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What is Absorbed Dose – Formula – Equation – Definition

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This article summarizes key formulas and equations for calculation of the absorbed dose and the absorbed dose rate. Absorbed Dose – Formula – Equation

Absorbed Dose – Equation

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.

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.

Absorbed Dose Rate – Equation

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:

absorbed dose rate - definition

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.

Absorbed Dose Rate Calculation

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.

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:

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 - gray - 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 also:

Absorbed Dose

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