Radioactive Decay (DP IB Physics)

Background radiation is the ionising radiation that exists around us all the time.

False.

Background radiation is a natural phenomenon that has always existed on Earth and in outer space.

Natural sources of background radiation include:

• radon gas

• cosmic rays from space

• radioactive elements in rocks and soil

• carbon-14 in living tissue

• some food and drink

Artificial sources of background radiation include:

• nuclear medicine

• nuclear waste

• nuclear fallout

• nuclear accidents

The count rate of a radioactive source is measured using a GM (Geiger-Marsden) tube connected to a counter, or ratemeter.

When measuring the count rate of a radioactive source, the background count is accounted for by

• measuring the count rate without the source present (background count)

• measuring the count rate with the source present

• subtracting the background count from each measurement of count rate

It is better to use larger count rates in radioactivity experiments as the background count will be a smaller percentage of the overall count.

As a result, the random variation in each measurement is reduced.

False.

Accounting for background count improves the accuracy of readings.

This is because background count is a form of systematic error (zero error).

Nuclei emit radiation when they are unstable due to having

• an imbalance of protons or neutrons

• an excess amount of energy

False.

The composition of a nucleus changes following alpha and beta decay, but not following gamma decay.

An alpha particle is a helium nucleus:

When a nucleus emits an alpha particle, the effect is:

• nucleon number decreases by 4

• proton number decreases by 2

A beta-minus particle is an electron:

When a nucleus emits a beta-minus particle, the effect is:

• nucleon number stays the same

• proton number increases by 1

A beta-plus particle is a positron:

When a nucleus emits a beta-plus particle, the effect is:

• nucleon number stays the same

• proton number decreases by 1

Gamma radiation is electromagnetic radiation:

When a nucleus emits gamma radiation, the effect is:

• nucleon number stays the same

• proton number stays the same

The types of nuclear radiation in order of increasing ionising power are:

• gamma (least ionising, creates fewest ion pairs per cm)

• beta (creates a moderate amount of ion pairs per cm)

• alpha (most ionising, creates most ion pairs per cm)

The types of nuclear radiation in order of increasing penetrating power are:

• alpha (least penetrating, can be stopped by paper)

• beta (can stopped by a few mm of aluminium)

• gamma (most penetrating, can be reduced by a few mm of lead)

In the same electric field, , the force, , on a beta particle will be slightly less due to having a smaller charge, , but it will have a much greater acceleration, , due to having a smaller mass,

• electric force:

• acceleration:

In the same perpendicular magnetic field, , the force, , on a beta particle will generally be higher as, despite having a smaller charge, , it will typically travel at a much greater speed, . It also has a greater acceleration, , due to having a smaller mass,

• magnetic force:

• acceleration:

False.

Electron anti-neutrinos are emitted during beta-minus decay.

Beta-minus decay is when a neutron turns into a proton and emits a beta-minus particle and an electron anti-neutrino.

True.

An electron neutrino is emitted along with a beta-plus particle when a proton turns into a neutron.

False.

Nuclei with too many neutrons decay by beta-minus decay only.

True.

Nuclei with too many protons decay by either beta-plus decay or electron capture.

False.

Nuclei with too many nucleons (protons and neutrons) decay by alpha decay.

Therefore, alpha decay usually occurs in very large unstable nuclei.

True.

Gamma decay usually occurs after alpha or beta decay when a nucleus becomes excited and has too much energy.

The nuclear equation for the decay of carbon-14 is:

Where:

• = carbon-14 isotope

• = nitrogen-14 isotope

• = beta-minus particle

• = electron anti-neutrino

The nuclear equation for the decay of fluorine-18 is:

Where:

• = fluorine-18 isotope

• = oxygen-18 isotope

• = beta-plus particle

• = electron neutrino

The nuclear equation for the decay of polonium-212 is:

Where:

• = polonium-212 isotope

• = lead-208 isotope

• = alpha particle

Activity is the number of nuclei which decay in a given time. It is measured in becquerels.

One becquerel (Bq) is equivalent to a nucleus decaying every second.

Activity is the rate at which radiation is emitted, whereas count rate is the rate at which radiation is detected.

Half-life is the time taken for half the undecayed nuclei of a particular isotope in any sample to decay.

