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## Nuclear fission

Lesson for 16-19

This topic does not lend itself to much practical work; there are a few analogue demonstrations which can be valuable.

Students may have strong feelings about nuclear technology – power stations and bombs. You could make this a focus of your coverage of this area: the physics ideas won’t tell you what’s right or wrong, but they should allow you to make more informed judgments on questions such as nuclear waste disposal or the use of depleted uranium in weaponry.

## Episode 526: Preparation for nuclear fission topic

Teaching Guidance for 16-19

- Level Advanced

This topic does not lend itself to much practical work; there are a few analogue demonstrations which can be valuable.

## Main aims of this topic

Students will:

- Use balanced equations to represent transmutation, fission and fusion events
- Calculate mass and energy changes in such events
- Understand how a chain reaction can arise in fissile material
- Explain how a controlled chain reaction is managed in a nuclear power reactor

## Prior knowledge

Students should already be familiar with standard notation for nuclides and with balanced nuclear equations. They should know how to calculate energy changes from changes in nuclide masses.

## Where this leads

If your students are to study an astronomy topic, this work forms a basis for understanding nuclear processes in stars. Mass-energy calculations using *E* = *m* × *c*^{ 2}, as well as the ability to balance nuclear equations, will also be useful in any study of particle physics.

### Up next

### Nuclear transmutation

## Episode 527: Nuclear transmutation

Lesson for 16-19

- Activity time 130 minutes
- Level Advanced

Students need to move beyond the idea that nuclear changes are represented solely by alpha, beta and gamma decay. There are other decay processes, and there are other events that occur when a nucleus absorbs a particle and becomes unstable.

Lesson Summary

- Discussion: Transmutation of elements (15 minutes)
- Student questions: Balancing equations (30 minutes)
- Discussion: Induced fission (10 minutes)
- Demonstration: The nucleus as a liquid drop (10 minutes)
- Discussion: Fission products and radioactive waste (10 minutes)
- Worked example: A fission reaction (10 minutes)
- Discussion and demonstrations: Controlled chain reactions (15 minutes)
- Discussion: The possibility of fission (10 minutes)
- Student questions: Fission calculations (20 minutes)

## Discussion: Transmutation of elements

Start by rehearsing some assumed knowledge. What is the nucleus made of? (Protons and neutrons, collectively know as nucleons.) What two natural processes change one element into another? ( α and β decay). This is transmutation.

Using a Periodic Table, explain that α decay moves two places down the periodic table. What about β ^{-} decay? (Moves one place up the periodic table.) Introduce the idea of β ^{+} decay. (Moves one place down the periodic table.)

Write general equations for these processes.

There is another way in which an element may be transmuted; for example, the production of radioactive 146C used in radio-carbon dating in the atmosphere by the neutrons in cosmic rays.

147N + 01n → 146C + 11H

Rutherford found that protons exist in the nucleus by bombarding nuclei with alpha particles. Patrick Blackett carried out further experiments and showed that the bombarded nucleus had transmuted. Ask your students to complete the following nuclear equation that summarises the transmutation of nitrogen into oxygen:

He + 147N → O + 11H

They should get:

42He + 147N → 178O + 11H

Cockroft and Walton were the first to split

the atom, by bombarding lithium with protons from their accelerator.

11H + 73Li → 84Be → 2 42He

## Student questions: Balancing equations

Students can practise balancing equations.

Episode 527-1: Isotope production (Word, 50 KB)

## Discussion: Induced fission

In the examples above, small parts are chipped off

nuclei. The behaviour of the heaviest natural element, uranium, is different. It breaks up into two large chunks – into two elements nearer to the middle of the periodic table – so-called *induced fission* . The two lighter elements are referred to as *fission fragments* .

How do the two common isotopes of uranium 23592U and 23892U differ? (23892U has three more neutrons than 23592U.) It is the 23592U not the 23892U that fissions. It absorbs a neutron, then splits into fission fragments, i.e. any two smaller nuclei that can be made from the 235 nucleons of the 23592U.

