Earlston High SchoolPhysics

Unit 1: Waves and Radiation

Summary Notes

SOUND

Vibrations

Musical instruments produce sound when part of the instrument vibrates.

A guitar string vibrates when it is plucked.

A trumpet blasts out sound when the air inside it vibrates.

Energy is transferred from the vibrating object to the listener by sound waves which travel through the air. These sound waves make the air vibrate.

Frequency

Each note or sound has a frequency which is measured in hertz (Hz).

A tuning fork will have its frequency value engraved on it.If a tuning fork has a frequency of 256 Hz, this means that 256 sound waves are produced every second.

2

Frequency = number of waves produced in one second

DETECTING SOUND

Sound can be detected by a microphone and a trace displayed on an oscilloscope.

Loud and Quiet

The amplitude of a wave is the distance from the middle of the wave to the top or the bottom of the wave.A loud sound transfers more energy so the oscilloscope trace will have a large amplitude.A quiet sound transfers less energy so the oscilloscope trace will have a small amplitude.

High and low frequency

The effect of changing the frequency can also be seen on the oscilloscope screen.

If the frequency is higher, more waves can be seen on the screen.

SPEED OF SOUND

3

During a thunderstorm, the lightning flash is seen a short time before the roll of thunder is heard. This is due to the fact that light travels much faster than sound through air.

Calculating the speed of sound

The speed of sound can be calculated using the following formula:

USING SOUND

Sound can travel through solid, liquids and gases. The only place that sound cannot pass through is a vacuumA vacuum is an empty space, so there are no particles to pass on the vibrations.When listening to music, you hear sounds of many frequencies. Humans can detect frequencies between 20 and 20 0000 Hz. As we get older, the upper limit gradually falls to about 15 000Hz.

4

Speed of sound = 340 m/s

Speed of light = 300 000 000 m/s or 3x108 m/s

speed = distancetime

v = dt

metres (m)

seconds (s)

metres per second (m/s)

Some animals can detect higher frequency sounds than humans,

SOUND LEVELS

Sound level is measured in decibels (dB).

130 Jet engine at 50m Sound level 100 Pneumatic drill

in dB 70 Rush hour traffic60 Normal conversation at 60m0 Silence

When sound levels rise to an unacceptable level, the problem is described as noise pollution. Exposure to high level sounds over a long period of time can damage our hearing. Listening through stereo headphones would also produce a harmful effect if the volume is turned up too high.

Ultrasound

Sound beyond the upper limit of human hearing (20 000Hz) is called ultrasound.

Ultrasound can be used in hospitals to scan the baby in the mother's womb. This can be used by a computer to produce an image of the baby on a screen.

A system called sonar is used by fisherman at sea. The ultrasound signal is transmitted towards the sea bed and anecho is detected. Shoals of fish are located by this method.

5

WAVE CHARACTERISTICS

With the increase in mobile technology most of our day to day communications are completed using waves passing through the air, wires or fibre optics. These are different from sound waves and we need to understand how to describe a wave so that we are able to talk about waves in a meaningful way.

Wavelength (symbol λ units metres, m). It is the distance between two successive points on a wave in phase.

Amplitude (symbol A, units metres, m)It is measured from the centre line to the crest or trough. It is a measure of how much energy a wave carries.

Frequency (symbol f, unit hertz, Hz) This is how many waves are produced each second. This is the same as the number of waves that pass a point in one second.

Period (symbol T unit second s)This is the time to produce one wave.

Speed (symbol v, unit metres per second, m/s) This is the distance a wave travels in one second.

6

A

A

THE WAVE EQUATION

In the speed of sound experiment the speed of a wave could be measured by measuring how far the wave travels in a known time interval.

It is also possible to calculate the speed of a wave if we know the wavelength and frequency of the wave.

Worked Example:

A water wave has a wavelength of 50cm. Twenty waves pass a point in 10 seconds. Calculate the speed of the wave.

v = ?f = 20 waves in 10s = 20/10 waves in 1s = 2Hzλ = 50cm = 0.5 m

v = f x λ = 2 x 0.5 = 1m/s

A second equation that relates the frequency of a wave with the period of a wave is

Worked Example:

In the above example what is the Period of the water wave?

f = 2Hz

T = 1/f = 1/2 = 0.5s

LONGITUDINAL AND TRANSVERSE WAVES

Sound waves are longitudinal waves. Longitudinal waves are ones where the vibration of the particles is in the same direction as the direction of travel.