It is also the time taken for the activity of a source to fall to half its original value.

False.

The half-life for a particular isotope is a constant value. Therefore, different isotopes have different half-lives.

The value of the activity of a radioactive sample after two half-lives is of its original value.

After three half-lives, the proportion of original nuclei remaining in the sample will be .

To determine the half-life of an isotope on a graph of activity over time:

• identify the point at which the activity has halved and draw a line to the curve

• track that point down to the time axis

The half-life of the sample is 5 hours:

• half-life is the time taken for the activity to fall to half its original value

• the time for the activity to fall from 800 to 400 counts per second is 5 hours

Uses of radioactivity include:

• nuclear power

• medicine e.g. radiotherapy, tracers and sterilising equipment

• carbon dating

• determining the age of rocks

• detecting leaks in underground pipes

• controlling the thickness of materials

• smoke detectors

The decay constant is the probability that an individual nucleus will decay per unit of time.

Carbon dating is a method used to determine the age of once-living matter by

• measuring the ratio of carbon-14 atoms to carbon-12 atoms that it contains

• comparing this to the well-known ratio in living matter

• using the half-life of carbon-14 to determine the time that has passed

The equation linking activity and the decay constant is:

Where:

• = activity, measured in becquerel (Bq)

• = decay constant, measured per second (s^-1)

• = number of nuclei

Uranium-lead dating can be used to determine the age of the Earth by

• assuming the sample starts with 100% uranium and finishes with 100% lead

• determining the percentage of these two elements in a rock

• estimating the time since the decays started

The negative sign indicates that the number of undecayed nuclei, , decreases with time.

The ideal properties of a radionuclide used for detecting leaks in underground pipes are:

• gamma emitter - this is the most penetrating type of radiation

• short half-life - activity needs to be at detectable levels but not for too long

The equation linking half-life and decay constant is:

Where:

• = half-life, measured in seconds (s)

• = decay constant, measured per second (s^-1)

Beta radiation is used to monitor the thickness of materials because

• it can penetrate materials such as paper and aluminium foil

• the amount of beta radiation detected depends on the material thickness

The equation linking half-life and decay constant is derived by

• using the exponential decay equation:

• substituting when

• applying rules of logarithms

Alpha radiation is used in smoke detectors.

False.

A radionuclide with a short half-life will decay at a faster rate.

The shorter the half-life of a radionuclide, the greater the decay constant and activity.

Gamma radiation is used in radiotherapy (the treatment of cancer) because

• it can damage or kill cancerous cells

• it is penetrating enough to reach cancerous cells in the body

The activity of a sample decreases over time because:

• unstable nuclei emit radiation to become more stable

• after each decay, the number of unstable nuclei remaining decreases

• activity is directly proportional to the number of nuclei, so activity decreases

A radioactive tracer is a substance containing a radionuclide which is introduced into a system and tracked by detecting the radiation it emits.

The relationship represented by the linear decay curve is:

Where:

• = the initial number of undecayed nuclei

• = number of undecayed nuclei

• = decay constant, measured per second (s^-1)

• = time interval, measured in seconds (s)

The ideal properties of a radioactive tracer in medical imaging, such as technetium-99m are:

• gamma emitter - penetrating enough to be detected outside the body

• short half-life - activity needs to be at detectable levels for the duration of the test, but not for long after

The relationship represented by the logarithmic graph is:

Where:

• = the initial number of undecayed nuclei

• = number of undecayed nuclei

• = decay constant, measured per second (s^-1)

• = time interval, measured in seconds (s)

Gamma radiation is used in the sterilisation of food and equipment because

• it is highly penetrating, so it is able to irradiate entire surfaces

• it is ionising enough to kill bacteria and viruses

The gradient of the logarithmic graph is equal to the decay constant, .

• equation of graph:

• equation of a straight line:

• therefore, gradient =

Exponential decay is when the rate of change of a quantity decreases at a constant rate.

Mass defect is the difference between the mass of a nucleus and the total mass of all the constituent nucleons if they were separated.

The law of radioactive decay states that the rate of decay is proportional to the number of undecayed nuclei, or

Where:

• = decay constant, measured per second (s^-1)

• = number of nuclei

True.

