02 - Radiation
Summary
Radioactivity is the spontaneous emission of high energy particles due to the decay of unstable nuclei. We’ll look at the types of radiation, their sources, how they effect the elements we see in nature, and the safety implications of radioactivity.
Contents
- types of radiation
- αdecay
- βdecay
- γrays
- Radioactive decay series
- safety aspects of radioactivity
- measurement of radiation / units radiation limits
| Summary of Properties of Radiation | |||
|---|---|---|---|
| α | β | γ | |
| nature | 2 protons + 2 neutrons | electron | light ray |
| effects of em fields | weakly afected | strong | no effect |
| penetration | cm's in air, sheet of paper | mm's of aluminium | cm's of lead |
| ionise atoms | strongly | weakly | very weakly |
| speed | 10% speed of light | 50% light | speed of light |
| typical energy | 5MeV | 1MeV | 100keV |
Nucleus emits an α particle
- loses two protons and two neutrons
- Z decreases by 2 and A decreases by 4
- AZParent=>A−4Z−2Daughter+α
- examples
- 23892U=>23490Th+α
- 21084Po=>20682Pb+α
Nucleus emits a β particle
- neutron in the nucleus splits into a proton and an electron
- electron emitted as a beta particle
- Z increases by 1 and A remains the same
- AZP=>AZ+1D+β−+ˉν
- examples
- 9942Mo=>9943Tc+β−+ˉν
- 146C=>147N+β−+ˉν
Nucleus emits an γ ray
- no change in A, Z, just loss of excess energy from nucleus
α decay
α decay is caused by Coulomb Repulsion between protons
binding energy increase as A
Coulomb repulsion increases as Z2
heavy nuclei want to offload some nucleons
almost everything with A > 190 is energetically unstable
but for some lifetimes are so long we don’t consider them radioactive, e.g. 204Pb with half-life of 1.4×1017 years.
also, sometimes β decay more likely so it masks the α’s.
energetically, emitting a single proton or neutron or some lighter nuclei (e.g. 31H) not possible
- but 42He unusually stable
Energy in α Decay
energy released given by the differences in rest masses
Q=(Mparent−Mdaughter−Mα)×c2
or, in terms of binding energy:
- Q=AdaughterBEdaughter+4BEα−AparentBEparent
typical figures of about 4MeV
this is much less than particle rest mass energies
so non-relativistic
α particle energy release from 226Ra to 222Rn
226Ramass=226.0253g/mol
222Rnmass=222.0175g/mol
4Hemass=4.002604g/mol
(226.0253−222.0175−4.002604)×(1.660539×10−27)×c2/1.60218×10−19
= 4.84MeV
- compares to experimental value of 4.78MeV
Using Binding Energies
226RaBE=7.6620MeV/nucleon
222RnBE=7.6945MeV/nucleon
4HeBE=7.0739MeV/nucleon
(7.6945×222+7.0739×4−7.6620×228)=4.87MeV
How is this energy shared between α and Daughter Nucleus - Momentum Conservation
total energy released is Q=(Mparent−Mdaughter−Mα)×c2
this is equal to the kinetic enegies, T, of the daughter nucleus and the α
assume parent nucleus at rest, so for momentum pdaughter=pα
as these are non-relativistic, we can use Kinetic Energy = p22m
get Q=Tα+Td=p2α2mα+p2d2md=p2α(12mα+1md)
get Tα=Q(1+mαmd)≈Q(1−mαmd)
for 4MeV α decays, daughter nucleus gets about 100keV.
- enough to escape surface of material
Relation between Half-Lives and α energies
α’s with high energies come from nuclei with short half-lives
- note how adding neutrons stabilises nucleus
β Decay
actually three types of β decay
negative β decay: n→p+e− this is β−
negative β decay: p→n+e+ this is β+
orbital electron capture: p+e−→n this is ϵ
β decay is via the weak force, because of this the half lives tend to be quite long.
Neutrinos
the reactions above are missing something
protons, electrons, and neutrons are all spin 1/2.
also find spectrum of energy for the emitted β particles
answer is the neutrino
- β decay: n→p+e−+ˉν
Neutrinos
- vaste numbers produced in the Sun
- 1 trillion solar ν’s pass through you every second
- you’ll only absorb one in your lifetime
- really hard to detect
- take an old gold mine in South Dakota
- fill it with cleaning fluid
- wait
- about once a day get νe+ 37Cl⟶ 37Ar++e−
Neutrinos
- following on from Homestake, other neutrino observatories such as:
- SuperKamiokande in Japan
- Sudbury (SNO) in Ontario
- IceCube at the South Pole (literally) - 1km3
- in February 1987, sudden burst of ν’s detected at various neutrino observatories
- several hours later, light from a supernova in a nearby galaxy reached Earth
- first time we’d seen this
Sources of Radiation
α particles
- almost all α particles originate in the radioactive decay of heavy nuclei e.g. 238U, 226Ra, etc.
- 208Pb is the heaviest stable nucleus known.
- typically α energy of 4MeV (6.4×10−13 Joules)
- ~highest is: 21284Po→20882Pb+α+8.78MeV
β particles
- naturally occuring sources of beta particles are rare.