7

Speed = frequency x wavelength

v = f x λ

metres per second (m/s)

Hertz(Hz)

metres(m)

Period = 1 / Frequency

T = 1/f

Seconds (s)

Hertz (Hz)

In transverse waves the vibration of the particles is at right angles to the direction of travel.

Every wave in the electromagnetic spectrum and water waves are transverse waves.

ELECTROMAGNETIC SPECTRUM

Light waves travel at 300 000 000 m/s through air or a vacuum. Visible light is a small part of a family of waves called the electromagnetic [EM] spectrum. The spectrum is illustrated below.

Electromagnetic Radiation

Detector Some uses

Radio and TV waves Aerial CommunicationMicrowaves Aerial Communication

8

REDVIOLET

Heating foodInfra Red waves Infra Red film Treating damaged

musclesThermal imagingDetecting tumours

Visible spectrum Photographic filmPhoto diode

Laser surgeryEndoscopesSight

Ultra Violet waves (UV) Fluorescent materials Used by our skin to produce vitamin D

X-Rays X-Ray film Detecting broken bonesCAT scansRadiotherapy treatment for cancer

Gamma Rays Geiger counterGamma camera

Tracers in the human body to detect abnormalities.Sterilising surgical instruments

All of the waves in the electromagnetic spectrum travel at the speed of light. As the frequency of the electromagnetic waves increases so does the amount of energy the waves have.

Reflection

The diagram shows a ray of light hitting a plane mirror. A line drawn at right angles to the mirror where the light hits it is called the NORMAL to the surface at that point.

9

The angle between the incoming light ray and the normal is called the angle of incidence (i) and the angle between the outgoing light ray is called the angle of reflection (r).

Laws of reflection

1. The angle of incidence is equal to the angle of reflection

2. The incident ray, the reflected ray and the normal all lie in the same plane.

REFRACTION

Light rays normally travels in straight lines – which is why shadows are created behind objects.

Light rays can change direction when they reflect off a surface.

The direction of rays of light can change more subtly as demonstrated by the distorted image of the spoon.

Light travelling from one transparent substance into another transparent substance undergoes a change in direction as it enters. This change in direction of the light is called refraction.

10

The reason the light refracts is because it travels at different speeds in different substances.

Light travels as a wave. If one part of the wavefront strikes a new substance before the rest of it then this part of the wavefront slows down (in this case) while the rest continues to move at the same speed.

Once all of the wavefront is in the new substance the wavefront is again

moving in a straight line but in a new direction. The frequency of the wave stays the same.

It is not just light that refracts, all waves (e.g. water, sound, radio) do.

LIGHT REFRACTION

Light refracting through a glass block.

When light moves from a less dense material, in this case air, in to a more

dense material, in this case glass, the direction of the wave bends towards the

normal. At the same time the speed and wavelength of the light decrease.

i

rr

i

Normal

Normal

glassair air

11

When light moves from a more dense material, in this case glass, in to a less

dense material, in this case air, the direction of the wave bends away from the

normal. At the same time the speed and wavelength of the light increases.

A normal is a line we draw at right angles (90o) to the boundary between the

two materials, in this case air and glass.

Angle i is the angle an incoming wave to a boundary between two materials,

makes with the normal. The angle is called the angle of INCIDENCE.

Angle r is the angle the refracted wave makes with the normal. This angle is

called the angle of REFRACTION.

There are two angles of incidence and refraction in the above diagram because the light passes through two boundaries.

When light rays travel along a normal they do not change direction, but their

speed and wavelength still change.

Light refracting through other glass prisms.

12

Notice how the ray does not bend because it is travelling along a normal.

Normal

air

airglass

ri

NormalNormal

rrii

glass airair

The Eye

Our eyes have a number of different parts, each of which do different things. The most important parts are:

(a) lens - this makes fine adjustments to the focus of the view that we see

(b) cornea – the transparent part at the front of our eye. This helps to focus the

view on our retina. Most of the refraction of the light occurs here.

(c) retina – the part of the eye that is sensitive to light. It is on the retina that 13

the image of the view that we are looking at is focused.

(d) optic nerve - this takes the signals from out retina to our brain so that we can

see

(e) muscles – there are two different sets of muscles in your eyes.

