The potassium isotope 4219K has a half-life of 12 hr, and disintegrates with the emission of a γ-ray to form the calcium isotope 4220Ca. What other radiation besides γ-rays must be emitted? How many electrons, protons, and neutrons are there in an atom of the calcium isotope?
The amount of radiation received in unit time by a person working near a radioactive source, commonly called the dose rate, is measured in rem hr-1. The safety regulations forbid dose rates in excess of 7.5 * 10-4 rem hr-1.The γ-ray dose rate from the 4219K source is found to be 3 * 10-3 rem hr-1 at a distance of 1 m. What is the minimum distance from this source at which it is safe to work?
After how long will it be safe to work at a distance of 1 m from this source?
Answers: 2.0 m; 24 hours.
2. The attempt at a solution
4219K → 4220Ca + 0-1β + 00γ.
4220Ca: electrons = protons = 20, neutrons = 22.
Minimum distance is (3 * 10-3) / (7.5 * 10-4) = 4. So 1 m from the source is 4 times more dangerous than it should be. So the distance should be increased 4 times, so the safe distance is 4 m. Why the answer is 2 m?
I used A = A0 e- λ t to find time. The dose should decrease from 3 * 10-3 rem hr-1 to 7.5 * 10-4 rem hr-1. So: 7.5 * 10-4 = 3 * 10-3 e- (ln 2 / 12) t → t = 4.3 hours. Why not 24? I also calculated everything in seconds, not hours, still same result when I change the final answer to seconds.
Why the distance is wrong and how to get the correct time?