furthermore, not every neutron hits another atom. Neutrons are minscule. Atoms have a lot of empty space. So, it's possible that the neutron completely misses and leaves the system.

How do we measure nuclear reaction propagation? We use the average neutron multiplication factor ($k$). It measures the average number of neutrons that produce more fission reactions.

There are three possible scenarios for $k$.

• $k<1$: Each fission reaction averages less than one subsequent reaction. In this scenario, the nuclear reaction is unsustainable. We call this situation subcritical.

• $k=1$: Each fission averages one more reaction. In this scenario, the nuclear reaction is sustainable. We call this situation critical. It has a constant rate and energy output. So, it's ideal for reactors.

• $k>1$: Each fission averages more than one further reaction. In this scenario, the nuclear reaction proliferates exponentially. So, we call this situation supercritical. A supercritical reaction has an increasing rate and energy output. The exponential increase can happen within microseconds. So, this is the goal of atomic weapons. For nuclear power plants, an uncontrolled supercritical situation is unbelievably dangerous.