(i) One set goes round the lens. These are used in fine focusing of the eye. When

these muscles contract they squeeze the lens and so it gets fatter, this enables

you to focus on things close to you. When the muscles relax the lens becomes

thinner and in this condition you can see distant objects.

The normal eye and correction for long and short sight

Our eyes are amazingly delicate instruments but sometimes they need minor adjustments to help them work properly. The most common defects are those of long and short sight.

A person who has LONG SIGHT can only see things clearly that are far away from them while a person with SHORT SIGHT can only see things clearly that are close to them.

The first two diagrams below show how the eye focuses the image of a near and far object on the retina by squeezing or relaxing the eye lens.

The next two diagrams show long sight and its correction with a convex lens. Without correction only distant objects can be correctly focused and so seen clearly.

14

The next two diagrams show short sight and its correction with a concave lens. Without correction only near objects can be correctly focused and so seen clearly.

Lenses

The convex lens

Convex lenses converge light to a focus.

Uses of convex lensesEye, camera, overhead projector, focus sunlight, projector, microscope, simple telescope, glasses (correct for long sight), magnifying glass.

The concave lens

15

Concave lenses diverge or spread out the light.

Uses of concave lensesglasses (correct for short sight), spy holes in doors,some telescopes, back window of coaches.

TOTAL INTERNAL REFLECTIONLook at the following diagrams showing what happens when the angle of incidence (i) in the glass increases.

16

Normal

air

airglass

ri

Normal

air

airglass

ri

Normal

air

airglass

r = 90o

Critical angle

When the angle of incidence inside the glass reaches a certain value called the critical angle, the angle of refraction in air is 90o. Any angle of incidence inside the glass greater than the critical angle will lead only to reflection of the ray with no refraction into the air. This is called TOTAL INTERNAL REFLECTION.

Total internal reflection is used in optical fibres. An optical fibre is a very narrow (less that the thickness of a human hair) long strand of very pure glass. Light can be transmitted over large distances through an optical fibre before all the light energy is lost, this is because of the purity of the glass.

Optical fibres transmit light energy as in the diagram below

Optical fibres have many uses:

1. They are used to transmit information in the telephone system. Their main advantages are that they can carry much more information than a copper

cable of the same size, the information can travel much further before the signal needs a boost of energy, the signal is more secure and much harder to tap

into. This means they are cheaper than copper cables. Light in optical fibres

does not travel as fast as in air and is a bit slower than electricity through wires. The light is produced by LASERS, a very intense source of light.

2. They are used in fibre scopes to allow doctors to see inside the human body

without the need for invasive surgery. A fibre scope consists of two bundles of

17

Normal

air

airglass

r = angle of reflection

i

optical fibres, one to take light down into the patient, this light then illuminates

the dark insides of the patient, the other bundle then takes the reflected light

back out of the patient to an eyepiece for the doctor to see.

3. The same technology as 2 above can be used by for example plumbers to see

blockages in drains or spies to look into a building without being detected.

A diagram of a fibre scope

18

DIFFRACTION

When waves reach the edge of a barrier they bend around the barrier. This is known as diffraction. In the diagrams below we can see the effect of changing the size of the gap the waves are diffracting through. Notice how the narrower the gap the more diffraction we get. Also notice that as the wavelength of the wave increases we get more diffraction.

19

DIFFRACTION AND RADIO WAVES

The next diagram shows a wave bending round the edge of a barrier. This explains why it is possible to hear sounds and receive radio signals even if there is something between you and the source of the waves.

If the wavelength of the waves is shorter the spreading, diffraction, effect is much smaller as well. This explains why television waves are much more difficult to receive in hilly areas than radio waves which have a longer wavelength and why the diffraction of light is so difficult to observe.

20

This diagram below shows how it is possible to receive long wavelength radio signals in hilly areas at the bottom of deep glens. Terrestrial TV reception is not possible in these areas because TV waves have a much shorter wavelength that radio waves.

Its very small wavelength (about 600 nanometres (600 thousand millionths of a metre) for yellow light) is also the reason why diffraction of light is only big enough to be observed with very small obstacles. The fact that it can be seen at all is very good evidence for light being a wave.

21

Nuclear Radiations

AtomsEvery substance is made up of atoms. Each element is made up of the one kind of atom, sometimes these atoms are combined together to form molecules.Inside each atom there is a central part called the nucleus. The nucleus contains two particles:Protons: these have a positive chargeNeutrons: these have no charge.

