Particles and Waves3. Nuclear Reactions

Knox Academy, Haddington

Particles and Waves: Nuclear Reactions

ContentsUnit Specification............................................................................................................................................................3

3. Nuclear Reactions...................................................................................................................................................3

Notes...........................................................................................................................................................................3

Contexts......................................................................................................................................................................3

Nuclear Reactions...........................................................................................................................................................4

A basic model of the atom..........................................................................................................................................4

Components of the atom............................................................................................................................................4

Particle......................................................................................................................................................................4

Mass number..........................................................................................................................................................4

Charge......................................................................................................................................................................4

Symbol......................................................................................................................................................................4

Radioactive decay...........................................................................................................................................................5

Radioactive Decay Particles.........................................................................................................................................5

Radiation..................................................................................................................................................................5

Nature.......................................................................................................................................................................5

Symbol......................................................................................................................................................................5

Radioactive decay: representing by symbols and equations.......................................................................................5

Alpha decay.............................................................................................................................................................5

Beta decay...............................................................................................................................................................6

Gamma decay..........................................................................................................................................................6

Fission: spontaneous decay and nuclear bombardment.................................................................................................6

Spontaneous fission....................................................................................................................................................6

Induced Fission............................................................................................................................................................6

Mass difference in fission reactions................................................................................................................................7

Nuclear fission and E = mc2..........................................................................................................................................7

Interactive guide to E=mc2..........................................................................................................................................8

Einstein and nuclear energy............................................................................................................................................8

Nuclear chain reactions...............................................................................................................................................8

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The electron volt.............................................................................................................................................................9

Energy released from each fission reaction.................................................................................................................9

Nuclear Power.............................................................................................................................................................9

Nuclear fission in nuclear reactors..........................................................................................................................9

Nuclear fusion: energy of the future?...................................................................................................................10

A Fusion Reactor....................................................................................................................................................10

Induced current.....................................................................................................................................................11

Neutral beam heating............................................................................................................................................11

Radio-frequency heating.......................................................................................................................................11

Self-heating of plasma...........................................................................................................................................11

Breakeven and Ignition..........................................................................................................................................11

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Unit Specification

3. Nuclear Reactionsa) Nuclear equations to describe radioactive decay and fission and fusion reactions.b) Identify fission and fusion reactions.c) Calculate mass defect and energy released by nuclear reactions.d) Discuss the advantages and disadvantages of nuclear reactors

Notes a) A nuclear reaction produces a change in mass. This mass difference is converted in to energy.

Calculations can be carried out to determine the energy released.

Contexts a) Hazards, e.g. naturally occurring radioactive elementsb) Operation and requirement of Nuclear Power to meet current energy requirements.c) Alternatives to nuclear fission as a source of nuclear energy.

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Nuclear ReactionsWhen we consider nuclear energy, we are dealing with energy released from the nucleus of the atom. A basic model of the atom, and its nucleus, is required.

A basic model of the atomThe nucleus consists of protons, with mass number 1 and charge +1, and neutrons, with mass number 1 and charge 0. Protons and neutrons are collectively known as nucleons. This is shown on the right

The total number of protons and neutrons in the nucleus is the mass number, A. The number of protons in the nucleus is called the atomic number, Z. In a neutral atom the number of protons equals the number of electrons.

Components of the atomInformation on the three main atomic particles is given below.

*The mass of an electron is = 1/1840 of the mass of a proton.

Each element in the periodic table has a different atomic number and is identified by that number. It is possible to have different versions of the same element, called isotopes. An isotope of an atom has the same number of protons but a different number of neutrons, i.e. the same atomic number but a different mass number.

An isotope is identified by specifying its chemical symbol along with its atomic and mass numbers. For example C6

12 and C614

are two isotopes of carbon with 6 protons

and 6/8 neutrons respectively.

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Particle Mass number Charge SymbolProton 1 +1 1

1p

Neutron 1 0 10n

Electron 0* -1 0−1e

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Radioactive decayRadioactive decay is the breakdown of a nucleus to release energy and matter from the nucleus. This is the basis of the word ‘nuclear’. The release of energy and/or matter allows unstable nuclei to achieve stability. Unstable nuclei are called radioisotopes or radionuclides.

