3.1 Fill in the follwing table in order to find out how many ²³⁸U atoms would be left after 27 billion years, if you started out with 8 billion.

3.2 Sketch the decay of the virtual "test sample" in the space provided below.

Average background per 100 s = _______________

Average background per 50 s  = _______________

When plotting data:

1. Label axes and title the graph (underline).

2. Start the time axis at Interval 1 (t = 10 sec) and continue for 30 intervals.

3. Determine the order of the vertical (activity) axis from lowest and highest counts (2 decades).

1. The isotope Ag¹¹⁰ has a much shorter half-life than Ag¹⁰⁸. Therefore, the majority of counts during the first few time intervals is due to the decay of Ag¹¹⁰. Pretend that all of these counts were due to the decay of Ag¹¹⁰, and determine its half-life from your best-fit curve. (Remember there are 10 + 1.5 = 11.5 seconds between measurements.)

2. Use your answer to #1 to determine how long you have to wait before there is only 1/32 of the original amount of Ag¹¹⁰. How many time intervals does this correspond to?

3. Once the amount of Ag¹¹⁰ is negligible (say less than about 1/32 of its initial amount), the counts are due primarily to decay of Ag¹⁰⁸. Keeping your answer to #2 in mind, determine the half-life of Ag¹⁰⁸ from your best-fit curve.

4. Is your result for #3 consistent with the assumption you made in #1? Why or why not?

5. Why are neutrons used in bombarding the silver?

6. Which decay products are detected by the counters?

7. Is there a maximum amount of radioactive silver which can be produced in our process? Why or why not?

8. Radioactive dating experiments assume that half-lives are constant in time and independent of physical conditions. Is this a good assumption? Why or why not?