- #1

- 704

- 12

## Homework Statement

The potassium isotope

^{42}

_{19}K has a half-life of 12 hr, and disintegrates with the emission of a γ-ray to form the calcium isotope

^{42}

_{20}Ca. 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

^{42}

_{19}K 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**

^{42}

_{19}K →

^{42}

_{20}Ca +

^{0}

_{-1}β +

^{0}

_{0}γ.

^{42}

_{20}Ca: 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 = A

_{0}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?

Last edited: