Unit 1.17 Radioactive Emissions
What is Radioactivity?
The nuclei of certain atoms are unstable. This may be because they have too many neutrons or too few neutrons or are just too big or have been left with too much energy after having changed to a more stable nucleus (decayed).
The atom
• Most matter is made up of atoms.
• An atom consists of two main parts.
The Nucleus
The orbiting electrons
The Nucleus
• The nucleus contains two sorts of particles - Protons and Neutrons.
• The nucleus contains all of the positive charge.
• The nucleus contains almost all of the mass of the atom.
• The size of the nucleus is very very small compared to the size of the atom.
The Orbiting Electrons
• The electrons are negatively charged.
• Because the whole atom has no overall charge,
the number of electrons = the number of protons.
• Electrons are very, very, very small and so an atom is mostly empty space.
The Particles in an Atom
Particle Mass Charge
Proton 1 a.m.u. +1 e
Neutron 1 a.m.u. 0
Electron 1/1840 a.m.u. -1 e
where 1 a.m.u. is one atomic mass unit.
and e is the size of the charge on an electron
Atomic Symbols
We can describe an atom by recording
the number of protons - the Atomic Number (the Proton Number Z)the number of nucleons - the Mass Number (the Nucleon Number A) the chemical symbol for the element.
Isotopes
• All of the atoms of an element have the same number of Protons.
• The atoms can have different numbers of neutrons.
• Versions of an element with different numbers of neutrons are called Isotopes.
• The Isotopes of an element have the same Atomic Number but different Mass Numbers.
• All elements have different Isotopes.
• Some Isotopes may be radioactive.
Models of the Atoms
Models of the Atoms
Dalton's Model
• Dalton's model of atoms was tiny spheres.
• These were thought to be the tiniest bits of matter that could exist.
• They could not be split into smaller bits.
The Electron and the Plum Pudding Model
• J.J.Thompson discovered the electron and showed that it was negatively charged, was very small and came from inside atoms.
• The new model was a positively charged sphere with electrons scattered about inside (the plums in the pudding).
• The negative charge on the electrons balanced the positive charge on the pudding.
Rutherford's Alpha Particle Scattering Experiment and the Nuclear Atom
Main Results
i. Most alpha particles go straight through the thin gold foil
ii. Some alpha particles are scattered through a small angle.
iii. A very small number are deflected through very large angles i.e. they bounce back
Alpha Radiation (a)
Ionising Ability
• Alpha radiation causes a great deal of ionization.
Absorption - Range
• Each time an alpha particle ionises an atom it uses some of its energy.
Because it ionises a lot of atoms per millimetre along its path, its range is short.
5 - 6cm of air or a thin sheet of paper will stop alpha radiation.
Electric Charge
• An alpha particle is positively charged.
It carries twice the charge of a proton, +2e.
( e is the size of the charge on an electron,
e = electronic charge = 1.6 x 10-19C)
An alpha particle can be deflected by electric and magnetic fields.
Mass
• An alpha particle has a mass of 4u.
1u is approximately the mass of a neutron or a proton.
( 1u is the mass of 1/12 of the mass of an atom of the isotope Carbon-12)
Nature
• An alpha particle consists of two protons and two neutrons.
This is the same as a nucleus of Helium-4 (42He).
Uses
• Alpha emitters (Americium-241) are used in smoke detectors.
Smoke particles absorb the Alpha particles and trigger the alarm.
The Mechanism of Alpha Decay
• When a nucleus emits an Alpha Particle
the proton number decreases by 2
the nucleon number decreases by 4.
Example - Americium-241
24195Am 23793Np + 42a
Beta-minus (b-) Radiation
Ionising Ability
• Beta-minus radiation causes much less ionization than alpha particles
Absorption - Range
• Because the Beta-minus particles cause less ionization, they are far more penetrating.
Beta-minus particles can travel through more than 30cm of air and through several millimetres of aluminium.
Electric Charge
• A Beta-minus particle carries negative charge.
Beta-minus particles carry the same charge as an electron, -1e.
A Beta-minus particle can be deflected by electric and magnetic fields.
Mass
• The mass of a Beta-minus particle is the same as the mass of an electron.
The mass of a Beta-minus particle is 1/1800 u.
Nature
• A Beta-minus particle is a very fast electron that has been emitted from the nucleus.
Uses
• Beta-emitters such as Strontium-90 are used to measure the thickness of paper and plastic sheets.
