Question

If a neutron causes a fission reaction that releases three neutrons, how many neutrons have been produced from the third fission step? (Assume each step in the fission process releases three neutrons.)

Short answer

27 neutrons are produced in the third fission step.

Step-by-step solution

Understand the Initial Condition

The problem states that one neutron causes a fission reaction that releases three neutrons. This means for every fission step, it initiates three times the number of reactions.

Calculate the First Fission Step

In the first fission step, we start with one neutron, which initiates a reaction that releases three neutrons.

Calculate the Second Fission Step

In the second fission step, each of the three neutrons from the first step causes a new fission reaction. Each of these reactions releases another three neutrons. So, we have \( 3 \times 3 = 9 \) neutrons produced.

Calculate the Third Fission Step

In the third fission step, each of the nine neutrons from the second step causes yet another fission reaction, producing ne another three neutrons each. Therefore, \( 9 \times 3 = 27 \) neutrons are produced in the third step.

Key concepts

Neutron Production

In the process of nuclear fission, when a heavy nucleus, like Uranium-235, splits, it releases additional particles, specifically neutrons. Each fission reaction is sparked by a neutron and generates more neutrons. These neutrons are critical as they are responsible for perpetuating further fission reactions.

Here's how it works: a single neutron collides with a nucleus, splitting it into smaller nuclei and releasing energy along with two or three neutrons. This release of additional neutrons in each fission event is integral to maintaining and potentially expanding a sequence of reactions. The ability to produce multiple neutrons is what enables fission to become a powerful source of energy.

- **Key points about neutron production:**
- Neutrons are the particles that trigger and sustain the fission process.
- Each fission reaction releases more neutrons, typically two or three.
- The released neutrons can go on to initiate additional fissions, which is the basis for a chain reaction.

Chain Reaction

A chain reaction in nuclear physics refers to a series of reactions where each event initiates further events. This is exactly what happens in nuclear fission with neutron production. For fission to result in a chain reaction, a sufficient number of the neutrons produced need to cause further fission events.

In our case study, we started with one fission event causing three neutrons which then induce further reactions. By the second step, nine neutrons have been produced, and the process continues to amplify. This amplification results in an exponential increase in the number of reactions and neutrons, which could either be harnessed as a powerful source of energy or could lead to dangerous, uncontrolled reactions without proper intervention.

- **Important aspects of chain reactions:**
- They can lead to a large release of energy.
- Without control, a chain reaction could become hazardous.
- Control mechanisms, such as neutron-absorbing rods, are essential to harness chain reactions safely in reactors.

Fission Steps

The term 'fission steps' refers to the sequential stages of fission reactions occurring after an initial reaction. Each step represents another layer in the chain reaction where previous neutrons produce more of themselves by causing further fission events.

### Understanding the Fission Steps
- **First Fission Step:** Begins with one neutron causing one fission event, which releases three free neutrons.
- **Result:** 3 neutrons.
- **Second Fission Step:** Each of these three neutrons induces a new fission, generating three more neutrons per reaction, totaling nine new neutrons.
- **Result:** 9 neutrons total by the second step.
- **Third Fission Step:** Each of the nine neutrons from the second step creates three new neutrons, summing into 27 neutrons.
- **Result:** 27 neutrons after the third fission step.
This exponential growth at each stage underscores the efficiency and power potential of nuclear fission.