Radioactivity 07

transcript

RADIOACTIVITY

12 SACE PHYSICS-STAGE 2SECTION 4 TOPIC 3PRINCE ALFRED COLLEGE

RADIOACTIVITY

Henri Becquerel, a French physicist was working with potassium uranyl sulfate (a very fluorescent compound) in the 1890’s.

RADIOACTIVITY

He placed samples of the salt on photographic plate wrapped in light tight black paper. After leaving it in the sun for a while, the plate was developed. As the plate was ‘fogged’, he assumed that X-rays were produced.

RADIOACTIVITY

He repeated the same experiment on a cloudy day and since there was no sun, there should be no UV to cause the fluorescence and so no X-rays produced. However, the plates were ‘fogged’. Becquerel had stumbled upon the fact that something in the salt was unstable (Uranium).

RADIOACTIVITY

The reason why the plates were fogged was that the Uranium was emitting particles to become more stable. We call this phenomena radioactivity.

RADIOACTIVITY

The Curies (Marie and Pierre), were interested in his work and named it “Radioactivity”.

RADIOACTIVITY

They continued the work and managed to discover two new elements polonium (named after Marie’s homeland) and radium (named due to its intense radioactivity).

RADIOACTIVITY

It has been determined that many isotopes of radioactive nuclei are unstable. They become more stable by emitting sub atomic particles or photons. Radioactive nuclei decay by the emission of alpha or beta particles or gamma radiation. These methods will be covered in more detail later.

NEUTRON/PROTON STABILITY

By comparing stable nuclei, we can examine their neutron/proton ratio. This is shown on the graph where protons are on the x-axis and neutrons are on the y-axis. The line shows stable isotopes.

Anything off the line will spontaneously decay. For light elements (up to approx. 20) the N/Z ratio is close to 1.Towards the top end, the ratio is more like 1.6/1.

This suggests that protons and neutrons bind in pairs. However, as the line curves upwards, more neutrons are needed to overcome the repulsive force between protons.

Eventually, at 84 protons, no amount of neutrons can dilute the repulsive force and all elements above Z = 84 are radioactive. Elements Z = 84 to 92 can be found in the Earth’s crust but above 92 the nuclei are too unstable to still be present in the crust.

Remember, the reason why a nucleus stays together is because of the strong NUCLEAR FORCES found between NUCLEONS (Neutrons and/or protons).We discussed this in the last topic (topic 2).The ELECTRICAL REPULSION between like charged (positive) protons tries to tear the nucleus apart.

At low atomic numbers (under 20), the attractive nuclear forces overcome the repulsive electrical forces within the nucleus.

The protons and neutrons exist in a 1 to 1 ratio.

At higher atomic numbers (between 20 and 84), the nucleus gets larger.The repulsive electrical forces act between all protonsThe attractive nuclear forces are only found between adjacent nucleons.The nucleus needs more neutrons to create a stronger nuclear force without adding to the repulsive electrical force.

This is why elements with high atomic numbers have a greater number of neutrons than protons.Eventually the nucleus gets so large (atomic number = 84) that no number of neutrons would create enough of a attractive nuclear force to counteract the high number of protons. The nucleus then becomes unstable and will eventually break apart. This is called radioactive decay.

THE FOUR TYPES OF RADIOACTIVE DECAY

There are four types of radioactive decay included in the syllabus.

They are:– alpha,– beta minus– beta plus– gamma decay.

ALPHA DECAY

Very heavy nuclei are often unstable as they contain too many protons. Typical alpha emitters have an atomic number > lead (82).Alpha particles are helium nuclei . Alpha particles are emitted, as they are extremely stable. They have high binding energy.

ALPHA DECAY

When a nucleus undergoes alpha decay, the parent nucleus will suffer a decrease in atomic number (Z) of two and a decrease of four in mass number (A). The daughter nucleus is now a different element.Alpha Decay Example

ZAX Y+ (Note: He)2

ALPHA DECAY

An example is:Parent Daughter

This is a “Nuclear Reaction” as new elements have been produced.The daughter nucleus will be more stable than the parent nucleus (the daughter nucleus has a lower atomic number).

