Distance-Intensity Calculation

Inspectors often use the crank-out method when working with radioactive sources.I1/ I2 = D22/ D12

I1 = Intensity 1 at D1
I2 = Intensity 2 at D2
D1 = Distance 1 from source
D2 = Distance 2 from source

Example Calculation 1

The intensity of radiation is 530 R/h at 5 feet away from a source. What is the intensity of the radiation at 10 feet?

Rework the equation to solve for the intensity at distance 2
            I2 = I1 x D12 / D22

Plug in the known values
           I2 = 530R/h x (5ft)2 / (10ft)2

Solve for I 2
           I2 = 132.5 R/h

In this instance the distance has been doubled and the intensity at that point has decreased by a factor of four.

Example Calculation 2

A source is producing an intensity of 456 R/h at one foot from the source. What would be the distance in feet to the 100, 5, and 2 mR/h boundaries.

Convert R/hour to mR/hour

       456R/h x 1000 = 456,000 mR/h

Rework the equation to solve for D2

D 2 = I 1 D 1 2 I 2 D_{2}=\sqrt{\frac{I_{1}D_{1}^{2}}{I_{2}}}

Plug in the known values and solve

D 2 = 456 , 000 m R / h × ( 1 f t ) 2 100 m R / h D_{2}=\sqrt{\frac{456,000mR/h \times (1ft)^{2}}{100mR/h}}

         D2= 67.5 feet

Using this equation the 100mR/h boundary would be at 68 feet, the 5mR/h boundary would be at 301.99 feet, and the 2mR/h boundary would be at 477.5 feet. Sources are seldom operated for an entire hour, and collimators are often used which reduce these distances considerably.