Topic 10 - Shielding

External Radiation Protection

Basic Principles

• Minimize exposure time
• Maximize distance from the source
• Shield the radiation source

Distance Effects on Dose Rate

• Radiation Field Geometry Considerations
  • Point Source
  • Line Source
  • Plane Source

Calculating Fluence and Flux From a Point Source

• F = Fluence g/cm²
• f  = Flux g/cm²s
• D = total number of photons emitted
• S₀ = source strength (photons/s)
• r  = distance from source

Point Source Calculations - Photons

• Dose rate dictated by inverse square law
• I₁ = radiation intensity at distance R₁ from the source
• I₂ = radiation intensity at distance R₂ from the source

Example

• ⁶⁰Co
  • 2 photons (1.17, 1.31 MeV)
• Given 3700 MBq source
  • What is the exposure rate a 1 m?
  • What is the exposure rate at 7.2 m?

Point Source Calculations - Photons

• Dose equivalent rate
• G = specific gamma ray constant
• A = source activity
• d = distance
• w_r = radiation weighting factor
• V = velocity of approach to source
• t = total time of exposure

Example

• 10 Ci ⁶⁰Co source failed to retract into its shield
• Operator walks to source at 1 m/s
• Stops 1 m away, looks for 15 s and leaves at a rate of 2 m/s
• What is the dose commitment?

Line Source (Cember)

• Pipe carrying contaminated waste
• C_l is linear concentration of activity (e.g., Ci/cm or MBq/m)
• Source strength isG

Line Source (Cember)

• Dose rate at point p from small amount dl is

Line Source (Cember)

• Dose rate at point p from total length of pipe is

Example

• ²⁴Na in a cooling water line passes through a pipe in an access room 6 m wide
• Door to the room is in the center of the 6m wide wall, 3 m from the pipe
• Activity concentration is 100 MBq/m
• What is the dose equivalent rate in the doorway at point D₁ & D₂

Example Layout

Line Source Exposure Rate - Photons

• S = source strength in photons per s per unit line length (cm)
• h = perpendicular distance from point of interest P to the horizontal plane of the source>
• f = flux at point of interest in photons per cm2 per s
• r = distance from source to point of interest, P
• q = angle in radians
• Z₂ - Z ₁ = line length of source in cm

Ratio of Dose Rates as a Function of Distance Midpoint from a Line Source

Calculating Flux From Complex Geometries

• Point Kernel method
  • Source broken into many small kernels
  • Contribution from each kernel evaluated for a common point
  • Contributions are summed

Plane Source

Plane Source Activity

Plane Source Activity, Std Units

Ratio of Dose Rates as a Function of Distance from a Plane Source

Example

• 50 MBq of ²⁴NaCl solution spilled over a circular area of 50cm
• Find the dose equivalent rate at
• 30 cm
• 1 m

Volume Source

• Uniformly distributed activity
• Estimate based on “effective surface activity”
  • Allow for self-absorption in slab
• Slab
  • Thickness t
  • Contains C _v MBq m^-3 uniformly distributed activity
  • Linear absorption coefficient of slab is µ
• Observed intensity at surface due to activity in layer dx at depth x is:
  • D(C_a) = C_vdx·e^-µx