Ans.

(i)

Sol. In the introduction to the passage, the “half life” of an isotope is defined as the amount of time needed for one-half of the isotope’s nuclei to decay. To figure out the half-life of look at the first graph. When half of the nuclei have decayed, the N/N 0 ratio would be 0.5 (since the original ratio was 1.0). Draw a horizontal line across the graph at the level of 0.5. The horizontal line will intersect the curve at a specific point; from this point, draw a vertical line down to the x-axis. The vertical line intersects the x-axis somewhere between 2.5 and 3 days, which means that the amount of the time it takes for half of the nuclei to decay is between 2.5 and 3 days.

(ii)

Sol. Since N 0 is the same for both samples, you can use the two graphs to figure out the ratio of to after 2.7 days. You know from having done the previous question that after 2.7 days about half of remains. Take a look at the graph for . After 2.7 days, hardly any will have decayed at all. Therefore, the ratio of to will be 0.5 to 1, or 1 to 2.

(iii)

Sol. After one half-life has passed, half of the original 1,000 nuclei will have decayed, leaving 500. After the second half-life has passed, half of the 500 will be gone, leaving 250. When the third half-life has passed, half of the 250 will have decayed, leaving 125.