Radioactive Decay Particles

The following is a summary of the 3 types of nuclear radiation. Notice that gamma radiation has zero mass and zero charge. It is an electromagnetic wave.

Radiation Nature SymbolAlpha particle Helium nucleus Beta particle Fast electron Gamma ray High freq electromagnetic

wave

The beta particle is an electron released from the nucleus. It is not an orbiting electron.

Radioactive decay: representing by symbols and equationsIn the following equations both mass number and atomic number are conserved, ie the totals are the same before and after the decay.

The original radionuclide is called the parent and the new radionuclide produced after decay is called the daughter product (Which sometimes may go on to decay further).

Alpha decayIn alpha decay, a positively charged particle consisting of 2 protons and 2 neutrons is emitted spontaneously from a nucleus. It is identical to a helium nucleus. It was discovered by Ernest Rutherford in 1899.

Alpha decay usually occurs in heavy nuclei such as uranium or plutonium, and therefore is a major part of the radioactive fallout from a nuclear explosion. It can be stopped by a sheet of paper and cannot penetrate human skin. It can only travel a few cm in air.

Although the range of an alpha particle is short, if an alpha decaying element is ingested, the alpha particle can do considerable damage to the surrounding tissue. This is why plutonium, with a long half-life, is extremely hazardous if ingested.

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Beta decayIn (negative) beta decay, a nucleus releases a negatively charged beta particle, called an electron, and an antineutrino. There is a less common type of beta decay called positive beta decay where a positron and a neutrino are released. As described in section 1, the neutrino and antineutrino are high-energy elementary particles with little or no mass and are released in order to conserve energy during the decay process. The beta particles travel about 3m in air and are stopped by 5 cm of wood or a few mm of aluminium.

Gamma decayGamma rays are a type of high frequency (and therefore high energy) electromagnetic radiation. They are emitted when the charge within a nucleus is redistributed. Often gamma waves are given off with alpha or beta radiation, as a nucleus emitting those particles may be left in an excited (higher-energy) state.

Gamma rays are more penetrating than either alpha or beta radiation, but less ionising. Gamma rays from nuclear fallout would probably cause the largest number of casualties in the event of the use of nuclear weapons in a nuclear war. They produce damage similar to that caused by X-rays, such as burns, cancer and genetic mutations.

Fission: spontaneous decay and nuclear bombardment

Spontaneous fissionFission occurs when a heavy nucleus disintegrates, forming two nuclei of smaller mass number and several free neutrons. This radioactive decay is spontaneous fission. A large amount of energy is also released. Most elements do not decay in this manner unless their mass number is greater than 230.

The stray neutrons released by a spontaneous fission can prematurely initiate a chain reaction. Scientists have to consider the spontaneous fission rate of each material when designing nuclear power stations or other nuclear devices.

Induced FissionFission can also be induced, ie persuaded, to happen by neutron bombardment. This is shown in the equation:

92235 U + 0

1 n →3692 Kr + 56

141 Ba + 3 01 n + energy

(Why are neutrons used not protons?)

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Mass difference in fission reactionsMass number and atomic number are both conserved during this fission reaction. However, even though the overall mass number is conserved, when the actual masses before and after the fission are compared very accurately, there is in fact a small mass difference (or mass defect). The total mass before fission is greater than the total mass of the products afterwards. This leads to possibly the most famous equation in Science!

Nuclear fission and E = mc2

In 1905, Albert Einstein proposed the famous relationship. E = mc2

Where E is energy measured in joules (J), m is mass that is converted measured in kilograms (kg) and c is the speed of light in a vacuum (m s–1).

The equation above assumes that all of the mass of an object is converted into energy. In most nuclear reactions however, m represents the difference in mass (the “lost” mass) before and after a reaction, i.e. a more accurate equation would then be:

Where Δm represents the mass difference =

(total mass before fission – total mass after).

In fission reactions, the energy released is carried away as the kinetic energy of the fission products.

Worked exampleIn the fission reaction below, a nucleus of uranium-235 absorbs a neutron and splits into two lighter nuclei releasing neutrons and energy. Calculate the energy released.