Episode 527-2: Nuclear fission (Word, 123 KB)

## Demonstration: The nucleus as a liquid drop

In many ways, nuclei behave like a drop of liquid. Show a water filled balloon – a good model for a nucleus. After the absorption of the neutron, the nucleus of 23892U wobbles. As soon as the electric charge distribution departs from the spherical (pinch the balloon into a dumbbell like shape) the mutual coulomb repulsion between the two ends drives the fission process. An alternative is to grease a plate and put a large drop of water on it. Wobble the plate about and watch the drop split.

## Discussion: Fission products and radioactive waste

Most of the energy released is carried off in the high speeds of the fission fragments. Because they have a relatively high fraction of neutrons, they are unstable, and decay with short half-lives. They form the high-level

radioactive waste that cannot be simply disposed of; it has to be stored somewhere for a minimum of 20 half lives.

By what factor will the activity fall after 20 half lives? ( ½ ^{20} is about 10^{-6} , or one-millionth)

13755Cs has a half life of 30.23 years: 20 half lives is 605 years

9038Sr has a half life of 28.1 years: 20 half lives is 562 years

Think about the consequences if waste disposal has to be engineered to remain intact for many centuries. (Which engineering structures have existed for the last 600 years?)

## Worked examples: A fission reaction

Here is the nuclear equation for a typical fission process:

01n + 23592U → 23692U → 13853I + 9539Y + ?

What is required to balance the equation? (3 neutrons)

Why are there some neutrons left over? (Relate this to the *N*-*Z* curve. The heaviest elements have the largest neutron excess to remain stable. The two lighter fission fragments have a higher fractional neutron excess; hence some are left over

.) These left over

neutrons are the vital key to unlock nuclear power using fission.

## Discussion and demonstrations: Controlled chain reactions

If at least one surplus neutron can induce fission in another 23592U nucleus and so on, then a self sustaining release of energy is possible. For a power station a *controlled* chain reaction is needed. Should each fission result in *more* than one further fission, then the chain reaction is said to diverge. In a bomb the aim is to get the chain reaction to diverge as fast as possible.

Blow up two balloons; let one fly off; release the other slowly, to illustrate the difference between uncontrolled and controlled energy release.

There are a number of analogues of chain reactions that can be demonstrated at this point, using matches or lines of dominoes.

Episode 527-3: Chain reactions (Word, 173 KB)

Episode 527-4: Fission analogues (Word, 26 KB)

## Discussion: The possibility of fission

What are the chances that a neutron will strike another nucleus? First recall that atoms are mostly empty space. The nuclei of two adjacent uranium atoms are typically 10,000 nuclear diameters apart. Emphasise this by picking a pupil in the middle of the class, and estimating her/his width (0.3 m?). Where will the next pupil nuclei

be situated? (3 km away.) A fast-moving neutron will travel a long way before it strikes another nucleus.

In fact, most neutrons are absorbed by 23892U nuclei, which are much more common than 23592U, and quite good at absorbing fast neutrons. Instead of fissioning they transmute into 23994Pu which is fissile, the favourite explosive material for making nuclear bombs. Pure natural uranium is incapable of sustaining a fission reaction – *less* than one fission neutron succeeds in inducing a further fission.

Ask your students how this problem might be overcome in order to have a controlled chain reaction. (The answer is the introduction to the next episode.)

## Student questions: Fission calculations

Calculations of energy released in fission events.

Episode 527-5: Fission – practice questions (Word, 36 KB)

### Download this episode

## Episode 528: Controlling fission

Lesson for 16-19

- Activity time 125 minutes
- Level Advanced

In this episode, you can look at the different features of the core of a nuclear reactor, and explain its operation using your students’ knowledge of nuclear physics.

Lesson Summary

- Discussion: The construction of a nuclear reactor (10 minutes)
- Discussion: Moderation (10 minutes)
- Discussion: Enrichment (10 minutes)
- Discussion: Critical mass (10 minutes)
- Discussion: Control rods and coolant (10 minutes)
- Student questions: Power reactors (30 minutes)
- Discussion: Nuclear fusion (15 minutes)
- Student questions: Fusion calculations (30 minutes)

## Discussion: The construction of a nuclear reactor

Look at a diagram or animation of a nuclear reactor. Check what your students already know about the reactor’s construction.