24Ra Rn+ He 86

ALPHA DECAY

Note, the sum of the atomic numbers and the mass numbers are the same on both sides of the equation. Conservation laws still hold.

The above equation is EXOTHERMIC as there is a loss of mass in the reaction. The energy produced goes to the alpha particle as kinetic energy.

24Ra Rn+ He 86

ALPHA DECAY

Alpha particles have a relatively high mass and so are ejected with a moderate speed, typically about 2 x 107 ms-1. Because their charge is high (2+) and speed low, they interact with matter easily, thus they are able to penetrate air only by a few centimetres.

ALPHA DECAY

A thin piece of cardboard is enough to stop a beam of alpha particles.As alpha particles do have large amounts of kinetic energy, they can damage human flesh by destroying parts of cells on impact.

ALPHA DECAY

When alpha particles come near atoms, they are strongly ionising. Their high charge means they can displace electrons easily leaving behind an ion pair (an ion and free electron). This will slow an alpha particle down.

ALPHA DECAY

Alpha particles are emitted with quantised energy, which suggests that the nucleus may have a discrete energy level structure.

DISCRETE ENERGY LEVELS

Let’s take a look at the alpha decay of Radium to Radon.

Radium decays to Radon at different energy levels.

N uc le us S he lls

R ad o n 222Exc ited S ta te 3

R ad o n 222G ro u n d S ta te

A B C D

E ne rg ya bo v etheg ro undsta te o fR a do n

– This suggests that the nucleons are arranged in the nucleus into energy shells (just like electrons).

N uc le us S he lls

A B C D

-particles are ejected at certain discrete velocities (energies). The energy depends on which level the Radium decays to in the Radon.

N uc le us S he lls

A B C D

Example: In the diagram, Ra226 decays giving off an B particle that has a specific Kinetic Energy when it decays to Rn222 in the 2nd excited state.

N uc le us S he lls

A B C D

The Rn222 then might return to the ground state giving off a photon of energy in the MeV range called a GAMMA PHOTON ()

N uc le us S he lls

A B C D

THE EFFECTS OF ELECTRIC AND MAGNETIC FIELDS ON DECAY

As alpha particles are positively charged, they will be deflected by electric fields and magnetic fields. The force they experience can be found from F = Eq. -ive p la te

+ ive p la te

24 ++He

This is in contrast to gamma rays or an x-ray that would not be deflected by an electric field because they do not have a charge.

The path of the alpha particle is parabolic. As the mass of an alpha particle is relatively large, the acceleration is low compared to other forms of radiation.

In a magnetic field, the deflection can be either upwards or downwards (depending on the direction of the field), in a circular path. The force can be found by F = Bqv.

24 ++He

Note- gamma photon radiation has no charge, therefore it is not affected by electric or magnetic fields, it instead passes straight through them.

Remember that the reason an atom undergoes alpha decay is because it has too many protons or neutrons.

It therefore ejects a helium nucleus.

BETA DECAY

Nuclei that have an imbalance of protons or neutrons can be unstable and also undergo radioactive decay. The process involves the change of a proton into a neutron or more commonly a neutron into a proton with the ejection of an electron from the nucleus.This decay is called beta decay, and the electron is referred to as a beta particle.

BETA+ DECAY

BETA+ DECAY (too many protons)-When a nucleus has to increase its neutron number to become more stable, a proton can spontaneously change into a neutron.

Alpha decay

Stable Isotopes

BETA+ DECAY

An electron (positively charged) is ejected with a neutrino.The positive electron is called a positron and is an example of antimatter. The atomic number is reduced by one but the mass number is unaffected.

BETA+ DECAY

On the line stability on the graph, any atom below the line would decay this way.

+eY+X 01+1

BETA+ DECAY

In the nucleus, the reaction is:

An example of this is:Beta + Decay Example

+ e+ CN 01+

BETA+ DECAY

Notice that both mass and charge are conserved.

A ‘positron’, a positively charged electron (the same mass as an electron) is ejected.The positron is an example of antimatter (“opposite of”).This is known as ‘proton decay”.

