Some Charged Particle Ranges

An approximate general formula for the range of alpha particles in air is:

R_air = 0.56 E ......................... for E < 4 MeV
R_air = 1.24 E - 2.62 ................ for 4 < E < 8 MeV
R_air is in cm

In other media, the range in the media (R_m, in units of mg/cm²) is given as:

R_m = 0.56 A^1/3 R_air is in mg/cm²

where A is the atomic mass number of the absorber.

An approximate formula for beta particle range in low Z materials as a function of beta energy is given as:

R = 412 E^{1.265 - 0.0954 lnE} ................ for 0.01 < E < 2.5 MeV
R = 530E – 106 ............................... for E > 2.5 MeV

The range is expressed in units of mg/cm². This expression is a bit cumbersome to calculate by hand, so naturally we at RADAR have made a useful tool to help you out. Just enter an energy value for the cell in this handy-dandy spreadsheet (in the correct energy region), and the approximate range is given. Approximate values can also be read off the supplied graph.


For dosimetry, we cover here four cases of interest to external dose assessment:

Dose from an External Point Source

The form here is much like our standard equation, with some modifications. Effective doses calculated at 1 m from the point source are used to calculate the dose at other distances, assuming no shielding. The equation is:

The product of activity and time (A x t) gives the number of disintegrations (N_S), and the source strength (given in the conversion factor, CF) is normalized to a unit amount of area (on the surface of a sphere of radius d surrounding the source). Further details, and our recommended dose factors and some attenuation factors for many radionuclides can be found in the following document: External Point Source

Another helpful resource is the Rad Pro calculator, which gives a user friendly interface for calculation of dose rates from point sources of commonly used radionuclides given the point source activity and distance from the source. Simple shielding calculations may also be performed.

Beta dose to skin

Skin dose is very difficult to measure directly and is usually estimated. The beta dose rate to the skin expressed in terms of average surface concentrations of a radionuclide on the skin gives more reliable estimates for this exposure pathway. However, the data in the literature vary as much as an order of magnitude. The dose calculated here is to the basal layer of the skin (70 micrometers in depth) due to beta rays and electrons. The gamma contribution to the dose rate is generally a few per cent. The contamination is supposed to be uniformly and thinly spread over the skin. The equation is:

where:

H_T(skin) = Equivalent dose to the skin [mGy],
C_skin = Average surface concentration of radionuclide on skin or clothing [Bq/cm²],
CF_Beta-skin = Conversion factor: skin beta dose rate [(mGy/h)/(Bq/cm²)],
SF_Beta-skin = Shielding factor due to clothing; representative values of shielding factors are approximately 3 - 5 for light clothing and 1000 for heavy clothing,
t = Time of exposure [h]

The equation should be calculated for each radionuclide present and the equivalent doses should be summed. Now, the product of concentration and time gives the number of disintegrations per unit area of skin. More information, dose factors and shielding factors can be found in Beta Dose to Skin

Immersion in Air

The direct exposure pathway for gamma-emitting radionuclides released in to the atmosphere will be external g-dose to the whole body from the radioactive material in the plume. Estimates for external exposure to g radiation due to immersion in contaminated air provide conservative estimates for exposure to an overhead plume, due to the factor of distance. The values are derived under the assumption that the plume is correctly approximated by a semi-infinite cloud. The equation is:

where:

E_immersion = Effective dose from external exposure due to immersion in contaminated air [mSv],
C = Average concentration of radionuclide in air [kBq/m³],
CF_immersion = Conversion factor for radionuclide,
t = Exposure duration [h].

See the document Immersion in Air for conversion factors and example calculations. Also see the page on Internal Exposure for Occupational sources for some similar dose factors given by the IAEA.

Dose from Ground Contamination

The effective dose calculated includes the external dose and committed dose from inhalation (resuspension) resulting from remaining on contaminated ground for the period of concern – 1st month, 2nd month or lifetime (50 years). Once the radionuclide concentrations on the ground are known, the effective dose can be estimated. The equation is:

where:

E = Effective dose from deposition for the period of concern [mSv],
C_ground = Average ground concentration of radionuclide [kBq/m²],
CF_ground = Conversion factor: effective dose per unit deposition for radionuclide (mSv/kBq/m²). Includes external dose and committed effective dose from inhalation due to resuspension resulting from remaining on contaminated ground for the period of concern.

The equation should be calculated for each radionuclide present and the effective doses should be summed. See the document Dose from Ground Contamination for dose factors and more information.