- often occur subsequent to nuclear fission.
- They can be prepared by irradiating target nuclei with neutrons ( e.g. 125I for thryoid treatments ).
- The beta emitter 14C is produced by cosmic rays in the upper atmosphere
- bigger range of energies than α particles
- 3.5MeV for 13754Xe→13755Cs+β+ˉν
- 18keV for 31T→32He+β+ˉν
γ rays
- after α or β decay, the daughter nucleus contains excess energy.
- This is liberated by the release of a γ ray
- about 100keV typical energy
Decay Series
- α decay changes nuclear mass by 4 units, β and γ don’t change it at all. Means there are 4 families of nuclei.
| Disintegration Series of the Heavy Elements | ||||
|---|---|---|---|---|
| Name | Type | Final |
Longest Lived Member
|
|
| Nucleus | Half-Life | |||
| Thorium | 4n | 208Pb | 232Th | 14.1 GYr |
| Neptunium | 4n + 1 | 209Bi | 237Np | 2.14 MYr |
| Uranium | 4n + 2 | 206Pb | 238U | 4.47 GYr |
| Actinium | 4n + 3 | 207Pb | 235 | 0.704 GYr |
Radiation Safety
- radiation damages tissue
- produces reactive chemicals (radicals) in the body
- α particles are the most dangerous, considered 20 times more dangerous than β’s
- because they all their energy in a smaller volume
- γ rays are more difficult to control because of their greater penetration
Radon
- large dose of radiation due to the build up of radon in houses
- radon decays to polonium, bismuth, etc. These latch onto dust particles and can be absorbed by the lungs. They emit a cascade of alpha particles
- 20,000 deaths (lung cancer) per year in the USA due to radon
- radon dose determined by:
- amount of uranium in underlying rocks
- permeability of topsoil
- cracks and fissures in floor
- ventilation in house
- buildings from 1980’s on
- fine, contain impermeable plastic layer in foundations
- buildings from before 1950’s
- fine, because so draughty
Measurement of Radiation
Activity
- This is the number of disintegrations occurring per second.
- It is easily measured with a Geiger counter.
- This activity is proportional to the number of radioactive atoms in the sample.
- Activity=−dNdt=λN
The units of activity are:
- Curie (Ci)
- 1Ci=3.7×1010disintegrations/sec
- A clinical source of 60Co has an activity of several Ci
- An internally administered dose for cancer treatment would have an activity of 10−3 Ci
- Becquerel (Bq)
- 1 Bq = 1.0 disintegrations /sec
- This is the SI. unit (1 Ci = 3.7×1010 Bq)
Absorbed Dose
- This is the effect of the radiation on the absorbing material
- The SI unit for absorbed dose is the gray (Gy) which is the amount of radiation which deposits energy at a rate of 1 J / kg in any absorbing material.
- (The old unit was the rad … 1 Gy = 100 rad)
- The absorbed dose depends on
- the strength of a given radiation beam (number of particles per second)
- the energy per particle but also on the type of material absorbing the radiation
- This is not the most meaningful units for measuring the biological damage produced by radiation.
- This is because equal doses of different types of radiation cause differing amounts of damage (1 gray of α particles produces 10 to 20 times the damage of 1 gray of β particles or γ rays)
- This is because the α particles move more slowly than β and γ rays of equal energy due to their greater mass and ionising collisions occur closer together resulting in more irreparable damage
- The relative biological effectiveness (RBE) or quality factor (QF) of a given type of radiation is defined as the number of grays of X-ray or γ radiation that produces the same biological damage as 1 gray of the given radiation.
- The product of the dose in grays and the QF gives a unit of sieverts (previously rem)
- 1 sievert of any type of radiation does the same approximate biological damage
- Radioactive background 1.3 mSv /year
- X-rays 0.7 mSv / year
Exposure Limits
- 5 mSv per year exposure to the general population
- 50 mSv per year to nuclear workers
- A 4 Sv dose in a short interval of time is fatal with 50% of cases but when spread over a few weeks it is not usually fatal.
- A 10 Sv dose is nearly always fatal
Principle sources of radiation
- Radon - 1mSv per year
- CT scans - 0.8mSv per year
- Nuclear Medicine - 0.4mSv per year
- Cosmic Rays - 0.15mSv per year
- internal radiation (mostly potassium, 40K) 0.03mSv per year
- get total of about 10μSv per day. Below legal limit.
Equations
AZParent=>A−4Z−2Daughter+α
AZP=>AZ+1D+β−+ˉν
Q=(Mparent−Mdaughter−Mα)×c2
Q=AdaughterBEdaughter+4BEα−AparentBEparent
Bq=Ci×3.7×1010
(energyinjoules)=MeV×1.6×10−13
Gray=Bq×(energyinjoules)(personmassinkg)
Sv=Bq×(energyinjoules)×RBE(personmassinkg)
(expectednumberofdeaths)=(doseinSievert)×(population)50
typical daily dose = 10μSv.
LD50/30 = 4Sv
References
Nuclear Physics