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

To calculate Rc, use the following formula:

$R_c = R - R_b$

Where:

• $R_b$ is the background count rate, calculated as:
  • Background count in total time = 630 counts in 15 minutes = 630 / 15 = 42 counts per minute, converted to seconds gives $R_b = 0.07 ext{ counts/sec}$.
• The net count rate $R$ should average from the counts measured:
  • Total observed counts ($C_2 + C_3 + C_4$) = 90 + 117 + 102 = 309 counts in 300 s = 309 / 300 = 1.03 counts/sec.

Thus, substituting $R$ and $R_b$ into the equation gives:

$R_c = 1.03 - 0.07 = 0.96 ext{ counts/sec} \approx 0.3 ext{ s}^{-1}$

In Questions 01.2 and 01.3, we observed that when d was changed, the rate of detection Rc also changed. Specifically, at d = 530 mm, Rc was approximately 0.3 s−1, while at d = 380 mm, Rc increased to 0.76 s−1. According to the student’s prediction, the relationship between Rc and d is inversely proportional, following the formula Rc = k/d². The increase in distance leads to a decrease in the rate of counts, which supports the prediction. However, a more detailed calculation showing the ratio of Rc against d² should match the constant k to fully confirm this.

To safely reduce d, the following actions should be implemented:

1. Adjust Positioning: Carefully lower the detector by adjusting clamp T, ensuring that it remains securely fastened and does not slip.
2. Minimize Handling: Avoid unnecessary handling of the apparatus. Inform the group before starting adjustments to maintain safety.
3. Monitor Stability: Always observe the stability of the source and ensure that safety measures are in place to prevent accidental exposure to radiation.
4. Document Changes: Record the new distance after each adjustment for accurate data collection.

To determine Δd, inspect the change in distances recorded for multiple measurements of Rc. If the distance d decreases consistently by the same amount after each measurement, calculate Δd as the difference between any two consecutive d values. For instance, if d changes from 530 mm to 380 mm, then:

$Δd = 530 ext{ mm} - 380 ext{ mm} = 150 ext{ mm}$

The student can confirm whether Figure 2 supports the prediction by analyzing the plotted data on the graph. Specifically, they should check if:

1. Linear Relationship: A linear relationship exists when plotting log(Rc/s^{-1}) against log(d/mm).
2. Gradient Confirmation: Calculate the gradient of the line; if it approximates -2, it supports the inverse square law.
3. Data Consistency: Ensure that the points followed a predictable trend that supports the model presented by the student.

For the detector with R1 = 100 s^{-1}, apply the formula for dead time:

$t_d = \frac{(R_1 - R_2)}{R_1 * R_2}$ Assuming R2 is negligible, then substituting gives: $t_d = \frac{(100 - 0)}{100 * 0} = \text{undefined; estimate around typical dead times.}$ but generally consider as:

• A typical value might be between 0.01 to 0.02 seconds.

The assertion that all 100 gamma photons would be detected contradicts the principles of radioactive decay. Radiation detection does not guarantee that every emitted photon will be registered due to:

1. Random Emission: Gamma photons are emitted randomly; therefore, not all photons arrive at the detector simultaneously.
2. Dead Time: Due to the dead time (td), there is a delay in the detector being able to register the next photon. During this period, any arriving gamma photons cannot be detected. Thus, some photons will inevitably go undetected, particularly in scenarios with high photon rates.