Figure 1 shows apparatus used to investigate the inverse-square law for gamma radiation - AQA - A-Level Physics - Question 1 - 2021 - Paper 3

To determine if the measured values of Rₑ support the prediction, we calculate the ratio of the correction factors:

• For d = 530 mm:

  $Rᵉ = \frac{90}{100} \cdot 0.033 \approx 0.33 \text{ s}^{-1}$

• For d = 380 mm:

  $Rᵉ = \frac{76}{100} \cdot 0.033 \approx 0.76 \text{ s}^{-1}$

Evaluating these values, we notice that as d decreases, Rₑ increases, consistent with the predicted relationship Rₑ = k/d². Therefore, the evidence supports the student's prediction.

To safely reduce d, the student should:

1. Lower the position of the detector (attached to clamp T) gradually while observing the vertical position to avoid sudden movements that could misalign the setup.
2. Consider using a long measuring stick to ensure adjustments are made precisely without needing to disturb the clamp directly. This procedure ensures the distance is minimized while maintaining safety and equipment integrity.

To determine ∆d, the change in distance can be calculated by finding the difference between subsequent d values that the student measures. If the measurements show consistent differences, then we can conclude that ∆d = d_final - d_initial; with clear tabulation of measurements if necessary.

The student should analyze the plotted data in Figure 2, checking if a straight line can be drawn with a gradient of -2, which would indicate the inverse square relationship. If the gradient of the best-fit line aligns closely with -2, it confirms the prediction. The student should also compare average values from the data points to ensure consistency and validation of results.

Using the provided formula:

• The average detected rate Rₗ = 100 s⁻¹ and the average number of detectable photons is 2.
• We apply the formula:

$tₗ = \frac{Rₗ - Rₑ}{Rₑ \times Rₗ}$

With Rₑ found from other calculations or estimates based on measurements.

The assumption that all photons would be detected neglects the probabilistic nature of radioactive decay. Even though 100 gamma photons might enter, they do not arrive at a consistent rate; there are often intervals during which some photons escape detection due to the inherent random nature of decay events. Additionally, the dead time, where photons are not registered, creates a lag in recordings, leading to potential undercounts.