Surrounding the nucleus are negatively charged electrons.

An uncharged atom will have the same number of protons and electrons.Consider the element helium, which has two neutrons and two protons in the nucleus, and two electrons surrounding the nucleus. This can be represented as:

Atom of Helium

Neutron (no charge) Electrons (negative charge)

Protons (positive charge)

IonisationAtoms are normally electrically neutral but it is possible to add electrons to an atom or take them away. When an electron is added to an atom a negative ion is formed; when an electron is removed a positive ion is formed. The addition or removal of an electron or electrons from an atom is called ionisation. It is important to remember that the nucleus remains unchanged during this time.

Ionising RadiationsThere are some atoms which have unstable nuclei which throw out particles to make the nucleus more stable. These atoms are radioactive. The particles thrown out cause ionisation and are called ionising radiations.

There are three types of ionising radiation:

Alpha particles are the nuclei of helium atoms. They have 2 neutrons and 2 protons in the nucleus and are therefore positively charged. Symbol: αBeta particles are fast moving electrons. They are special electrons because they come from within the nucleus of an atom. They are caused by the break

22

up of a neutron into a positively charged proton and a negatively charged electron. Symbol: β

Gamma rays are caused by energy changes in the nuclei. Often the gamma rays are sent out at the same time as alpha or beta particles. Gamma rays have no mass or charge and carry energy from the nucleus leaving the nucleus in a more stable state.Symbol: γ

Cloud chambers: A cloud chamber can be used to view ionising radiations.

α-particles will leave short thick tracks as they are large and collide easily with air molecules. This causes a lot of ionisation.

β-particles are much lighter than α-particles so make fewer collisions. During their collisions they are more likely to be deflected so the tracks are longer but more scattered. β-particles are less ionising than β-particles.

γ-rays have no mass and have very little ionisation. They leave no trace.

A cloud chamber Traces seen in a cloud chamber

Detecting Radiation:

A Geiger-Müller (GM) tube is used to detect α, β and γ radiation. If any of these enter the tube, ions are produced resulting in a small current flow. The current is amplified and a counter (or rate meter) counts the number of events giving an indication of the level of radioactivity.

Geiger Muller Tube and Rate-Meter or Counter.23

Geiger Muller Tube in more detail:

Radiation can also be detected by photographic film. Film badges containing photographic film are used by radiographers and engineers in nuclear power stations to monitor exposure to radiation.

Windows of different thicknesses can detect different types of radiation. Photographic film is kept behind the window. The film has a thin layer of silver-based chemical on its surface. The silver-salt is affected by light landing on it. Wherever the light lands, it changes the chemical and blackens or fogs the film surface. α, β or γ radiation have a similar effect on the film, and so it is used to detect them.

A third method of detecting radiation is the gamma camera. This uses the fluorescent property of certain substances such as zinc sulphide. This absorbs the radiation and gives out energy again as a tiny burst of light, called a scintillation. They may be observed by the naked eye or counted by a light detector.

Properties of radiationAlpha particles will travel about 5 cm through the air before they are fully absorbed. They will be stopped by a sheet of paper. Alpha particles produce much greater ionisation density than beta particles or gamma rays. They move much more slowly than beta or gamma radiation.

24

Beta particles can travel several metres through air and will be stopped by a sheet of aluminium a few millimetres thick. They have a lower ionisation density than alpha particles.

Gamma rays can only be stopped by a very thick piece of lead or by concrete. They travel at the speed of light and have a very low ionisation density.

You should be able to:

1. Write down three ways in which radiation can be detected.

2. Explain how one of these ways works.

3. Describe how gamma cameras work?

4. Explain why radioactive tracers should be gamma emitters? (Think about how penetrating each type of radiation is and where they are going to be detected.)

Activity:

When any of α, β or γ radiation is produced the nucleus of a radioactive atom decays. The activity of a source is the number of decays per second. This is measured in Becquerels or more usually kilo- or mega-Becquerels.

Becquerels (Bq) No unitActivity = Number of decays time

Seconds (s)Absorbed doseThe greater the transfer of radiation energy to the body the greater the chance of damage to the body. The absorbed dose, D, is the energy absorbed per unit mass of the absorbing material and is measured in Grays, Gy. 1 Gray is 1 Joule per kilogram. 1 Gy = 1 J/kg

A = N t

25

Grays (Gy) Joules (J)Absorbed dose = Energy mass Kilograms (kg)

The biological effects of radiationAll ionising radiation can cause damage to the body. There is no minimum amount ofradiation which is safe. The risk of biological harm from an exposure to radiation depends on:

• the absorbed dose• the kind of radiation• the body organs or tissue exposed.

