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Dosimetry
Activity
Some materials are radioactive because their nuclei are unstable. It is impossible to tell when a particular nucleus will break apart. What we can measure is the number of nuclei (N) in a quantity of a radioactive substance that will decay in a particular time (t).
The average activity (A) of a quantity of radioactive substance is given by
Activity is measured in becquerels (Bq) where one Bq is one nucleus decaying every second. Kilobecquerels (kBq) and Megabecquerels (MBq) are more usual units for activity.
Activity relates to a quantity of a radioactive substance. It is meaningless to refer to the 'activity of uranium oxide' for example, since the activity depends on how much of the substance is present.
Radioactive decay happens spontaneously. The number of nuclei in a quantity of radioactive substance still to decay depends on how many have already decayed. Because of these factors, activity is not constant over time.
- Question
One litre of seawater has an activity of 10 Bq.
Approximately how many nuclei decay every day in this quantity of seawater?
- Answer
Absorbed dose
Ionising radiation carries energy. This energy can be absorbed by tissue and possibly cause damage to the tissue.
Absorbed dose (D) is the energy (E) absorbed per unit mass (m) of the absorbing material. The absorbed dose can be calculated by using the following relationship.
The unit of absorbed dose is the gray (Gy) where one gray is one joule per kilogram (J kg-1).
It is important to use the correct mass of tissue. If the energy is concentrated on a small mass of tissue, the absorbed dose is greater.
- Question
A patient of mass 70 kg receives radiotherapy. During the treatment, a tumour of mass 250 g receives 20 J of energy.
Calculate the absorbed dose.
- Answer
Dose equivalent
The risk of harm to biological tissue from an exposure to ionising radiation depends on three factors:
- the absorbed dose, D
- the type of radiation that is absorbed, for example alpha or beta particles, gamma rays or slow (thermal) neutrons
- the type of body organs or tissue that is exposed to the radiation
To allow comparisons of the risk of harm due to different ionising radiations, each type of radiation is assigned a radiation weighting factor (WR) as a measure of its biological effect.
The radiation weighting factor for some types of ionising radiation is given in the table.
| Radiation | Radiation weighting factor (WR) |
|---|---|
| alpha particles | 20 |
| beta particles | 1 |
| gamma rays | 1 |
| slow neutrons | 3 |
Dose equivalent (H) measures the biological effects of ionising radiations. It takes account of
- the type of radiation
- the energy carried by the radiation
- how much tissue absorbs the energy
Dose equivalent is the product of absorbed dose and radiation weighting factor. The equation can be written as
H = DWR
Dose equivalent is measured in sieverts (Sv).
Since the radiation weighting factor has no unit, both the gray and the sievert are equal to one joule per kilogram.
- Question
A worker in the nuclear industry receives an absorbed dose of 400µ Gy from slow neutrons and an absorbed dose of 2 mGy from gamma radiation.
Calculate the total dose equivalent received.
- Answer
To calculate the total dose equivalent calculate the dose equivalent from each radiation separately and add all the dose equivalents together.
Dose equivalent from slow neutrons
Hneutrons= DWR
= 400 × 10-6 × 3
= 1.2mSv
Dose equivalent from gamma radiation
Hgamma = DWR
= 2 × 10-3 × 1
= 2.0mSv
Total dose equivalent
H = Hneutrons + Hgamma
= 1.2 + 2.0
= 3.2mSv
The time of exposure (t) to ionising radiation is also important. A dose equivalent of 100 mSv received in one day is more dangerous than the same dose equivalent received over the course of one year.
dose equivalent rate =
Dose equivalent rate can be quoted in a variety of units - sieverts/millisieverts/microsieverts per second/minute/hour. Make sure that the units you use in any problem are consistent.
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