+ e+ CN 01+

BETA+ DECAY

The positron is known as the B+ particle.A Neutrino (v) is also released. We will discuss the purpose of the Neutrino later in the topic.Note a new element is formed. There are no natural positron emitters since positron half-lives are very small.Note- as the 13N might decay into a metastable form of 13C, the 13C could then drop down to a more stable state, giving off a GAMMA RAY.

BETA- DECAY

B- DECAY – (Too many neutrons).If a neutron is converted to a proton to become more stable and decrease neutron numbers, a normal negative electron is created and the anti neutrino ( ) is also ejected.

BETA- DECAY

This time the atomic number increases by one but the mass number remains constant. On the line stability on the graph, any atom above the line would decay this way.

BETA- DECAY

The reaction is…

In the nucleus, the reaction is:

This would be considered to be neutron decay.

_01-1 +eY+X A

10 +e pn

BETA- DECAY

An example of this is:Beta - Decay Example

The neutron has a half-life of about 1000 seconds (16.5 minutes) while the proton, electron and neutrino are all stable. Some recent research suggests the proton has a half -life of 1030 years, which is long enough to be of no concern to us.

125 +eC+B

PENETRATING POWERS OF BETA PARTICLES

Once free of the nucleus, beta particles are found to be more penetrating than alpha particles. They have a range of up to several metres in air but are absorbed by light metals such as aluminium.

As they have lower mass than an alpha particle but the same kinetic energy, they travel at higher speeds (near speed of light). As they have high speeds but only a single charge, they are less interactive with matter so they are less ionising than alpha particles.

THE EFFECTS OF ELECTRIC AND MAGNETIC FIELDS ON PARTICLES

Beta particles are charged like alpha particles and so can be deflected by electric and magnetic fields.

-ive p la te

+ ive p la te

Electron

Positron

As their charge can be either negative or positive, they can be deflected towards the negative or positive plates in a uniform electric field.

-ive p la te

+ ive p la te

In a magnetic field, their paths will be circular. As their masses are exactly the same, the radius of curvature will also be exactly the same.

Electron

Positron

SUMMARY OF +, -, and DECAY

The way in which a radioactive isotope decays can be predicted. The stability line diagram gives a clue to the general decay patterns.

Any nuclei with an atomic number greater than 83 will decay by alpha decay.Any nuclei with an excess of neutrons will decay by beta minus decay (-). It is above the line of stability.

Alpha Decay

Any nuclei with an excess of protons will decay by beta plus decay (+). It is below the line of stability.

Below is a summary of how an electron can be ejected from an atom.

(a) Photoelectric effect(b) Thermionic emission(c) Radioactive decay

Note (a) and (b) involve outer orbital electrons, while (c) involves a change in the nucleus.

NEUTRINOS AND ANTINEUTRINOS

Beta particles are emitted with a range of energies up to a maximum of a few MeV.It seemed strange that the electrons with the maximum kinetic energy carried away all the available energy, yet those with less than he maximum kinetic energy appeared to have energy missing.

This did not obey the law of conservation of energy. Other experiments with momentum confirmed that linear momentum was not conserved.

7N146C14 e- Speed and direction

of the electron if momentum was conserved.

e- Actual speed and direction of the electron.

In 1934 Enrico Fermi developed the theory of beta decay and that the conservation laws did hold because there was a particle that had yet to be detected carrying the lost energy and momentum.

He called this particle a neutrino (Italian for ‘little neutral one’). The antimatter of the neutrino ( ) is the antineutrino ( ).

Using the conservation laws, he postulated the properties for the neutrino. Neutrinos are uncharged. This is

because charge is already conserved. A neutron decays into a proton and an electron.

Neutrinos have zero rest mass but carry energy and momentum. The conservation laws would not hold otherwise.

Neutrinos react very weakly with matter. It took 25 years to detect them and there are millions of neutrinos that pass through the Earth from the sun as if the Earth was not there. This is because they have no real mass or charge.

– Finding Neutrinos (Open Explorer)

Neutrinos travel at the speed of light. As they have no mass but have energy, they must travel at the maximum speed possible - the speed of light.

The neutrino was accepted readily as it solved awkward problems but was not discovered until 1956. It is given the symbol (the Greek letter nu) and has zero atomic number and mass number.Beta decay can now be more fully described.