The body tissue or organs may receive the same absorbed dose from alpha or gammaradiation, but the biological effects will be different. To solve this problem a radiation weighting factor WR is used. This is simply a number given to each kind of radiation as a measure of its biological effect. See below:

Type of radiation WR

Β particles, γ and X-rays 1Slow or thermal neutrons 3Protons and fast neutrons 10α 20

Equivalent dose:

When scientists try to work out the effect on our bodies of a dose of radiation they prefer to talk in terms of equivalent dose. The equivalent dose H is the product of D and WR.

Equivalent dose = absorbed dose x radiation weighting factor

Sieverts, Sv. Grays, Gy No unit

Example

A worker in the nuclear industry receives the following absorbed doses in a year.

30 mGy from gamma radiation, WR = 1300 μGy from fast neutrons, WR = 10

Calculate the equivalent dose for the year.

D = E m

26

H = DWR

H = DWR

For gamma H = 30 x 10³ x 1 = 30 x 10³SvFor neutrons H = 300 x 106 x 10 = 3.0 x 10³SvTotal H = 30 x 10³ + 3.0 x 10³ = 33 x 10³Sv or 33 mSv.

Background radiationEveryone is exposed to background radiation from natural and from man-made radioactive material. Background radiation is always present. Some of the factors affecting background radiation levels are:• Rocks which contain radioactive material, expose us to ionising particles• Cosmic rays from the sun and outer space emit lots of protons which causeionisation in our atmosphere• Building material contain radioactive particles and radioactive radon gas seeps upfrom the soil and collects in buildings, mainly due to lack of ventilation.• The human body contains radioactive potassium and carbon• In some jobs people are at greater risk. Radiographers exposed to X-rays used inhospitals and nuclear workers from the reactor.Natural radiation is by far the greatest influence on our exposure to background radiation.

Source of RadiationNatural

Annual Dose (mSv)

Source of RadiationMan Made

Annual Dose (mSv)

From Earth 0.40 Medical 0.25Cosmic 0.30 Weapons (fall

out)0.01

Food 0.37 Occupational 0.01Buildings (Radon) 0.80 Nuclear

Discharges0.002

TOTAL 1.87 TOTAL 0.272

The individual values above do not need to be memorised but notice that the annual dose equivalent per year is about 2 mSv.

The Effect of Ionising Radiation

Effects of radiation on living thingsAll living things are made of cells. Ionising radiation can kill or change the nature of healthy cells. This can lead to different types of cancer.

27

Uses of the properties of radiation:

Radiation can be used in the treatment of cancer. The radioactive source, cobalt-60 kills malignant cancer cells. Cobalt-60 is a γ-source which is kept in a thick heavy metal container. The source is rotated around the body centred on the cancerous tissue so the cancerous cells receive radiation all the time. However, as the source is moving the healthy tissue only receives the radiation for a short time. In order to minimise damage to healthy cells the applied dose has to be very accurately calculated.

The apparatus is arranged so it can rotate around the patient. The patient is irradiated from different directions. The tumour receives a maximum radiation dose from the beam while other organs and tissue get as little as possible.

Radioactive tracers help doctors to examine the insides of our bodies. Iodine-131 is used to see if our thyroid glands are working properly. The thyroid gland controls the rate at which our body functions. The thyroid gland absorbs iodine, so a dose of radioactive iodine (the tracer) is given to the patient. Doctors can then detect the radioactivity of the patient’s throat, to see how well the patient’s thyroid is working.

Iodine-131 is chosen so that:1. It concentrates in the organ to be examined.2. It loses its radioactivity quickly.3. It emits gamma rays which can be detected outside the body.

Sterilisation:As radiation can be used to kill cells it can also be used to kill bacteria or germs. In the past, medical instruments such as syringes had to be sterilised by heat or chemicals. Now cheap, plastic throw away syringes can be used. They are pre-packaged and then irradiated by an intense gamma-ray source. This kills any germs but does not make the syringe radioactive.

Other medical equipment such as scalpels and bandages can be sterilised by the same method.