Mass defect and binding energy are equivalent.

True.

The number of undecayed nuclei never reaches zero in radioactive decay.

Nuclear binding energy is the energy required to separate a nucleus into its constituent nucleons.

The number of undecayed nuclei in a radioactive sample decreases exponentially with time.

Mass defect is caused by the energy released when a nucleus forms, or the energy needed to separate all the nucleons in a nucleus.

False.

The steeper the slope of a decay curve, the greater the decay constant.

True.

A system of separated nucleons has a greater mass than a system of nucleons bound in a nucleus.

The y-intercept of a decay curve represents the initial value of the measured quantity, such as

• = initial number of undecayed nuclei

• = initial activity of the sample (Bq)

• = initial count rate (cpm)

False.

The term mass defect can only be used to describe the change in mass when all the nucleons are separated (equivalent to binding energy).

The decrease in mass which occurs during nuclear reactions (e.g. radioactive decay) should not be described as a mass defect.

The number of undecayed nuclei is:

Where:

• = the initial number of undecayed nuclei

• = number of undecayed nuclei after time

• = decay constant, measured per second (s^-1)

• = time interval, measured in seconds (s)

The equation used to convert mass to its equivalent energy is:

Where:

• = change in energy, measured in joules (J)

• = change in mass, or mass defect, measured in kilograms (kg)

• = speed of light in a vacuum (3.00 × 10⁸ m s^-1)

The activity of a sample as a fraction is:

Where:

• = the initial activity of the sample

• = the activity of the sample after time

• = decay constant, measured per second (s^-1)

• = time interval, measured in seconds (s)

An atomic mass unit (u) is the mass of a neutral atom of carbon-12.

Binding energy per nucleon is the binding energy of a nucleus divided by the number of nucleons.

False.

A low binding energy per nucleon means a nucleus is less stable.

It means less energy would be required to separate the nucleons in the nucleus.

The curve of binding energy per nucleon against nucleon number is:

The steeper gradient at low values of A indicates that fusion reactions release greater binding energy than fission reactions.

Heavy nuclei undergo fission because they have high binding energies per nucleon, but this gradually decreases with A, making the heaviest elements the most unstable.

True.

In both fusion and fission, the mass of the original nuclei is greater than the mass of the products. This missing mass has been converted into energy.

The strong nuclear force is an attractive force which acts between nucleons and holds the nucleus together.

The range of the strong nuclear force is between 0.5 and 3.0 fm, where:

• it is repulsive below a separation of 0.5 fm

• it is attractive up to a separation of 3.0 fm

The strong nuclear force has its maximum attractive value at a separation of around 1.0 fm.

The equilibrium position is the point where the resultant force is zero and occurs at a separation of about 0.5 fm.

The line of stability shows N and Z values that produce stable nuclei.

A nucleus will be unstable if it has:

• too many neutrons

• too many protons

• too many nucleons (protons and neutrons)

• too much energy

True.

The neutron-to-proton ratio for stable light isotopes (Z < 20) is about 1.

This means these nuclei usually contain equal numbers of protons and neutrons.

For heavy isotopes (Z > 20), the neutron-proton ratio increases up to a maximum of around 1.5.

This means these nuclei can contain up to 50% more neutrons than protons.

Heavy isotopes need more neutrons than protons to be stable to add distance between protons to reduce the effects of electrostatic repulsion.

Nuclear energy levels are similar to electron energy levels in that nuclei can exist in excited states and emit energy as photons when transitioning to lower states.

False.

The nucleus emits gamma rays with a range of discrete energies.

When a nucleus changes from an excited state to a lower energy level, a gamma-ray photon will be emitted.

True.

Alpha particles emitted from the same radionuclide possess a range of discrete energies.

The spectra of alpha and gamma radiation provide evidence for discrete nuclear energy levels.

False.

Beta particles emitted from the same radionuclide possess a continuous range of energies.

The curve in the beta particle energy distribution graph indicates that the energy released in beta decay is shared between the beta particle and neutrino (or anti-neutrino).

Alpha particles are emitted with discrete energies, while beta particles have a continuous range of energies.

The continuous spectrum of beta decay provides evidence for the neutrino.