Masses: uranium-235: 390.2 × 10–27 kgneutron: 1.675×10–27 kgbarium-137: 227.3×10–27 kgmolybdenum-97: 160.9×10–27 kg

Mass before fission (kg) Mass after fission (kg)

U 390.2 × 10–27 Ba 227.3 × 10–27

n 1.675 × 10–27 Mo 160.9 × 10–27

___________________ 2n 3.350 × 10–27

391.875 × 10–27 ___________________________

391.550 × 10–27

Decrease in mass = (391.875 – 391.550) × 10–27 = 0.325 × 10–27 kg

Energy released during this fission reaction, using E = mc2

E = 3.25 × 10–28 × (3 × 108)2 = 2.9 × 10–11 J

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E = Δmc2

This is the energy released by fission of a single nucleus. (Note the need to work with six significant figures for mass due to the small difference.)

Interactive guide to E=mc2

There are many excellent resources on the web which explain the meaning of this equation.

The best person to explain the significance of this equation is Albert Einstein himself. You can listen to his explanation here: http://www.aip.org/history/einstein/voice1.htm.

This website shows a useful timeline of scientific discovery relevant to the equation E = mc2.http://www.pbs.org/wgbh/nova/teachers/activities/3213_einstein_06.html

The following website offers more detail to better understand the equation E = mc2.http://www.pbs.org/wgbh/nova/teachers/activities/3213_einstein_04.html

Einstein and nuclear energy Einstein’s equation led directly to the development of nuclear power. Scientists realised that some nuclear reactions could release huge amounts of energy. In the 1930s it was believed that Adolf Hitler in Germany was attempting to develop a nuclear bomb. For this reason, Einstein wrote to the President of the United States urging him to develop nuclear weapons to counter this threat. The American project to develop the nuclear bomb was called the Manhattan project and thousands of scientists worked on this, mainly to prevent Germany from developing it first. Einstein later called this the “greatest mistake of his life”.However, in 1945 the first nuclear bomb was tested in New Mexico. The image shows the characteristic “mushroom cloud” from the first nuclear test. The leader of the project, Robert Oppenheimer famously said.

‘Now, I am become Death, the destroyer of worlds.’ You can hear and watch Oppenheimer at http://www.atomicarchive.com/Movies/Movie8.shtml.

The following section gives more detail about how a chain reaction can lead to a nuclear explosion and how nuclear power stations are designed to safely harness this energy.

Nuclear chain reactionsA chain reaction refers to a process in which neutrons released in fission produce an additional fission in at least one further nucleus. This nucleus in turn produces neutrons, and the process repeats. The process may be controlled (nuclear power) or uncontrolled (nuclear weapons).

U235 + n → fission + 2 or 3 n + 200 MeV

If each neutron releases 2 more neutrons, then the number of fissions doubles each generation. In 10 generations there are 1024 fissions and in 80 generations about 6 × 1023 (a mole) of fissions.

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The electron voltPhysicists often use the electron volt as a small unit of energy. Since E = QV, 1 electron volt is the energy required to move an electron through a voltage of 1V (1.6 × 10-19 J).

In the reaction below, 1 MeV (1 million electron volts) = 106 × 1.6×10-19 = 1.6 × 10-13 J.

Energy released from each fission reactionA single nuclear reaction releases approximately 200 MeV of energy. Most of this is made up of the kinetic energy of the fission products (about 165 MeV). The remainder is carried away by the gamma rays and anti-neutrinos which are produced as well as the kinetic energy of the neutrons (between 5-10 MeV each)

Nuclear PowerNuclear power has been used to produce electricity in the UK since 1956, when the first large-scale power plant was opened in Cumbria, England. In Scotland there are two nuclear power stations currently producing electricity: Torness in East Lothian (pictured left) and Hunterston B in North Ayrshire on the West Coast. These produce almost 50% of Scottish electricity. Hunterston B is currently operating at only 70% of its maximum capacity but it is still able to supply electricity for around 1.5 million homes. At present, all commercial nuclear power stations are fission reactors.