28

In industry the penetrating power of gamma rays is also used to trace materials, often through pipelines. The strength of the source has to be very great so that the gamma rays get through the steel pipes and surrounding concrete and its strength usually has to remain high for longer as the pipelines can be very long. Similarly, by the use of tracers, pollution levels or water flow in rivers can be monitored using mobile detectors.

Gamma rays can also be used to check for tiny cracks in aircraft or to check the thickness of materials.

In agriculture, it is important to know how well plants make use of fertilisers. To do this, a small amount of radioactive tracer is sometimes added to the fertiliser.. The tracer’s progress through the plant can then be monitored to give an indication of how the fertiliser is being used by the plant.

Safety with radioactivity• Always use forceps or a lifting tool to remove a source. Never use bare hands.

• Arrange a source so that its radiation window points away from the body.

• Never bring a source close to your eyes for examination. It should be identifiedby a colour or number.

• When in use, a source must be attended by an authorised person and it must bereturned to a locked and labelled store in its special shielded box immediatelyafter use.

• After any experiment with radioactive materials, wash your hands thoroughlybefore you eat. (This applies particularly to the handling of radioactive rocksamples and all open sources.)

• In the U.K. students under 16 may not handle radioactive sources.

Reducing the equivalent dose:• Use shielding, by keeping all radioactive materials in sealed containers made ofthick lead. Wear protective lead aprons to protect the trunk of the body. Anywindow used for viewing radioactive material should be made of lead glass.

• Keep as far away from the radioactive materials as possible.

• Keep the times for which you are exposed to the material as short and as few aspossible (dentists often ask you to hold the X-ray film in place while they keep

29

well behind the screen. This may seem unfair - but the dentist takes lots of X-raysover the year and so is at greater risk.)

Radioactive hazard warning sign

The following symbol for a radioactive substance should be on the front of all containers of radioactive sources.

• The sign should be displayed on doors/corridors leading to where radioactivematerials are stored.

• The sign should be displayed on all containers of radioactive materials.

Half-life

Radioactive decay is a random process. This means that for a radioactive source, it can never be predicted when an atom is about to decay. In any radioactive source, the activity decreases with time because the number of unstable atoms gradually decreases leaving fewer atoms to decay.The half-life of a radioactive source is the time for the activity to fall to half its original value.

We can model this process in the Lab. by using small building blocks, about 500 in total. Each person in the class can get a small handful of these. Taking great care not to let any fall on the floor they can be thrown over the desk. Any which land with the bump sticking directly upwards can be removed. Just keep these to the side and don’t use them again. One person then needs to count the total number of blocks which have been removed. A table with two columns, number of decays and time can be drawn. This can be recorded on the board with the number of blocks representing the number of decays and each time the blocks are thrown representing a time of 1 s. The process is then repeated and again the total number of decays for the class is recorded. Repeat again until no more blocks are left.

When you have finished a graph can be drawn like the one shown underneath. A curve of best fit should be drawn smoothly through the points.

30

0

5

10

15

20

25

30

35

40

45

0 5 10 15 20 25 30 35 40 45 50

Time

Coun

t rat

e

Graph of half-life simulation with lego blocks

This demonstration is a model of what happens when a radioactive material decays.

Your teacher may show you a demonstration of protactinium decaying; otherwise watch the video of this. Note that the count rate needs to be corrected for background radiation. The results can now be recorded in a table. These can be used to plot a graph and compare it to the one above. You should notice the graphs are the same shape.

Examples:1. A Geiger-Muller tube and rate meter were used to measure the half-life of radioactive caesium-140. The activity of the source was noted every 60 s. The results are shown in the table. By plotting a suitable graph, find the half-life of caesium-140.

Time (s) 0 60 120 180 240 300 360

Count rate (counts/s) corrected for background

70 50 35 25 20 15 10

Correctedcount rate (counts/s) 70 _

31

60 _ 50 _ 40 _ 30 _ 20 _ 10 _ 0 _ Time (s) 0 60 120 180 240 300 360

From the graph the time taken to fall from 70 counts/s to 35 counts/s = 120 s 35 counts/s to 17.5 counts/s = 120 s

Average half life of caesium-140 = 120 s.

