Topic 5 - Dose Units

Beta Radiation

Beta-ray interactions

• Use “beta-particle absorption curve” relationship given in Cember with caution

Beta Radiation

• Beta radiation can be approximated by semilog behavior (see Fig 5.2).
• Intensity of radiation can be described by:
  
  • j is the beta intensity at depth t (energy/area/time)
  • j_o is the initial intensity
  • m_b is the beta-ray absorption coefficient

Calculating m_b

• If maximum beta-ray energy E_m is in MeV, then m_b for air and tissue is given by:

Beta-Dose from Surface Contamination

• C_a, Bq cm²
  • 50% betas up
  • 50% betas down
• Energy flux at surface is
  
  • j, fluence rate, energy area^-1 time
  • Ē, average energy per dis
• Surface dose-rate:
  
• Calculating in SI units:
  
  • where k is a constant of unit conversions
    • (MeVZJ)
    • (sZh)
• See Cember, p 188

Beta Skin Dosimetry

• Dead layer of skin provides some shielding
• After going through the dead layer of skin
  • All the beta energy is generally deposited in the living tissue
  • Betas generally only travel about 1 cm or less in tissue
  • Energy deposited in tissue = dose

Anatomy of skin

Beta Skin Dosimetry

• Shielding provided by the dead layer of skin can be approximated by (Equation 6.20):
• Energy absorbed by living tissue
  • 0.007 g cm²
  • Equation 6.26:

Beta Surface Dose

• If the beta emitter is not in contact with the skin, add in other attenuating material, such as air, using appropriate coefficients
• Equation 6.20 gives attenuation in air
• Other attenuation by clothing

Standard Thickness

Submersion Dose

• Inside an infinite cloud of a radionuclide
  • rate of energy emission = rate of energy absorption
• Given
  • C Bq m³
  • Ē beta energy (MeV)
• The dose rate is:

Submersion in ⁸⁵Kr

• Assume the person is in an infinite cloud
  • Rate of energy emission = rate of energy absorption
• Assume half the betas are emitted towards the skin, half away
• Assume tissue absorbs 10% more energy than tissue on a per kg basis
• Equation 6.40 is useful, but it is not necessary to memorize

Convert to Useful Units

• 1 ´ 10^-6 microCi/cm³
  
  = 3.7 ´ 10⁴ Bq/m³

Calculating Submersion Dose

• 1.1 = 10% greater energy absorption
• 0.5 = Half up, half down
• e^{-0.007 ´ m} = dead skin shielding
• Dose rate in seconds is found (UNITS!)

Submersion

• Combine terms
  
  
  = 4.9 ´ 10^-10 Gy/s = 1.7 ´ 10^-6 Gy/hr
  = 0.17 mrad/hr

Volume Source

• Useful for finding beta dose rates from container surfaces
• Assume infinite thickness
• Calculate dose rate in infinite medium
  • Divide in half to find dose rate at surface
  • Half go in, half go out
• Add in any shielding