Episode 528-1: Nuclear fission reactor (Word, 61 KB)

## Discussion: Moderation

How can we make it more likely that a neutron will collide with a 23592U nucleus? There are two ways, both used in nuclear power reactors:

Slow down the fast neutrons to increase their chance of being captured by a fissile 23592U nucleus. This process is called *moderation*.

Concentrate the 23592U compared to the 23892U. This process is called *enrichment*.

The speed of the fast fission neutrons is slowed down (moderated

) by allowing them to collide with a suitable moderator nucleus. Conservation of momentum tells us that the speed of a light neutron colliding with a massive nucleus will be little affected. We need a material with relatively light nuclei to absorb momentum and energy from the neutron.

Look at the periodic table for some ideas:

- Hydrogen – i.e. protons. Virtually the same mass (great), but gaseous (not very dense) and explosive. Hydrogen in water maybe? Yes, pressurised water reactors use water as the moderator (as well as the coolant), but the protons are attached to the rest of the water molecule and have an effective mass of 18 times that of a free proton
- Helium – inert (good) but gaseous, so not dense enough
- Lithium – too rare (expensive), melting point too low anyway
- Beryllium – possible but expensive
- Boron absorbs neutrons
- Carbon – mass equivalent to 12 protons, solid (good), flammable (bad). Used in the first generation of UK
Magnox

reactors

So there are a number of possibilities, each with a balance of advantages and disadvantages.

## Discussion: Enrichment

Nuclear power stations use uranium enriched to typically 2.5% – a factor of 2.50.7, so 3.6 times the proportion found in natural uranium. Ask your students how much 23892U must be discarded to produce 1 tonne of enriched uranium, i.e. with the fraction of 23592U increased from 0.7% to 2.5%. (You need 3.6 tonnes of natural uranium, so you discard 2.6 tonnes of 23592U.)

Bombs require 90% enrichment. Power station enrichment can be easily extended to get pure fissile 23592U. Herein lies an easy route to the proliferation of nuclear weapons by countries that have nuclear power programs.

## Discussion: Critical mass

Extend your earlier discussion of chain reactions to introduce the idea of *critical mass*. At least one of the fission neutrons must induce a further fission to allow for a chain reaction. Some may simply escape from the fuel assembly; others may be absorbed by the 23892U, by structural materials used in the construction, by the coolant, by the fission fragments etc. Fewer will escape if there is a smaller surface area to volume ratio.

For enriched uranium, the critical mass is roughly the size of a grapefruit. Picture bringing two half-grapefruit together to cause an explosion. Why would the critical mass be different for shapes other than a sphere? (A sphere has the lowest area to volume ratio. Other shapes with the same mass would have greater areas, so more neutrons would escape, making a chain reaction less likely.)

## Discussion: Control rods and coolant

The chain reaction in a nuclear power stations must be controlled, which means that the number of neutrons must be *continuously* regulated to stop the chain reaction diverging or closing down. To do this *control rods* are moved into or out of the reactor core. They are made from a substance that absorbs neutrons (e.g. boron).

A coolant carries energy away from the core. What are the desirable properties of the coolant? (It must not absorb neutrons; it must have high thermal conductivity, high specific heat capacity and high boiling point.)

## Student questions

These questions compare Magnox and PWR reactors.

Episode 528-2: Fission in a nuclear reactor – how the mass changes (Word, 42 KB)

## Discussion: Nuclear fusion

You can now look at the process of nuclear fusion. (This will have been touched on when considering the graph of binding energy per nucleon.) Students should be able to calculate the energy changes from values of nuclide mass. Emphasise that the energy released per nucleon in fusion is larger than for fission.

Episode 528-3: Fusion (Word, 40 KB)

## Student questions: Fusion calculations

Calculating the energy released in fusion reactions.

Episode 528-4: Fusion questions (Word, 27 KB)

Episode 525-3: Fusion in a kettle? (Word, 35 KB)