2. A source falls from 80 MBq to 5 MBq in 8 days. Calculate its half-life.80 → 40→ 20 → 10→ 5

This takes 4 half-lives (count the arrows) = 8 days Therefore one half life = 2 days

Nuclear Reactors

Nuclear reactors are used in many countries to produce electricity and are fuelled by Uranium. This is not a fossil fuel, so it does not produce Carbon Dioxide, but it is non-renewable and does produce radioactive waste which needs to be stored for a long time. However, for each kilogram of Uranium used it produces the equivalent energy of 25,000 kg of coal. While Uranium will eventually run out, it will last a lot longer than all fossil fuels.

Nuclear fission: Uranium decays naturally over a very long period of time. It will decay very quickly if hit by slow neutrons. The slow neutron hits the Uranium-235 isotope which causes it to split into smaller nuclei and emit 3 further neutrons. A large amount of energy is also emitted. Each of these 3 neutrons hits 3 other Uranium atoms and so on. This is known as a chain reaction (see diagram below). If this continues in an uncontrolled way the process would eventually result in a nuclear explosion. Nuclear fission involves the splitting apart of heavy nuclei. Note:

the incoming neutron is 'captured' before the nucleus splits the nucleus splits into several smaller nuclei

a number of neutrons are released during the fission reaction

32

Diagram showing a Chain Reaction: Uranium-235 is hit by a slow neutron producing a lot of energy, new elements and radioactive waste (not shown

above) with very long half lives.

In a controlled chain reaction only one neutron from each fission on average will strike another nucleus causing it to divide. In nuclear power stations the reaction is automatically controlled to give a constant release of energy. A serious accident in a nuclear power station could release tonnes of radioactive material into the atmosphere with disastrous and long term consequences, such as happened at Chernobyl in 1986. Even if no accidents happen, when the power station is decommissioned it will be contaminated.

Radioactive wasteNuclear power stations produce radioactive waste materials, some of which have half-lives of hundreds of years. These waste products are first set in concrete and steel containers then buried deep under ground or dropped to the bottom of the sea. These types of disposals are very controversial. Some scientists believe the containers will keep the radioactive material safe for a long time, other scientists are worried that the containers will not remain intact for such a long time. Most recently the British government has decided to dig up radioactive waste buried in the 1960’s near Dounreay in Scotland for fear of radioactive leakage.

The worst nuclear accident to date was the Chernobyl disaster which occurred in 1986 in Ukraine. That accident killed 56 people directly, and caused an estimated 4,000 additional cases of fatal cancer, as well as damaging approximately $7 billion of property. Radioactive fallout from the accident was concentrated in areas of Belarus, Ukraine and Russia. Approximately 350,000 people were forcibly resettled away from these areas soon after the incident.

33

Comparing the historical safety record of civilian nuclear energy with other forms of electrical generation, Ball, Roberts, and Simpson, the IAEA, and the Paul Scherrer Institute found in separate studies that during the period from 1970 - 1992, there were just 39 on-the-job deaths of nuclear power plant workers worldwide, while during the same time period, there were 6,400 on-the-job deaths of coal power plant workers, 1,200 on-the-job deaths of natural gas power plant workers and members of the general public caused by natural gas power plants, and 4,000 deaths of members of the general public caused by hydroelectric power plants. In particular, coal power plants are estimated to kill 24,000 Americans per year, due to lung disease as well as causing 40,000 heart attacks per year in the United States. According to Scientific American, the average coal power plant emits more than 100 times as much radiation per year than a comparatively sized nuclear power plant in the form of toxic coal waste known as fly ash.

You should be able to use information from the above article and your own research to find out about the advantages and disadvantages of nuclear energy. The table below is a useful way of summarising your ideas.

Advantages and Disadvantages of Nuclear Energy from Fission.Advantages Disadvantages

Nuclear Fusion:

This produces huge amounts of energy without producing carbon dioxide or radioactive waste. In this process two light nuclei join together to make a heavier nucleus. The reaction that releases energy in the Sun is a fusion reaction.

The reaction that releases energy in the Sun is a fusion reaction. Attemps are being made to build a fusion reactor on Earth. It is very hard to build a container that does not melt in the very high temperatures required for fusion to take place. Some experts predict that the problem will be solved within a

34

few decades. The article below explains some of the difficulties which need to be overcome. You do not need to know all the details just that it is technically very hard to produce energy this way.

Nuclear fusion – your time has come

(from The Observer 16 Sept, 2012.)

