RAD – Radiation Absorbed Dose

Absorbed dose is defined as the amount of energy deposited by ionizing radiation in a substance. Absorbed dose is given the symbol D. The rad (an abbreviation for Radiation Absorbed Dose) is the non-SI unit of the absorbed dose. The absorbed dose is also measured in a unit called the gray (Gy), which is derived from the SI system. The non-SI unit rad is used predominantly in the USA.

absorbed dose - definition

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.

RAD – Unit of Absorbed Dose

A dose of one rad is equivalent to the deposition of one hundred ergs of energy in one gram of any material. Note that, the erg is a unit of energy and work equal to 10−7 joules. A related unit, the roentgen, is used to quantify the radiation exposure. The F-factor can be used to convert between rads and roentgens.

One rad is significantly lower dose than one gray, which is a large amount of absorbed dose. A person who has absorbed a whole body dose of 100 rad has absorbed one joule of energy in each kg of body tissue (i.e. 1 Gy). Absorbed doses measured in industry (except nuclear medicine) often have comparable doses to one rad and the following multiples are often used:

1 mrad (millirad) = 1E-3 rad

1 krad (kilorad) = 1E3 rad

Conversions from the SI units to other units are as follows:

  • 1 Gy = 100 rad
  • 1 mGy = 100 mrad

The gray and rad are physical units. They describe the physical effect of the incident radiation (i.e., the amount of energy deposited per kg), but it tells us nothing about the biological consequences of such energy deposition in living tissue.

Examples of Absorbed Doses in rads

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.

  • 0.005 mrad – Sleeping next to someone
  • 0.009 mrad – Living within 30 miles of a nuclear power plant for a year
  • 0.01 mrad – Eating one banana
  • 0.03 mrad – Living within 50 miles of a coal power plant for a year
  • 1 mrad – Average daily dose received from natural background
  • 2 mrad – Chest X-ray
  • 4 mrad – A 5-hour airplane flight
  • 60 mrad – mammogram
  • 100 mrad – Dose limit for individual members of the public, total effective dose per annum
  • 365 mrad – Average yearly dose received from natural background
  • 580 mrad – Chest CT scan
  • 1 000 mrad – Average yearly dose received from natural background in Ramsar, Iran
  • 2 000 mrad – single full-body CT scan
  • 17 500 mrad – Annual dose from natural radiation on a monazite beach near Guarapari, Brazil.
  • 500 000 mrad – Dose required to kill 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 in rads

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:

Curie - Unit of Activity

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.

Calculate the primary photon dose rate, in rads per hour (rad.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:

dose rate calculation

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:

absorbed dose rate - rad - calculation

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:

absorbed dose rate - gray

References:

Radiation Protection:

  1. Knoll, Glenn F., Radiation Detection and Measurement 4th Edition, Wiley, 8/2010. ISBN-13: 978-0470131480.
  2. Stabin, Michael G., Radiation Protection and Dosimetry: An Introduction to Health Physics, Springer, 10/2010. ISBN-13: 978-1441923912.
  3. Martin, James E., Physics for Radiation Protection 3rd Edition, Wiley-VCH, 4/2013. ISBN-13: 978-3527411764.
  4. U.S.NRC, NUCLEAR REACTOR CONCEPTS
  5. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.

Nuclear and Reactor Physics:

  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
  9. Paul Reuss, Neutron Physics. EDP Sciences, 2008. ISBN: 978-2759800414.

See above:

Absorbed Dose