Nuclear Fission

Introduction

From weapons to electrical power generation, the chain reaction of certain radioisotopes has had a profound effect on society and the environment. How do these chain reactions occur and what do they look like? Use the common domino to create a dramatic visual model of this subatomic process. In this demonstration, domino tiles will be used to simulate both the critical process and the supercritical process. Students will time each event and use the data to estimate the relative energy release rates of each process.

Concepts

• Fission
• Neutron and neutron capture
• Chain reaction
• Neutron absorbers

Background

Naturally occurring uranium consists primarily of three isotopes, uranium-238, uranium-235 and uranium-234. All three are radioactive and decay by alpha emission.

In 1938, two chemists, Otto Hahn (1879–1968) and Fritz Strassman (1902–1980), discovered that when uranium was bombarded with neutrons, barium was produced. In collaboration with the chemist Lisa Meitner (1879–1968), they correctly interpreted these findings as resulting from the uranium nucleus splitting into smaller pieces, a reaction labeled nuclear fission. It was later determined that of the three isotopes of naturally occurring uranium, only uranium-235 undergoes nuclear fission (Equation 4). In this fission process, more neutrons are produced than are needed to start the process. These additional neutrons can then react with other atoms of uranium-235. Any process that creates reactants that can then initiate the process over and over again is called a chain reaction. The fission of uranium-235 is highly exothermic and releases about 2 x 10¹⁰ kJ/per mole of uranium atoms. This is roughly 25 million times greater than the amount of energy obtained in the combustion of hydrocarbons!

The chain reaction can be terminated in basically two ways. The extra neutrons may be absorbed by other materials before they collide with another uranium-235 atom, or the neutron may simply escape the container without striking another uranium nucleus. If, on average, less than one neutron produced by each fission reaction strikes another uranium atom and “splits” it, then the reactions ends and the process is called sub-critical. If the process averages one “active” neutron per fission, it is called a critical process. If the reaction averages more than one “active neutron per fission, it is labeled a supercritical process.

Naturally occurring uranium contains only 0.72% uranium-235. This concentration is subcritical and no chain reaction can take place with natural uranium. An increase in the concentration of uranium-235 to three to four percent is needed to achieve a critical reaction, and much greater enrichment is needed to reach a supercritical state.

For weapons, the U-235 enrichment needs to be 90% or higher. This concentration allows the fission process to rapidly continue to explosive levels before too many neutrons escape and terminate the chain reaction. For nuclear reactors, three to four percent enrichment allows the reactor to release energy at a controlled rate.

Experiment Overview

In this demonstration, domino tiles will be used to simulate both the critical process and the supercritical process. Students will time each event and use the data to estimate the relative energy release rates of each process.

Materials

Safety Precautions

This activity is considered safe. Follow all standard classroom safety guidelines.

Prelab Preparation

Prepare two arrangements of 100 domino tiles.

Critical Process

1. Begin laying tiles in a straight row on the demonstration surface. This surface should be stable, flat and hard. Space the tiles from one-half to three quarters of an inch apart.
2. When a turn is needed, make a 180 degree curve of at least six tiles, with the tiles closer on the inside of the turn than on the outside (see Figure 1).
   {12799_Preparation_Figure_1}
3. Continue the straight line parallel to the original row. Continue until all the tiles are positioned.

Supercritical Process

1. Begin by laying out the fission tile location template on the demonstration surface. This surface should be stable, flat and hard.
2. Place tiles on the designated lines, starting at number one and placing the tiles in numerical sequence. This sequence will minimize the likelihood of accidently knocking over other tiles. Place the tiles in front of the lines as they radiate from the center (see Figure 2).
   {12799_Preparation_Figure_2}
3. Continue until all the tiles are positioned. The tiles that form a straight line to the center are the “initiator” tiles.

Procedure

1. (Optional) Pass out the demonstration worksheet to each student.
2. Explain to the students that the two domino arrangements represent the two types of nuclear fission chain reactions. The straight line arrangement will model the critical process, the one used in nuclear reactors. The dense packing arrangement will model the supercritical process, that which occurs in atomic bombs.
3. Before initiating the straight line chain reaction, alert the students to begin timing when the first domino falls and to stop timing when the last domino falls.
4. Knock over the first tile to start the domino chain reaction. Have the students record the elapsed time in the data table.
5. Alert students to be prepared to start timing the supercritical model. Topple over the first “initiator” tile. Start the timing when the first “uranium-235” tile falls. Have students stop timing when all the tiles have fallen. Instruct students to record the time in the data table.
6. Have the students calculate the number of tiles toppled per second rate, then answer the Post-Demonstration Questions.

Student Worksheet PDF

12799_Student1.pdf

Teacher Tips

• The domino tiles and fission tile location template can be stored for future use.
• Practice placing the tiles before attempting the demonstration. Patience may be required to successfully set up all the tiles without knocking them over.
• The dense packing arrangement of tiles yields between one and two tiles per toppled tile. If a unit of time is defined as the time for one tile to topple the next ones in line, then the time needed to topple 100 tiles for the dense packing is 10 units. The first unit topples two tiles, the second unit topples 4, the third topples 6, the fourth 8, the fifth 10, the sixth 12 and so forth. For the straight line, the total time is 100 units, making the dense packing model 10 times more rapid.
• To increase the difference in elapsed time between the two processes, add additional tiles to each setup. 256 tiles would yield a time ratio of 256:17, or 15:1.
• The time for the supercritical process is very quick. Have the students use stopwatches that measure in tenths or hundredths of seconds.

Sample Data

Answers to Questions

1. If each tile that is knocked down represents a fission reaction of uranium-235, calculate the energy released per second for each chain reaction process. (The energy released by each fission is 3 x 10^–11 J.)
   {12799_Answers_Equation_5}
2. This graph represents the total number of tile “fissions” that have occurred for both processes after the first ten chain reaction steps. What happens to the rate of fusion for each process as the chain reaction steps increase?
   {12799_Answers_Figure_3}
   The rate of fissions will rapidly increase for the supercritical process, but remains the same for the critical process.
3. In the combustion reaction of CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(g)
   {12799_Answers_Equation_8}
   Calculate the energy released by the fission reaction of 1 mole of uranium-235. How does this compare to the combustion of methane?
   {12799_Answers_Equation_9}