Harnessing nuclear fusion to create cheap, safe and sustainable energy used to be a futuristic joke. But its day is almost upon us

The Joint European Torus (Jet) at Culham, Oxfordshire. Photograph: AFP/Getty Images

Every year, one typical coal-fired power station devours several million tonnes of fuel and produces even more carbon dioxide. Burning stuff has the virtue that it is simple but it is very brutal. That volume of carbon dioxide is damaging the atmosphere and, in the longer term, the fuel will run out. It is clear that the world needs an alternative to generating energy by setting fire to things.

For a good few years now, nuclear fusion has looked like offering a solution to the problem. For every 100 tonnes of coal we burn, fusion has the potential to deliver the same amount of energy, without any carbon dioxide emission, using a small bath of water and the lithium contained in a single laptop battery. Moreover, it would be inherently very safe and would not produce any significant radioactive waste. Lest there be any confusion, the science behind this way of harnessing the energy locked away inside the atomic nucleus is entirely different from that used in current nuclear fission reactors. It almost seems too good to be true … but it isn't.

35

A fusion reactor called ITER is currently under construction in France and is due to start operation in 2020. Its principal goal is to determine the viability of fusion at the scale of a power station. Success is widely anticipated and there are already plans afoot to build a "demonstration power plant" to start operating in the 2030s.

Fusion is the reason that our sun keeps shining. Deep in the sun's core is a hot, dense sea of electrons and protons – the remnants of hydrogen atoms that have been torn apart by the high temperature created as a huge mass of hydrogen falls in on itself under the action of gravity. Under these extreme conditions two protons can fuse together, releasing energy in the process. Without this, the sun would stop burning and collapse under the weight of its own gravity.

The Sun is very inefficient due to the fact that proton-proton fusion within the sun is very rare: it takes a proton in the sun around 5bn years to fuse. For that reason ITER will not fuse protons; instead it will fuse deuterium and tritium. These are heavy partners to the proton (deuterium has an extra neutron and tritium has two extra neutrons). The extra mass helps to ensure that fusion is far easier to achieve and, combined with the fact that ITER will operate at a temperature 10 times that in the sun's core, it should be possible for ITER to generate energy at a rate of 500M watts – the level of a small power station. Unlike the Sun, ITER cannot exploit gravity to compress the plasma (the name for the hot fuel mix): instead the idea is to squeeze it inside a doughnut-shaped container using magnets. The energy from a single deuterium-tritium fusion reaction is carried away by a neutron and a helium nucleus. The latter is used to heat the plasma, thereby reducing the need to heat it from an external source, while the neutron can be absorbed in the walls, heating them up. In a reactor, that heat can then be extracted and delivered to the grid.

The fuel is not too hard to come by either, and it won't run out in the next few million years at least: deuterium is plentiful in seawater and tritium can be manufactured by reacting those outgoing neutrons with lithium.

It used to be joked that fusion is always the fuel of the future, but that is no longer fair. In the words of Professor Chris Llewellyn Smith, director of energy research at Oxford University, "with enough money we could probably build a fusion reactor now but it would not be economical. The challenge is to make it reliable and competitive." This confidence is built upon the fact that fusion is now a routine event at the Joint European Torus (Jet) in Culham, Oxfordshire.

In many ways, Jet is a mini-ITER: the design is broadly similar and the basic physics is the same. Research at Jet over the past 20 years has led to continuous advances in understanding the behaviour of the plasma. These have led to reduced heat loss due to turbulence and that implies improved efficiency. It is research like this that makes the experts so confident that ITER's time has come. That is not to deny that challenges remain: materials to handle the heat and neutron damage need to be designed, the production of tritium using lithium needs to be demonstrated and the behaviour of a burning plasma has yet to be fully explored.

36

The construction phase of ITER is projected to cost €13bn (£10.5bn), a sum that is dwarfed by the annual subsidy to the fossil fuel industry, which the International Energy Agency estimated to be at least $400bn (£248bn) in 2010 alone. Moreover, the cost is shared between the seven ITER members (the European Union, China, India, Japan, South Korea, Russia and the US) and amounts to a UK contribution of a mere few tens of millions each year. The stakes are surely too high to quibble about funding at this level.

If we want to get by without burning fossil fuels then there is a huge gap to fill. With the exception of solar power, renewable energy sources can't satisfy the demand and it is not at all clear that renewables will ever be cheap enough to stop people burning fossil fuels. The wise course must surely be to invest in research across the board. As for fusion, the bottom line is not whether we can do it but whether we can do it at a price people will be prepared to pay.

37