A Se-75 source is producing 310 rem at a distance of 3.0 m. What is the distance needed to decrease the intensity of exposure to below 25 rem, the level at which no effects would be detectable.
To solve this problem, we need to use the inverse square law, which relates the intensity of radiation to the distance from the source. The inverse square law states that the intensity is inversely proportional to the square of the distance.
The equation for the inverse square law is:
I2 = I1 * (d1 / d2)²
Where:
I1 is the initial intensity of the source (310 rem)
I2 is the final intensity (25 rem)
d1 is the initial distance (3.0 m)
d2 is the final distance we are trying to find.
To find the distance (d2), we can rearrange the equation as follows:
d2 = √((I1 * d1²) / I2)
Substituting the given values:
d2 = √((310 rem * (3.0 m)²) / 25 rem)
Calculating this equation gives us:
d2 = √((310 rem * 9.0 m²) / 25 rem)
= √(2790 m² / 25)
= √(111.6 m²)
= 10.6 m (rounded to one decimal place)
Therefore, the distance needed to decrease the intensity of exposure below 25 rem, the level at which no effects would be detectable, is approximately 10.6 meters.