Figure 1 shows a sealed radioactive source used in schools and colleges - AQA - A-Level Physics - Question 1 - 2019 - Paper 3

The number of routes by which B can change into K can be counted from Figure 2. Analyzing the paths taken by B, it is found that there are three distinct routes leading to K.

The nuclei common to all pathways from $^{226}\text{Ra}$ to $^{206}\text{Pb}$ are B, C, D, and E. Each pathway utilizes these intermediates before reaching the stable lead isotope.

1. Calibration: Ensure the radiation detector is calibrated before starting the experiment, which helps in obtaining accurate readings.

2. Consistent Positioning: Keep the position of the source and detector the same throughout the measurements to eliminate positional error.

3. Multiple Trials: Take several measurements and compute the average to minimize random errors.

To determine the minimum thickness of the aluminium absorber, we can refer to Figure 4. It shows that for eta particles of 5.5 MeV, the maximum range is approximately 12 mm in aluminium. Therefore, the aluminium thickness needed to fully absorb eta particles should be at least 12 mm.

From Figure 6, the graph indicates a linear relationship between $d$ and rac{1}{A}\text{B} Q^{-0.5}. By calculating the gradient of the line, we find that $d$ is directly proportional to the inverse square of the count rate, allowing us to infer specific distances based on measured values.

$e$ can be calculated once the values for $A$ are confirmed. By substituting the suitable values into the established equation from Figure 6, we find $e$ to be approximately 3.2 mm.