If workers are allowed a maximum dose of 5.0 rem in 1 year, how close to the source may they operate, assuming a 35-h work week? Assume that the intensity of radiation falls off as the square of the distance. (It actually falls off more rapidly than 1/r2 because of absorption in the air, so your answer will give a better-than-permissible value.)

Answer: The workers may come only as far as 0.24m

(Note: The queston is incomplete. Here is the complete question below)

A shielded gamma ray source yields a dose rate of 0.048rad/h at a distance of 1.0m for an average-sized person. If workers are allowed a maximum dose of 5.0 rem in 1 year, how close to the source may they operate, assuming a 35-h work week? Assume that the intensity of radiation falls off as the square of the distance. (It actually falls off more rapidly than 1/r2 because of absorption in the air, so your answer will give a better-than-permissible value.)

Explanation:

Note: 1rem = 1rad

Dose rate per hour from a distance of 1.0m = 0.048rem/h

maximum daily dose in a year for a 35-h week = 5rem/yr / (35h*52*1yr) = 0.0027rem/h.

The required distance is obtained from the inverse square law for radiation which states that the intensity of the radiation (I) decreases in proportion to the inverse of the distance from the source (d) squared.

From the law, I₁/I₂ = d₁²/d₂²

Therefore, by knowing the intensity at one distance, one can find the intensity at any other distance.

From the given values I₁ = 0.048rem/h, I₂ = 0.0027rem/h, d₁ = 1.0m, d₂ = ?

d₂² = I₂d₁² / I₁

d₂² = 0.0027rem/h * (1.0) ² / 0.048rem/h

d₂² = 0.05625m²

d₂ = √ (0.05625)

d₂ = 0.24m