⚛️ E.4 Fission: Splitting the Atom for Energy 💥
Hello future Nuclear Physicists! Welcome to one of the most powerful and consequential topics in the IB Physics course: Fission. Don't worry if the term sounds intimidating; at its heart, fission is simply the process of splitting a very heavy nucleus into two lighter ones.
This topic is critical because it explains the physics behind nuclear power generation and, sadly, nuclear weapons. By the end of these notes, you will understand exactly why these heavy atoms split and how we harness the immense energy released, all within the context of the fundamental concepts of binding energy and mass defect. Let’s dive in!
1. What is Nuclear Fission?
Nuclear fission (from the Latin fissus, meaning ‘to split’) is a nuclear reaction where a heavy, unstable atomic nucleus splits into two or more smaller nuclei, often accompanied by the release of energy, neutrons, and gamma rays.
Key Characteristics of Fission:
- It typically involves very heavy nuclei (those with mass numbers greater than about 200), such as Uranium-235 (\(^{235}\text{U}\)) or Plutonium-239 (\(^{239}\text{Pu}\)).
- Fission is usually induced (forced), not spontaneous, by bombarding the heavy nucleus with a neutron.
- The products of fission are called fission fragments, which are generally highly radioactive.
Analogy: Imagine trying to break a large, heavy block of concrete. You need to hit it with a small, fast-moving object (like a neutron) to destabilize it enough to crack and split into smaller pieces.
Remember that the Binding Energy per Nucleon (BEN) tells us how stable a nucleus is. The higher the BEN, the more stable the nucleus. The BEN curve peaks around Iron-56 (\(^{56}\text{Fe}\)).
Heavy nuclei (like U-235) have a relatively low BEN. When they split into medium-sized nuclei (fission fragments), the fragments have a higher BEN, meaning they are more stable. This increase in stability is where the massive energy release comes from!
2. The Step-by-Step Fission Process (Uranium-235)
Uranium-235 is the most common nuclear fuel used in reactors because it is fissile—meaning it can easily undergo induced fission.
Step 1: Neutron Capture
The process begins when a relatively slow-moving neutron (often called a thermal neutron) collides with a Uranium-235 nucleus.
The neutron is absorbed, transforming the stable U-235 into a highly unstable compound nucleus, Uranium-236:
$$
^{235}_{92}\text{U} + ^{1}_{0}\text{n} \longrightarrow ^{236}_{92}\text{U}^* \text{ (unstable)}
$$
Step 2: Nuclear Splitting
The U-236 nucleus immediately oscillates violently and splits into two smaller, roughly equal-sized nuclei (fission fragments). This splitting releases a huge amount of kinetic energy.
Step 3: Neutron and Energy Release
Along with the fission fragments (which are typically elements like Barium and Krypton), two or three high-speed neutrons are released, as well as gamma rays (\(\gamma\)) and a large amount of energy (\(E\)).
A common example of a fission reaction is: $$ ^{235}_{92}\text{U} + ^{1}_{0}\text{n} \longrightarrow ^{141}_{56}\text{Ba} + ^{92}_{36}\text{Kr} + 3^{1}_{0}\text{n} + E $$
Important note: The number of neutrons released (2 or 3) varies, and the specific fission fragments (Ba and Kr in this example) are also variable. The key is that more neutrons are produced than are consumed.
Fission is like "Fishing" (Fiss-ing). You use a little hook (the neutron) to split open a giant fish (the heavy nucleus) and get two smaller fish and some new hooks (neutrons) to fish again!
3. Calculating the Energy Released (\(E=\Delta m c^2\))
Where does all this energy come from? It is a direct result of the mass defect. When the heavy nucleus splits into lighter fragments, the total mass of the products is measurably less than the total mass of the reactants. This missing mass has been converted into energy.
Step 1: Calculate the Mass Defect (\(\Delta m\))
The mass defect (\(\Delta m\)) is the difference between the total mass before fission and the total mass after fission:
$$
\Delta m = (\text{Mass}_{\text{Reactants}}) - (\text{Mass}_{\text{Products}})
$$
Since the products (fission fragments) are more stable (higher BEN), their total binding energy is greater than the binding energy of the original nucleus. This means mass has been converted to energy.
Step 2: Apply Einstein’s Mass-Energy Equivalence
The energy released (\(E\)) is calculated using the famous equation:
$$
E = \Delta m c^2
$$
Where:
- \(\Delta m\) is the mass defect (in kg or u, converted to kg).
- \(c\) is the speed of light in a vacuum (\(3.00 \times 10^8 \text{ m s}^{-1}\)).
Because \(c^2\) is such an enormous number (\(9 \times 10^{16}\)), even a tiny mass defect results in a massive energy release. This is why nuclear power is so potent compared to chemical reactions.
4. The Nuclear Chain Reaction
The crucial feature of fission is the release of excess neutrons. If these neutrons go on to hit other fissile nuclei (like U-235), they induce more fissions, releasing even more neutrons and energy. This self-sustaining process is called a chain reaction.
Uncontrolled Chain Reaction (Atomic Bomb)
If the reaction proceeds unchecked, the number of fissions and the energy released grows exponentially in milliseconds, leading to an enormous, catastrophic explosion.
Controlled Chain Reaction (Nuclear Reactor)
For electricity generation, the chain reaction must be controlled so that, on average, exactly one neutron from each fission causes exactly one subsequent fission. This results in a steady, manageable energy release (a steady-state reaction).
Critical Mass
For a chain reaction to sustain itself, a minimum amount of fissile material must be present. This is called the critical mass.
If the mass is sub-critical, too many neutrons escape before causing fission, and the reaction dies out. If the mass is super-critical, the reaction accelerates uncontrollably.
Natural uranium is mostly U-238 (non-fissile). Only about 0.7% is U-235 (fissile). To be useful in most reactors, the uranium must be enriched (the percentage of U-235 increased) to around 3-5%.
5. Components for Controlling Fission in a Reactor
Controlling the chain reaction is the core engineering challenge of nuclear power. This requires three essential components: fuel, moderator, and control rods.
A. Fuel (e.g., Uranium Oxide)
This is the material that undergoes fission. It must contain fissile isotopes (like U-235).
B. Moderator
When fission occurs, the neutrons released are fast neutrons (high kinetic energy). These fast neutrons are not very efficient at causing further fissions in U-235.
The moderator (often graphite, heavy water (\(\text{D}_2\text{O}\)), or light water (\(\text{H}_2\text{O}\))) surrounds the fuel rods. Its job is to slow down (thermalize) the fast neutrons through elastic collisions until they become thermal neutrons, which are much more effective at inducing fission in U-235.
C. Control Rods
Control rods are made of materials that are excellent at absorbing neutrons (e.g., Cadmium or Boron).
By inserting the control rods further into the reactor core, more neutrons are absorbed, slowing the reaction down. By withdrawing them, fewer neutrons are absorbed, and the reaction speeds up. They ensure the chain reaction remains steady (at a controlled rate of \(k=1\), where \(k\) is the multiplication factor).
In an emergency, these rods can be fully dropped into the core to halt the reaction instantly (known as a scram).
The importance of fission lies in the transition from an unstable heavy nucleus to stable medium-mass fragments, resulting in a large release of energy (\(E = \Delta m c^2\)). Control is achieved in nuclear reactors by using moderators to slow down neutrons and control rods to absorb excess neutrons, maintaining a sustainable chain reaction.