GAMMA DECAY

Gamma decay is the release of energy from an excited nucleus in the form of high-energy photons and usually accompanies alpha or beta decay.Refer to our discussion earlier in the topic where Radium-226 decays to Radon-222 with the ejection off an alpha particle PLUS A GAMMA PHOTON.

GAMMA DECAY

If gamma decay is to occur, the daughter nucleus from alpha or beta decay is left in an excited state. To become stable, energy is released without a change in atomic or mass number.

N uc le us S he lls

A B C D

GAMMA DECAY

When caesium-137 beta decays into barium 137, it is usually left in a metastable state (the nucleus is left in an excited state). The barium then undergoes gamma decay. (m indicates an excited nucleus).

GAMMA DECAY

Beta minus decay.

Gamma Decay.Gamma Decay

13755 +eBaCs m

56137Ba Ba +m

GAMMA DECAY

The half life of the Beta decay is 30.6 years while the half life of the Gamma decay is only 2.6 minutes.The energy contained in gamma photons is less than 1 MeV with values being as low as a few keV common. The wavelengths of gamma rays are in the region of 10-9 to 10-14 m. This means the wavelengths of gamma rays and X-rays are similar, their distinction is their source.

GAMMA DECAY

X-rays come from electron transitions outside the nucleus, while gamma rays come from the nuclear process. Gamma decay results in several photons of discrete energies being created so specific gamma sources will produce specific gamma photons (a line spectrum).

GAMMA DECAY

The properties of gamma rays include: As they are high energy e-m radiation,

they have high frequency and short wavelength and travel at the speed of light. This means they are extremely penetrating like X-rays.

Their range in air, depending on frequency, can be a number of metres.

GAMMA DECAY

They can penetrate several centimetres of lead or concrete before being absorbed. 4 cm of lead reduces the intensity of a gamma ray beam by 10%.

They carry no charge and are undeflected by electric and magnetic fields and are therefore only weakly ionising. They cannot attract electrons but can knock them out similar to the photoelectric effect.

Image from Fermi Gamma ray Telescope (2008)

HALF-LIFE AND ACTIVITY

Radioactive decay is a completely random process. No one can predict when a particular nucleus will decay into its daughter. Statistics however, allow us to predict the behaviour of large samples of radioactive isotopes.

We can define a constant for the decay of a particular isotope, which is called the half-life.This is defined as the time it takes for the activity of the isotope to fall to half of its previous value. From a nuclear point of view, the half-life of a radioisotope is the time it takes half of the atoms of that isotope in a given sample to decay.The unit for activity, Becquerel (Bq), is the number of decays per second.

An example would be the half-life of tritium (1H3), which is 12.5 years. For a 100g sample, there will be half left (50g) after 12.5 years.

12.5 years

After 25 years, one quarter (25g) will be left.After 37.5 years there will be one eighth (12.5g) and so on.AnimationAnimation 2 (with sound)

25years

37.5years

25 g12.5 g

The decay curve is exponential. The only difference from one sample to another is the value for the half-life.NOT EXAMINABLEIf a sample initially contains No atoms, then after n half-lives the number of remaining atoms, N, will be given by:

1 N Non .2

The half-life does not indicate when a particular atom will decay but how many atoms will decay in a large sample. Because of this, there will always be a ‘bumpy’ decay for small samples.

EXAMPLE 1

(a) Radium-226 has a half-life of 1622 years. A sample contains 25g of this radium isotope. How much will be left after 3244 years?

(b) How many half-lives will it take before the activity of the sample falls to below 1% of its initial activity? How many years is this?

EXAMPLE 1 SOLUTION

(a) 3244 years is 2 half lives (2 x 1622) N= No(1/2)n

= 25 x (1/2)2

= 25 x (1/4)=6.25

EXAMPLE 1 SOLUTION

(b) The activity of a radioactive sample is directly proportional to the number of remaining atoms of the isotope. After t1/2, the activity falls to ½ the initial activity. After 2 t1/2, the activity is ¼. It is not till 7 half-lives have elapsed that the activity is 1/128th of the initial activity.

