Fig. 17.1 shows a grid on which the decay of a radioactive isotope is to be plotted. The initial activity is 3200 Bq and the half-life is 15 minutes. (a) Ca...

(a) Calculating activity at each time [3]

The half-life is 15 minutes, so the activity halves every 15 minutes. Starting from 3200 Bq at time 0 and dividing by 2 at each half-life step:

Each value is exactly half of the previous one because during each half-life interval, half of the remaining radioactive nuclei decay. [3]

(b) Which data point sits at the 800 Bq grid line [1]

From the table above, the activity is 800 Bq at 30 minutes. This is the data point that would be plotted on the 800 Bq grid line. [1]

(c) Shape of the decay curve [1]

The curve falls steeply at first and then more gradually, approaching zero but never quite reaching it. This is the characteristic shape of an exponential decay curve. The rate of decrease is proportional to the current activity, so as the activity becomes smaller, the curve flattens out. [1]

(d) Fraction of nuclei remaining after 60 minutes [1]

Number of half-lives elapsed = 60 / 15 = 4 half-lives.

Fraction remaining = \(\left(\frac{1}{2}\right)^4 = \frac{1}{16}\). [1]

After 4 half-lives, only 1/16 of the original radioactive nuclei remain undecayed.

(e) Why radioactive decay is random [1]

Radioactive decay is described as random because it is impossible to predict which particular nucleus will decay next, or exactly when any given nucleus will decay. Each nucleus has the same probability of decaying in a given time interval, but the actual moment of decay for any individual nucleus is completely unpredictable. [1]