3.8.1.6 Mass and energy

[see here for whole topic index]

Appreciation that E = mc² applies to all energy changes

Simple calculations on nuclear transformations; mass difference and binding energy

Atomic mass unit, u

Conversion of units; 1u = 931.1 MeV

Fission and fusion processes

Simple calculations from nuclear masses of energy released in fission and fusion reactions.

Graph of average binding energy per nucleon against nucleon number, A

Students may be expected to identify, on the plot, the regions where nuclei will release energy when undergoing fission/fusion.

Appreciation that knowledge of the physics of nuclear energy allows society to use science to inform decision making.

Know that the mass of nuclear particles when associated together in a nucleus (and therefore all matter!) is less than the sum of the mass of the component parts.

Know the difference in mass between individual consitituents and the associated particles is called the 'mass difference'

Know that mass and energy are interchangable via the equation E = mc² (Einstein's equation).

Know that the conversion between mass (u) and energy (MeV) is possible via a shortcut in the databook that states the equivalence of mass and energy as: 1u = 931.1 MeV

Draw the graph of average binding energy per nucleon against nucleon number, A - including labelled axes with units and values on those axes!

Recall that fission is the splitting into two of a large nucleus and fusion is the fusing (joining into one) of two smaller nuclei.

Relate fission and fusion to the binding energy per nucleon graph to explain why the processes are energetically viable.

Now try some questions and even more...

Induced fission by thermal neutrons

Possibility of a chain reaction

Critical mass

The functions of a moderator, control rods and the coolant in thermal nuclear reactors

Details of particular reactors are not required.

Students should have studied a simple mechanical model of moderation by elastic collisions.

Factors affecting the choice of materials for the moderator, control rods and coolant.

Examples of materials used for these functions

You should recall that a thermal neutron is a neutron that has energy in the infra red photon range.

You should know that if U235 absorbs a thermal neutron (becomes U236) it is very unstable and will split into two (not usually equal) nuclei

You should know that a couple (on average 2 to 3) of free neutrons are also produced (these can go on to produce more fissions). The fragments are more stable (energetically viable reaction) and energy is released when this happens.The resulting nuclei are called fission fragments NOT daughter nuclei (that is the terminology in radioactivity!)

The freed neutrons can go on to produce further fissions, but are usually of too high energy to do this and need to be slowed down. This is done by a MODERATOR (moderates the speed of the neutrons!) such as graphite. It slows the neutron down by allowing multiple interactions (about 50) with the carbon lattice without absorbtion of the neutron into the carbon nucleus - graphite has a 'low cross section for neutrons'.

A chain reaction is a reaction in which the instigator of the reaction is also produced as a product. It is therefore possible for the product of one reaction to go on to take the role of the reactant in a future reaction. Each fission produces neutrons that could go on to produce further fissions so the more atoms you have (greater mass of sample) the more likely that the reaction will continue in a chain reaction. But those neutrons are produced isotropically (equally in all directions) - the production direction is random, so an atom on the surface could well shoot off a neutron out of the Uranium mass and no fissions would then occur from them.

The bigger the surface area of the Uranium sample the more likely that neutrons will be sent out and not be able to make more fissions. As mass increases so does volume and surface area of the sample. A very small mass will have a larger surface area relative to its size than a bigger one so a chain reaction is less likely (greater proportion of its atoms will be on the surface). There is therefore a minimum mass that allows a chain reaction to occur.

This is called the critical mass which has a mass/surface area ratio below which a chain reaction is not viable. As 2/3 neutrons are produced each time a nucleus of Uranium splits the energy produced by reaction would escalate by a factor of about 2/3 at each stage. This would be uncontrolled acceleration of the reaction and be very dangerous (bomb).

Control rods of cadmium or boron can be inserted into the reaction vessel to maintain the energy production at the required level. These have a 'high cross section for neutrons' - they absorb the neutrons, taking them out of the reaction preventing further fissions occuriing. The deeper the rods are inserted into the vessel the faster the rate at which energy is being produced will be diminished (more surface area of absorber - more absorbtion)

Moderator materials are chosen for low cross section for neutrons - don't absorb neutrons - interact to take kinetic energy from them instead.Control rods are made of materials that absorb neutrons effectively - have a high cross section for neutrons.

Coolant (eg. water or CO₂) needs to have a high specific heat capacity so that a large amount of heat energy can be absorbed without it getting too hot

Now try some questions

Safety aspects:

Fuel used, remote handling of fuel, shielding, emergency shutdown

Production, handling and storage of radioactive waste materials

Appreciation of balance between risk and benefits in the development of nuclear power.

Uranium is an alpha (and gamma!) emitter - uranium dust is very dangerous - highly localised ionisation in the body from alpha results in a high risk of cancer and mutaion in reproduction. (You might want to find out more about plutonium too as this can be used as a fuel)

All forms of radiation are produced by the cocktail of fission fragments so shielding must be thick concrete (lead to expensive!)

Control rods contain enough absorbing material to completely shutdown the reactor - absorb so many neutrons that the chain reaction is stopped.

Fission fragments are radioactive isotopes of many elements - variety of half lives and type of radiation produced.

Neutron absorbtion by an atom creates a radioactive isotope of that element - which then decays into something else! So the reactor itself and instruments used within the reaction vessel become highly radioactive.

You should know about the three categories of waste (low, intermediate and high) due to their half lives (how long they will be dangerous for) and their activity, how they are dealt with (stored, monitored).

Also revise safety when dealing with radioactive materials for handling of active waste.

Now try some questions