Radioactivity

Radioactivity

1. Radioactivity

   • Types of radiation
     • Alpha
       • Alpha particle
         • Helium nucleus
         • Charge
           • Positive
           • +2e
         • 2 Protons + 2 neutrons
       • interact with surrounding particles to produce strong ionisation.
       • Takes a few centimetres of air to absorb most alpha particles.
       • Large mass and charge
       • A thin sheet of paper completely absorbs alpha particles
     • Beta
       • Fast moving electrons/positrons
       • Small mass and charge
       • Longer range in air (about a meter)
       • Takes about 1-3mm of aluminum to stop most beta particles.
     • Gamma
       • high-energy photons
       • No charge
         • Less ionising
       • Emitted from the nuclei of atoms
         • Due to changes within unstable nuclei
       • Count rate for gamma rays decays exponentially, with the thickness of a lead absorber.
   • Charged particles through a uniform electric field
     • Negative beta-minus particles are deflected towards the positive plate
     • Positive alpha and beta-plus particles are deflected towards the negative plate
       • Alpha particles are deflected less than beta particles because of their greater mass.
     • The paths of the beta-minus and beta-plus particles are mirror images.
     • Gamma rays are not deflected, because they are uncharged.
   • Magnetic field
     • The direction of the force on each particle can be determined using Fleming’s left hand rule.
   • Dangers
     • All types of radioactivity cause ionisation, which means they can damage living cells.
     • Radioactive sources must be stored in lead-lined storage containers.
     • You must use a pair of tongs with long handles, in order to keep the source as far from your body as possible.
     • Never handle radioactive sources with bare hands.

2. Nuclear Decay equations

   • In all nuclear reactions - The Nucleon and Proton number must be conserved
   • Alpha Decay
     • Loss of an alpha particle removes two protons and two neutrons from a parent nucleus -
     • The nucleon number drops by four.
     • The daughter nucleus has a different proton number so is a different element.
     • Energy is also released in the decay.
   • Beta Decay
     • Beta Plus
       • Beta-plus happens in unstable isotopes that have many more protons than neutrons.
       • The weak force initiates changes within the parent nucleus by transforming one of the protons into a neutron.
       • In the process a Positron and a neutrino are emitted
     • Beta Minus
       • Beta-minus happens in unstable isotopes that have many more neutrons than protons.
       • The weak nuclear force is responsible for one of the neutrons decaying into a proton.
       • An Electron and an anti-neutrino are emitted
   • Gamma Decay
     • Gamma photons are emitted if a nucleus has surplus energy following an alpha or beta emission.
     • The composition of the nucleus remains the same.
   • Decay Chains
     • The radioactive decay of nuclei is complex, because the daughter nuclei can themselves be radioactive.
     • After a very long time, - following many transformations - The chain ends in a stable isotope

