How should I calculate this ?

Question

If the dose rate from a sample of Tc-99 was found to be 8.5 × 10⁻⁵ mSv per hour at 1.6 metres, calculate the dose rate at 4.8 metres. Show your calculations. Give your answer to two significant figures.

Answer 1

since the dose rate obeys the inverse square law: dose = 1/(distance^2) = 8.5 x10^-5 mSv/hr at 1.6m, we know that at triple the distance(3d =4.8 m), the dose rate will be 1/((3d)^2) = 1/(9d^2). since we know 1/(d^2) = 8.5x10^-5, we know that the dose at triple that distance will be 1/9th that amount.