Rich Text Content

I. Data

Mean = .25 ct/s

Median = .3 ct/s

II. Questions

1. When testing the sample, not all of the radiation we detect is due to the sample; some is due to background radiation. So to get a more accurate measurement, we need to subtract out the background radiation from the data.

2. The source of background radiation is naturally occurring (and maybe artificial) radioactive materials in our environment.

3. Data:

Peak: 96 ct/10 s, 98 ct/10 s

Mean: 102.3 ct/10 s

Median: 101.5 ct/10 s

Std dev: 9.40 ct/10 s

4. The mean and median are pretty close; they’re well within a standard deviation of each other.

5. Graph: see attached.

6. A normal distribution (the peak is in the center, and the frequency gets lower as you travel farther from the center).

7. We can’t predict the exact number of nuclei decaying at any given time; the peak only represents the highest probability.

8. If the decays weren’t random in some sense, then we would know exactly how many nuclei would decay over 10 seconds. That’s not the case, though; the radiation count per 10 seconds can vary significantly, suggesting some randomness.

9. 113 – 91 = 22 ct/10 s

This tells us that the distribution is fairly spread out. The frequency doesn’t drop off very fast; measurements 11 ct/10 s away from the peak still occur with significant frequency.

10. No, it is not possible to predict when an individual nucleus could decay. It might be today, or it could be thousands of years from now.

11. It’s possible, but very unlikely.

12. It’s possible, but very unlikely.

13. No; there would be fewer radioactive nuclei, so they would decay at a lower rate.

14. Not significantly. The half life of the sample is about 3-4 years, so there would not be a significant difference in the amount of radioactive material in a 50 minute period.

15. No, some is due to background radiation. If background radiation is taken into account, the count rate would decrease (by .25 ct/s).

16.

30 seconds:

Mean: 109.7 ct/10 s

Std dev: 4.93 ct/10 s

1 minute:

Mean: 107.8 ct/10 s

Std dev: 7.96 ct/10 s

2 minutes:

Mean: 104.5 ct/10 s

Std dev: 9.77 ct/10 s

5 minutes:

Mean: 106.7 ct/10 s

Std dev: 10.4 ct/10 s

10 minutes:

Mean: 104.1 ct/10 s

Std dev: 9.75 ct/10 s

20 minutes:

Mean: 103.2 ct/10 s

Std dev: 9.27 ct/10 s

30 minutes:

Mean: 102.3 ct/10 s

Std dev: 9.41 ct/10 s

As more measurements are made, the data seems to more or less converge on values for the mean and standard deviation, but there is still some variation.

17. If the detector was twice as far away, we would probably measure less radiation. Radiation should go out in all directions from the sample, so if the detector was further away, a smaller portion of the radiation would be picked up by the detector.

rich_text