Nuclear fission in nuclear reactorsIn a fission reactor, energy is produced in controlled fission reactions. The uranium fuel is contained within a fuel rod which releases neutrons when it undergoes fission. A graphite moderator is used to slow these neutrons and increase the chance of further fissions occurring. These slow (thermal) neutrons cause more fission reactions so that a chain reaction occurs.

To keep the reaction taking place at the correct temperature, boron control rods absorb some of the slow neutrons and keep the chain reaction under control. A coolant fluid (liquid or gas) is required to avoid the core overheating and the hot gases turn turbines which generate electricity.

Fission reactors require containment within reinforced concrete and lead-lined containers to reduce contamination. This is shown in the image.

Nuclear power remains a controversial issue. It produces vast amounts of electricity without the production of carbon dioxide, which is associated with climate change. It is a very reliable source of energy. However, the waste it produces is radioactive and must be stored, sealed, for thousands of years, during which time it must be protected, e.g. from geological threats such as earthquakes and volcanic eruptions.

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For this reason, scientists have been developing alternative ways of harnessing nuclear energy. These include nuclear fusion.

Nuclear fusion: energy of the future?The reaction that powers the sun comes from a nuclear fusion reaction. This is where two lighter elements join or fuse together to create a heavier atom plus additional fusion products. The products after the reaction are lighter than the total mass before, i.e. there is a mass difference. The equation E=Δmc2 can again be used to work out the energy released.

The image shows two heavy isotopes of hydrogen fusing to make helium with the release of a neutron. Deuterium is an isotope of hydrogen found in seawater which has one proton and one neutron. Tritium has 1 proton and 2 neutrons and can be made from lithium which is readily available on Earth.

This energy can be released in an uncontrolled way to make a hydrogen bomb however it is also possible to release this in a controlled way in a fusion reactor.

A Fusion ReactorThe Joint European Torus (JET) in Oxfordshire, is Europe’s largest fusion device1. In this device, deuterium and tritium are super-heated to form a plasma (the “fourth-state of matter.” A plasma is a super-hot gas where many of the electrons have so much energy that they are no longer bound to their atoms, resulting in a large number of ions.

To sustain fusion, 3 conditions must be met at the same time:

Extremely high plasma temperature (T): 100–200 million K A stable reaction lasting at least 5 seconds. This is called the energy

confinement time (t) A precise plasma density of around 1020 particles/m3 (This is one

thousandth of a gram/m3 = one millionth the density of air).

One type of fusion reactor is called a Tokomak. In this design the plasma is heated in a torus or “doughnut-shaped” vessel. The hot plasma is kept away from the vessel walls by applied magnetic fields. This is shown in the diagram on the right.

One of the main requirements for fusion is to heat the plasma particles to very high temperatures or energies. The following methods are typically used to heat the plasma – all of them are employed on JET.

1 To find out more, go to: http://www.jet.efda.org where you can see a short video of the plasma.

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Induced currentThe main plasma current is induced in the plasma by the action of a large transformer. A changing current in the primary coil induces a powerful current (up to 5 million amperes on JET) in the plasma, which acts as the transformer secondary circuit.

Neutral beam heatingBeams of high energy, (neutral) deuterium or tritium atoms are injected into the plasma, transferring their energy to the plasma via collisions with the ions.

Radio-frequency heatingElectromagnetic waves of a frequency matched to the ions or electrons are able energise the plasma particles. This is similar to the accelerating structures in a particle accelerator.

Self-heating of plasmaThe alpha particles produced during fusion can transfer their kinetic energy to the deuterium and tritium. The neutrons (being neutral) escape the magnetic field and their capture in a future fusion power plant will be the source of fusion power to produce electricity.

Breakeven and Ignition

Fusion power plants aim to reach breakeven state or better still, ignition.

Breakeven occurs when fusion power out just equals the power required to heat and sustain plasma then However, designers of the reactor only the fusion energy contained within the helium ions heats the deuterium and tritium fuel ions (by collisions) to keep the fusion reaction going.

Ignition occurs when the energy given out by the plasma is able to sustain an ongoing fusion reaction. The condition for ignition is approximately six times more demanding (in confinement time or in plasma density) than the condition for breakeven.’

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