A Radioactive Isotope is placed above the paper and a detector below.
The amount of Beta particles passing through the paper depends upon the thickness of the paper.
The count rate can be used to control the pressure acting on rollers which change the thickness of the paper
The Mechanism of Beta-minus Decay
• A neutron in the nucleus changes into a proton and a very fast electron - the Beta-minus particle.
The Beta-minus particle is emitted.
The proton number increases by 1.
The nucleon number is unchanged
(The number of neutrons has decreased by 1).
Example - Strontium-90
9038Sr 9039Y + 0-1b-
Beta-plus (b+) Radiation
• Beta-plus decay occurs only rarely in Nature but does occur when certain man-made radiaoactive isotopes decay.
Absorption - Range
• As soon as a Beta-plus partcle encounters an electron, they undergo mutual annihilation and a Gamma photon is produced.
Since all atoms contain electrons, the Beta-plus particle will not get very far except in a vacuum.
Electric Charge
• The Beta plus particle is positively charged.
It carries a charge of +1e.
Mass
• The mass of a Beta-plus particle is the same as the mass of an electron.
The mass of a Beta-plus particle is 1/1800 u.
Nature
• A Beta-plus particle is a fast positron.
A positron is the anti-particle of an electron.
The Mechanism of Beta-plus Decay
• A proton in the nucleus changes into a neutron and the fast positron - the Beta-plus particle.
The Beta-plus particle is emitted.
The proton number decreases by 1.
The nucleon number is unchanged
( the number of neutrons has increased by 1).
Example - Carbon-11
116C 115B + 0+1b+
Gamma (g) Radiation
• After Alpha or Beta decay, a nucleus may be left in an excited energy state.
It can give out this energy in the form of electromagnetic radiation.
The photons emitted have a high energy and frequency.
They are called Gamma (g) Rays or Gamma Photons
Ionising Ability
• Gamma radiation causes only a small amount of ionisation.
Absorption - Range
• Because it interacts so little with matter, it is very penetrating.
The amount of Gamma Radiation is reduced by several centimetres of lead but it is not stopped.
Electric Charge
• None
Mass
• None
Nature
• High frequency, short wavelength electromagnetic radiation.
Uses
• Tracers in medicine and in industry.
• Treatment of cancer - Cobalt-60.
• Gamma sometimes follows on from Alpha or Beta Decay.
The proton number is unchanged
The nucleon number is unchanged
Summary
Property Alpha ( Beta-minus ( Beta-plus ( Gamma (
Charge +2e -1e +1e 0
Rest Mass 4u 1/1800 u 1/1800 u 0
Penetrating Ability 5cm of air, thin paper 30cm of air, few mm of Al Annihilated during interaction with electron A long way. Keeps going through lead.
Nature Helium nucleus fast electron positron electromagnetic radiation
Ionising Ability heavily light very light.
Stable Nuclei
• For stable nuclei with small Proton Numbers, the number of Protons is almost equal to the number of Neutrons.
• For stable nuclei with larger Proton Numbers there are more neutrons than protons.
• Most stable nuclei have an even number of protons and an even number of neutrons.
Two protons and two neutrons (a Helium Nucleus) form a particularly stable combination.
Unstable Nuclei
• Radioactive decay tends to produce nuclei which are nearer to the line of stability until a stable nucleus is formed.
• Nuclei above the line tend to be Beta-minus emitters.
• Nuclei below the line may be Beta-plus emitters.
• Nuclei with very large Proton Number tend to be Alpha emitters.
Radioactive Decay
Activity
• The number of disintegrations per second is known as the activity of the source.
Activity is measured in Becquerels (Bq).
1 Bq = 1 disintegration per second.
• This is not quite the same as count rate as measured using a Geiger-Muller Tube and Scaler because the G-M Tube does not detect a count every time a nucleus decays.
• It is not possible to predict when a a particular radioactive nucleus will decay.
• Because large numbers of nuclei are involved it is possible to apply statistics and so it is possible to state
the chance of a nucleus decaying in a certain length of time (usually 1 second).
the fraction of nuclei which will decay in a given length of time (usually 1 second).
An Experiment
• The number of counts per minute is recorded many times for a radioactive sample with a long Half-life.
• The number of times a particular value occurs (the frequency) can be plotted against the value for the count rate as a Histogram.
