Ordinary soil contains typically 1 part per million (ppm) of uranium by mass. 

(a) How many uranium nuclei are in the top 10 m of soil under a typical house (20 m  20 m)? 

(b) Only 0.72% of the nuclei in part (a) are ²³⁵₉₂U; the rest are ²³⁸₉₂U, which has a much longer half-life. How many 23 92 5U nuclei are in the soil under this house? How many ²³⁸₉₂U nuclei are in the soil under this house? 

(c) How many of the ²³⁸₉₂U nuclei in part (b) undergo radioactive decay over a period of one day? 

(d) How many of the ²³⁸₈₆U nuclei in part (b) undergo radioactive decay over a period of one day? 

(e) The decay of ²³⁸ ₉₂U leads to radon gas (²²²₈₆Rn; see Fig. 30.9). If all the ²³⁸₉₂U decays to make ²²²₈₆Rn, how many ²²²₈₆Rn nuclei are produced under the house in one month? 

(f) If all the ²²²₈₆Rn nuclei in part (e) seep into the house above, what is the activity in the house?

Figure 30.9