3. Half-life and activity

   • Radioactive decay
     • Random
       • We can't predict when a particular nucleus in a sample will decay.
       • Each nucleus within a sample has the same chance of decaying per unit time.
     • Spontaneous
       • The decay of the nuclei is not affected by the presence of other nuclei in the sample.
       • The decay of the nuclei is not affected by external factors - such as pressure.
     • The probability of a given nucleus decaying in the next unit time interval is fixed for a given isotope.
     • Simulating
       • Flipping coins
       • Rolling a large number of dice
         • The probability of decay for each die is 1/6
           • This means that with each throw about 1 in 6 dice will ‘decay’ and about 5 in 6 will remain undecayed.
           • The actual number decaying and remaining will be determined by chance.
         • If you started off with 216 dice - each die representing a single undecayed nuclei in a sample.
           • Each throw represents a small interval of time
           • We assume the number 6 appearing on the top represents a decay.
           • The decay is random because you can’t predict which die will decay - you can only state their probability of decay.
           • After the first throw you would expect about 36 (216/6) dice to ‘decay’ and 180 to remain.
             • After the second throw, you would expect about another 30 to decay., with about 150 left.
               • After N throws you would expect (5/6)^n x 216 dice to be left
                 • This constant-ratio property means that the number of dice left decays exponentially with the number of throws.
                   • You can show it takes about 3.8 throws to halve the number of dice each time.
       • Popcorn cooking in microwave oven
         • The kernels represent the undecayed nuclei
         • a single pop represents a single decay.
         • At the start, there are many unpopped kernels and the poping rate is high.
         • As the amount of unpopped corn decreases, so does the popping rate.
       • The main differences of nuclear decay
         • The number of nuclei - which would be many trillions.
         • The probability of decay - which depends on the isotope.
           • The probability of decay governs how quickly the nuclei decay and therefore the half-life of the isotope.
   • Half-life
     • The average time it takes for half the number of active nuclei in the sample to decay.
       • This means that after a time equal to one half-life - The number N of undecayed nuclei in a sample will be halved.
         • The number N must therefore decay exponentially with time
     • Measuring Half-life
       • Protactinium-234 is a suitable isotope to measure half-life
         • Because it has a short half-life
         • The Protactinium-234 isotope is produced from the decay of thorium-234, which is itself produced from the decay of uranium-238.
         • 1. - A sealed plastic bottle containing an organic solvent and a solution of ur-a-nyl nitrate in water is used to separate the protactinium from thorium.
           • 2. The background count rate is determined - in the absence of the source.
             • 3. The plastic bottle is shaken for about 15s to dissolve the protactinium in the organic solvent, which floats to the top.
               • 4. The end of the GM tube is placed next to the organic layer.
                 • In order to avoid contamination, the GM tube must not touch the bottle.
                 • 5. The counts from the decaying protactinium can be recorded Taking 10 s count every half-minute.
                   • The corrected count rate is directly proportional to the activity of the source.
                   • The half-life of the protactinium-234 can be determined by plotting a graph of corrected count rate against time.
           • This works because the compound of the protactinium daughter isotope is soluble in the organic solvent - whereas the parent thorium compound is not.
   • Activity
     • The rate at which nuclei decay or disintegrate.
       • Measured in decays per second.
       • It can be thought of as the number of alpha, beta, or gamma photons emitted from the source per unit time.
       • E.g - An activity of 2000 Bq from an alpha source means 2000 nuclei decay per second or 2000 alpha particles are emitted per second.
     • Unit:: becquerel (Bq)
     • Depends on
       • The number of undecayed nuclei present in the source.
       • The half-life of the isotope.
     • The count rate measured using a GM tube and a counter - is only a fraction of the rate at which particles or photons are emitted by a radioactive source.
       • The actual activity of the source will be much higher than the count rate.
   • Decay constant - λ
     • If we consider a source with a very large number of nuclei - With N undecayed at time t = 0
       • In a small interval of time Δt, - The number of nuclei disintegrating would be directly proportional to both N and Δt.
         • Therefore the rate of decay of the nuclei is directly proportional to the number of undecayed nuclei (which is decreasing)
           • A = λN
             • We only want the value for activity so the minus sign is omitted
     • The probability of decay of an individual nucleus per unit time.
     • unit: s-1/ h-1/ y-1 (but not Bq)
     • The decay constant and half-life are inversely proportional to each other.
     • λt = ln (2)

4. Radioactive decay calculations

   • A ∝ N
     • VV Therefore activity also decreases exponentially VV
   • >> Solving the equation gives >>

5. Radioactive dating

   • Carbon dating
     • All living things on earth contain carbon atoms.
       • Through photosynthesis plants absorb carbon dioxide from the atmosphere. Animals eat the plants and therefore take in the carbon.
       • Once an organism dies it stops taking in carbon
         • The total amount of carbon-14 it contains continues to decay, so this ratio decreases over time.
     • Atmospheric carbon is mainly the stable isotope, carbon-12, but also a tiny amount of the radioactive isotope carbon-14.
       • Produced in upper atmosphere by cosmic rays.
     • Carbon-14 has a half-life of about 57000 years
     • Ratio
       • The ratio of carbon-14 to carbon-12 nuclei in the atmosphere is almost constant at 1.3 x 10-12.
       • The ratio is the same in all living things.
         • The activity from carbon-14 is a sample of organic material is proportional to the number of undecayed carbon-14 nuclei.
       • The time since the organism died can be determined by comparing the activities, or the ratio of carbon-14 to carbon-12 nuclei, of the dead material and similar living material.

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