This sort of shape is typical for a Random Event
Throwing Dice - A Model of Radioactive Decay
• The fact that radioactive decay is a random event suggests that we should be able to model it using dice.
• When a die is thrown, the numbers 1-6 are all equally likely.
For the sake of the model, landing on a 6 represents the die "decaying".
• We cannot say when a particular die will land on a 6.
But we can say that the chance of a die landing on a 6 is 1/6.
and that if a large number of dice are thrown, 1/6 of them will land on a 6.
• Suppose a large number of dice were thrown over and over again.
The number of dice landing on a 6 each time could be counted.
A histogram of the number of times a particular value for the number of sixes occurred against the value could be plotted.
• The shape of the histogram would be the same as for the Histogram of Count-rate.
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The Decay Equation
• The activity of a particular radioactive source depends upon just two factors.
the number of nuclei of that source present (N)
the radioactive isotope that is being measured.
Notice that it does NOT depend upon
Temperature, Pressure, Chemical Composition
or anything else.
• The activity is directly proportional to the number of nuclei present
activityN
This means that
activity = constant x N
The constant is called the decay constant and is represented by the symbol
activity = N
The Decay Constant
• The decay constant () has a different value for each radioactive isotope.
• The decay constant () has units second-1 (s-1).
• The decay constant () has two meanings.
It is the fraction of nuclei of an isotope decaying in 1 second.
It is the chance of a nucleus decaying in 1 second.
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Exponential Decay
• Radioactive Decay is typical of a process where the rate of change of a quantity depends upon the value of that quantity.
Stage 1
• The sample starts with N0 radioactive nuclei.
The number decaying during the first interval of time (say 1 second) depends upon N.
The change in N (N) is given by
N = -N0
The number left is
N1 = N0 -N
Stage 2
• The number of radioactive nuclei at the beginning of the next interval of time is smaller.
Some of the nuclei have decayed.
The number of nuclei decaying will also be smaller
N = -N1
The number left is
N2 = N1 -N
and so on.
• This gives rise to a graph of Number of Nuclei against Time with a particular shape - an exponential graph.
• Because the Activity of a source is directly proportional to the Number of Radioactive nuclei (N), the graph of Activity against time will have exactly the same shape.
Constant Ratio Property of Exponential Curves
• One of the more useful properties of an Exponential Curve is that the ratio of the y-value at the beginning of a period of time to the y-value at the end of that period is the same for all of the curve.
Example
• For the graph above
When t = 0s, N0 = 1000
When t = 20s, N20 = 600
The ratio N20 / N0 = 600/1000 = 0.6
• This ratio will be the same for any two times which are 20 s apart.
And so N40 / N20 = 0.6
or
N40 = N20 x 0.6 = 600 x 0.6 = 360
Half-Life (t½)
• Half-Life is the time that it takes for half of the radioactive nuclei of an isotope to decay on average.
• It is also the time that it takes for the activity to fall to half of the original value.
• Different radioactive isotopes have different half-lives.
Isotope Half-life
Radon-222 4 days
Strontium-90 28 years
Radium-226 1602 years
Carbon-14 5600 years
Plutonium-239 24 400 years
Uranium-235 700 000 000 years
• For a given number of nuclei
a short half-life means a high count rate
a long half-life means a low count rate.
Example
The isotope Radon-222 is unstable and has a half-life of 4 days.
The particular sample of Radon-222 contains 640000 nuclei.
The initial count rate as measured using a Geiger-Muller Tube and a counter is 80 counts/min.
Time Number of Half-lives Number of Nuclei Fraction Remaining Count Rate
Days /min
0 1 640000 1 160
4 2 320000 1/2 80
8 3 160000 1/4 40
12 4 80000 1/8 20
16 5 40000 1/16 10
20 6 20000 1/32 5
Measuring Half-life
Correcting for Background
• When trying to find the half life from some real measurements due allowance has to be made for the background count rate.
• This can be done in one of two ways.
o The whole experiment can be carried out inside a lead box.
This will keep the value of the background count rate to a minimum but it will not be zero.
o The value of the background count rate must be measured and subtracted from each measurement of the count rate for the sample being studied.
Example
In this example the background count rate was measured without the sample being studied present.
Background count rate = 50 counts/minute
Time Count Rate Corrected Count Rate
minutes /minute /minute
0 1650 1600
2 1150 1100
4 850 800
6 600 550
8 450 400
10 325 275
12 250 200
14 187 137
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