Absorbed dose is defined as the amount of energy deposited by ionizing radiation in a substance. Absorbed dose is given the symbol D. The absorbed dose is usually measured in a unit called the gray (Gy), which is derived from the SI system. The non-SI unit rad is sometimes also used, predominantly in the USA.
Units of absorbed dose:
- Gray. A dose of one gray is equivalent to a unit of energy (joule) deposited in a kilogram of a substance.
- RAD. A dose of one rad is equivalent to the deposition of one hundred ergs of energy in one gram of any material.
Absorbed Dose Rate
The absorbed dose rate is the rate at which an absorbed dose is received. It is a measure of radiation dose intensity (or strength). The absorbed dose rate is therefore defined as:
In conventional units, it is measured in mrad/sec, rad/hr, mGy/sec or Gy/hr. Since the amount of radiation exposure depends directly (linearly) on the time people spend near the source of radiation, the absorbed dose is equal to the strength of the radiation field (dose rate) multiplied by the length of time spent in that field. The example above indicates a person could expect to receive a dose of 25 millirems by staying in a 50 millirems/hour field for thirty minutes.
Examples of Absorbed Doses in grays
We must note that radiation is all around us. In, around, and above the world we live in. It is a natural energy force that surrounds us. It is a part of our natural world that has been here since the birth of our planet. In the following points we try to express enormous ranges of radiation exposure, which can be obtained from various sources.
- 0.05 µGy – Sleeping next to someone
- 0.09 µGy – Living within 30 miles of a nuclear power plant for a year
- 0.1 µGy – Eating one banana
- 0.3 µGy – Living within 50 miles of a coal power plant for a year
- 10 µGy – Average daily dose received from natural background
- 20 µGy – Chest X-ray
- 40 µGy – A 5-hour airplane flight
- 600 µGy – mammogram
- 1 000 µGy – Dose limit for individual members of the public, total effective dose per annum
- 3 650 µGy – Average yearly dose received from natural background
- 5 800 µGy – Chest CT scan
- 10 000 µGy – Average yearly dose received from natural background in Ramsar, Iran
- 20 000 µGy – single full-body CT scan
- 175 000 µGy – Annual dose from natural radiation on a monazite beach near Guarapari, Brazil.
- 5 000 000 µGy – Dose that kills a human with a 50% risk within 30 days (LD50/30), if the dose is received over a very short duration.
As can be seen, low-level doses are common for everyday life. The previous examples can help illustrate relative magnitudes. From biological consequences point of view, it is very important to distinguish between doses received over short and extended periods. An “acute dose” is one that occurs over a short and finite period of time, while a “chronic dose” is a dose that continues for an extended period of time so that it is better described by a dose rate. High doses tend to kill cells, while low doses tend to damage or change them. Low doses spread out over long periods of time don’t cause an immediate problem to any body organ. The effects of low doses of radiation occur at the level of the cell, and the results may not be observed for many years.
Calculation of Shielded Dose Rate
Assume the point isotropic source which contains 1.0 Ci of 137Cs, which has a half-life of 30.2 years. Note that the relationship between half-life and the amount of a radionuclide required to give an activity of one curie is shown below. This amount of material can be calculated using λ, which is the decay constant of certain nuclide:
About 94.6 percent decays by beta emission to a metastable nuclear isomer of barium: barium-137m. The main photon peak of Ba-137m is 662 keV. For this calculation, assume that all decays go through this channel.
Determine the primary photon dose rate, in gray per hour (Gy.h-1), at the outer surface of a 5 cm thick lead shield. Primary photon dose rate neglects all secondary particles. Assume that the effective distance of the source from the dose point is 10 cm. We shall also assume that the dose point is soft tissue and it can reasonably be simulated by water and we use the mass energy absorption coefficient for water.
See also: Gamma Ray Attenuation
See also: Shielding of Gamma Rays
Solution:
The primary photon dose rate is attenuated exponentially, and the dose rate from primary photons, taking account of the shield, is given by:
As can be seen, we do not account for the buildup of secondary radiation. If secondary particles are produced or if the primary radiation changes its energy or direction, then the effective attenuation will be much less. This assumption generally underestimates the true dose rate, especially for thick shields and when the dose point is close to the shield surface, but this assumption simplifies all calculations. For this case the true dose rate (with the buildup of secondary radiation) will be more than two times higher.
To calculate the absorbed dose rate, we have to use in the formula:
- k = 5.76 x 10-7
- S = 3.7 x 1010 s-1
- E = 0.662 MeV
- μt/ρ = 0.0326 cm2/g (values are available at NIST)
- μ = 1.289 cm-1 (values are available at NIST)
- D = 5 cm
- r = 10 cm
Result:
The resulting absorbed dose rate in grays per hour is then:
If we want to account for the buildup of secondary radiation, then we have to include the buildup factor. The extended formula for the dose rate is then:
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