So, 7 x 1622 = 11354 years

EXAMPLE 2

A Geiger counter is placed near a source of short lifetime radioactive atoms, and the detection count for 30-second intervals is determined. Plot the data on a graph, and use it to find the half-life of the isotope.

EXAMPLE 2

Interval Count1. 124562. 78043. 51504. 30345. 21936. 12787. 730

EXAMPLE 2 SOLUTION

The data are plotted on a graph with the point placed at the end of the time interval since the count reaches this value after the full 30 seconds.

EXAMPLE 2 SOLUTION

A line of best fit is drawn through the points, and the time is determined for a count rate of 12 000 in 30 seconds. Then the time is determined for a count rate of 6000, and 3000.

EXAMPLE 2 SOLUTION

t(12 000) = 30st( 6000) = 72s, so t1/2 (1) = 42st( 3000) = 120s, so t1/2 (2) = 48s The time difference should have be the half-life of the sample.

EXAMPLE 2 SOLUTION

Since we have two values, an average is taken.

t s1 2

EFFECT OF IONISING RADIATION ON LIVING MATTER

Besides alpha, beta and gamma radiation, there are other types of radiation that causes ionisation. This includes X-rays, neutrons and protons. Different types of radiation ionise atoms in different ways, however, the result on living tissue can be devastating.

Particles such as alpha, beta particles and protons are all charged themselves. As they pass through tissue, they can remove electrons using the coulombic force. As the energies required to remove electrons is in the order of 10 eV and alpha particles have energies of 10MeV, one alpha particle has the ability to ionise many atoms.

It can be seen that many alpha particles are released every second and so the likelihood of damage is great.

Neutral particles such as neutrons can only ionise atoms by direct collision with an atom. It can collide with a nucleus and fuse with it. This can make the nucleus unstable and then decay into new nuclei with large amounts of energy. They can then collide with other atoms and ionise them.

This breaks bonds and produces structural damage to the tissue. Neutrons can also collide directly with electrons knocking them out and ionising the atoms.

High-energy photons such as X-rays and gamma rays can remove electrons in photoelectric interactions. Gamma rays can be absorbed by the nucleus causing charged particles to be emitted with high energies causing further ionisation.

IONISING RADIATION DAMAGE TO LIVING MATTER

Removing electrons from atoms can…

- Cause molecules in living tissue to break down.

- DNA can be affected, this can lead to defective cells.

- Genetic defects.

IONISING RADIATION DAMAGE TO NON-LIVING MATTER

Ionising radiation can affect non-living material.

Plastics and paints often fade from high energy particles ionising the atoms within them.

Ionising radiation can be particularly devastating to materials used in space as there is no protection from our atmosphere.

POSITRON EMISSION TOMOGRAPHY - PET

What is PET?Nuclear medical imaging techniqueProduces 3D image which detects changes within tissues or organs.

Examines chemical activity for:– cancers,– heart problems– Depression– Alzheimer's disease– Epilepsy– Brain function after a stroke

.Why is PET special?Unique radiopharmaceuticals (radioisotopes) + Unique imaging technique– Equals

Unique information

Involves a radiopharmaceutical injected into the bloodstreamRadiopharmaceuticals become concentrated in body tissueDifferent tissues take up different radiopharmaceuticals– Different radiopharmaceuticals are required.

Radiopharmaceuticals absorbed by areas of interest e.g. tumoursThey then decay emitting a positronCollides with electronAnnihilates producing gamma photonsDetected by sensorsLocation then determined.

Man made radioactivity“Neutron poor” - does not happen in natureaccelerator - cyclotron

Protons

Add proton(cyclotron)

Radiopharmaceuticals are produced by:– Firing protons or deuterons into nucleus

Use cyclotrons– Or other particle accelerators

Produces radioactive isotopes which decays by: +

– Positron

Positron antimatterAnnihilates electron

Annihilation must obey conservation lawsCharge– Net charge is zero before and after collision

Linear momentum– Must be conserved before and after collision

Energy– Must be conserved before and after collision

Only final system which allows these conditions is:– 2 gamma ray photons simultaneously produced– traveling at 180o to each other.

Energy of Photons?

