The radioactivity of an isotope of radon was measured each day for a week and the following data were recorded - Leaving Cert Physics - Question b - 2018

1. Plot the given activity data against time on graph paper.

   • X-axis: Time (days)
   • Y-axis: Activity (MBq)

2. Mark the points: (0, 600), (1, 490), (2, 400), (3, 330), (4, 270), (5, 220), (6, 180), (7, 150).

3. Draw a smooth decay curve that connects these points, showing the exponential decrease in activity over time.

From the graph, the half-life is observed by identifying the time taken for the activity to drop from one-half of its initial value (300 MBq). Based on the plotted curve, it can be estimated that the half-life is approximately 3.3 days.

Using the decay constant $\'\lambda$ = \frac{\ln 2}{T_{1/2}}$where$T_{1/2} = 3.3$ days:

1. Calculate $\'\lambda$: $\lambda = \frac{\ln 2}{3.3} \approx 0.21 \text{ days}^{-1}$

2. Use the initial activity: $A = \lambda N$ Where $A = 600$ MBq, therefore: $600 = 0.21 N \\ N = \frac{600}{0.21} \approx 2857.14$

Thus, the number of nuclei in the sample at the beginning of the investigation is approximately $2.86 \times 10^3$.