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Ionizing Radiation Equations


1 - Inverse Square Law


I2 =  I1 [ d1 / d2 ] 2
I2, I1 = Intensity at d2, d1

d2, d1= Distance to source

2 - Activity

 

  • a) Ai = 0.693 / T1/2 Ni
  •  

  • b) A = Ai(0.5) t / T1/2
  •  

  • c) A = Aie  -0.693t / T1/2
  • Ai = Initial Activity in Becq. (ps)
  • Ni= Initial Number of Atoms
  • T1/2 = Half - Life in seconds
  • A = Activity (dps) in Becq.
  • t = time elasped in seconds
  •  
  • e = natural log

3 - Exposure & Dose

  • a)  Rad = 0.869 (f-factor) (Roentgens)
  • b)  rem = rad x Quality Factor
  • c)  Life Accumulation = 5 x (N-18) in rem      N = Age in years

 

4 - Exposure Rate



D = ΓA / d2  

D = Exposure rate (R/hr)

Γ = Specific gamma ray constant in units of R · cm2/mCi · hour

d = distance from source in cm

A = Activity in mCi of the isotope

5 - Shielding

  • a) I = (1/2) A I0
  •  

  • b) I = (1 / 10) B I0
  •  

  • c) I = I0 / 2 ( x / HVL )
  •  

     

    • d) x = 3.32 Log [I0 / I ]   [ HVL ] or x = Log ( I0 / I ) HVL / Log 2
  • I = Intensity on other side of shield
  • I0 = Intensity without shield (R/hr)
  • A = Number of Half-Value-Layers (HVL)
  • HVL = Shield thickness needed to reduce exposure by half.
  • B = Number of Tenth-Value-Layers (TVL)
  • TVL = Shield thickness needed to reduce exposure by 1/10th.
  •  
  • x = Shield thickness

6 - Effective Half - Life

  • 1 / T 1/2 eff = 1 / T 1/2 rad + 1 / T 1/2 bio
  • or
  • T 1/2 eff = T 1/2 rad  x  T 1/2 bio / T 1/2 rad   +   T 1/2 bio
  • T1/2eff = Effective Half - Life
  • T1/2rad = Half-Life of internal radioisotope or source
  • T1/2bio = Time for the body to eliminate half of the source.
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