E = mc2

E = 9.10938188 x 10-31 x (3.00 x 108)2

E = 8.198 x 10-14 JE = 5.124 x 105 eVE = 0.5124 MeV

Photons from annihilation are detected, not positrons.180° simultaneous production advantage– Detect 1 with standard gamma camera– Detect both with modified gamma camera– Detect both with dedicated PET scanner

PET CAMERAS

Full ringmulticrystal

Part-ringmulticrystal

Full-ring NaI

Gamma CamerasCoincidence Collimated

16cm 25cm 40cm

Speed(count rate) Resolution Contrast

Different Detectors

38cm 38cm 16cm 16cm38cm 25cm

Singlephoton

Slowinsensitive

FastInsensitiveResolution

OptimalMostversatile

Optimised for FDG

Detector block

Crystal

Photo- multipliers

Detecting Gamma Photons

What do you see?

What is FDG?Fluorodeoxyglucose2-fluoro-2deoxy-D-glucose

Radioactive 18F is used so that the glucose produces gamma rays for detection. 18F concentrates in high glucose using cells e.g.– Heart– Brain– Kidney– Cancer cells– Inflammatory conditions

Reflects very well the distribution of glucose uptake

Normal FDG Uptake

High: - Brain - Urinary tract (bladder, kidneys)

Medium: - Liver - Muscle - Bone marrow

Low/no: - Lung - Bone

Attenuation Corrected Scans

*Cardiac uptake varies from high-none* Bowel activity varies from high-none

Normal FDG UptakeMuscle

Muscle

High: - Renal system

Medium: - Muscles

Attenuation Corrected Scans

Influenced by Insulin, Blood Glucose etcPhosphorylated but not metabolised furtherTherefore is trapped 110 min half life allows remote transport

Another radioisotope which is used is:Oxygen 1515OUsed to measure:– Brain blood flow– Blood volume– Oxygen extraction

Uses 15O labelled gaseous tracers– CO2, CO, O2

Administered by inhalationAlso used for organ blood flow– Uses 15O labelled water or butanol

15O produced by particle accelerators– Cyclotron

Easiest is 14N– Lowest energy required

Reaction?

Calculate binding energiesType of reaction?Energy required?

01N H O n

15O Half-life2 minutes– Must be created on site

To create H215O

Heat (700oC) 15O with H2

Vapour extracted into saline

Old Technique!

Lawrence invented cyclotron in 1930!

Lawrence 1938

PET Study 1952

Brownell & Aronow

PET at the RAH 1968

18F bone scan

Modern PET Scanner

World PET Numbers (July 2000)Cameras Per Million

Belgium 18 1.78Germany 80 0.97Switzerland 7 0.95Denmark 4 0.75Sweden 6 0.67USA 144 0.52Austria 4 0.52Finland 2 0.38Japan 37 0.29Australia 5 0.26 (0.31)Canada 8 0.26Netherlands 4 0.24UK 14 0.23Italy 12 0.21Spain 8 0.21France 8 0.13

CT Acquisition

PET Emission acquisition

Combined PET-CT

Co-incident Detection

Normal Brain

Alzheimer’s

Brain Tumours

Viable tumour

Case Study 1: LymphomaThere is a focal region of increased activity in the mid to lower left lung laterally, consistent with

intraparenchymal lung involvement at this site and there is a small region of activity at the pleural margin of the mid to lower left lung posterolaterally.

Case Study 3: Lymphoma

Case Study 5: Head and Neck CancerMetastatic lymphadenopathy is seen in two mid right cervial nodes, one upper left cervical node, intensely

in the subcarinal region, right mid and infrahilar region and retrocarinal region.

As radiopharmaceuticals have short half lives– Cyclotron must be located close to PET

hospitals– Time is important, not distance.

Source of Tracer

Cyclotrons

PET scanners

0 1 2 3 4 5

Time (Hr)

55 Minutes between patients, 5mCi dose

Cyclotrons and PET at the AustinPET is a perfect example of how a cross-over question could be structuredBesides PET– From syllabus

Question could include:– Production of radioisotopes– Calculation of binding energy– Calculation of photon energies– Decay equations

Radioactivity 07

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