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

To find Rc when d = 530 mm:

1. Calculate the Background Count Rate:

   • Convert the background count from counts in 15 minutes to a count rate in seconds:

   $C0 = \frac{630 \text{ counts}}{15 \text{ minutes} \times 60 \text{ seconds/minute}} \approx 0.7 \text{ counts/s}$

2. Adjust Counts for Background:

   • Use the counts C1, C2, and C3 to find the average:

   $C = \frac{90 + 117 + 102}{3} = 103 \text{ counts/100 s} = 1.03 \text{ counts/s}$

3. Calculate Rc:

   • Subtract the background count rate from the measured count rate:

   $Rc = C - C0 = 1.03 - 0.7 = 0.33 \text{ s}^{-1}$

In Question 01.2, the value of Rc calculated when d = 530 mm is approximately 0.33 s−1, while in Question 01.3, with d = 380 mm, Rc is found to be 0.76 s−1. To determine if these values support the student's prediction, we can apply the prediction formula:

• The student suggested that Rc = k/d². Therefore, the ratio of the two readings should reflect this relationship.
• Given that d decreases, we would expect Rc to increase and indeed, the calculations demonstrate that as d decreases from 530 mm to 380 mm, Rc rises from about 0.33 s−1 to 0.76 s−1, thereby supporting the prediction that higher counts correspond to shorter distances.

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

1. Lower the Detector: Carefully adjust clamp T to lower the detector without touching the radiation source directly. This is important to avoid potential exposure to the radiation source.
2. Use Proper Tools: Ensure that the adjustment is made using tools (such as a long reach tool, if necessary) to maintain a safe distance from the radiation source.
3. Maximize Distance: It is crucial that the distance between the student and the radiation source is maximized during this procedure to minimize exposure. Moving only one stand ensures controlled adjustment without accidental change in the environment.

To evaluate Δd from Figure 2, we need to look at the recorded values of d:

1. Identify the increments between successive d values plotted in Figure 2. For example, if the values are 530 mm, 480 mm, 380 mm, then:
   • The change from 530 mm to 480 mm is: $Δd = 530 - 480 = 50 ext{ mm}$
   • Continue this method for other measurements and conclude the consistent change.

To calculate tdead:

1. Using the formula provided: $t_{dead} = \frac{R_1 - R_c}{R_1 \times R_2}$
2. Where R1 is 100 s−1 (the initial measured rate), and R2 = 1.96 s−1 (the rate corrected for dead time): $t_{dead} = \frac{100 - 0.76}{100 \times 1.96}$
3. After calculating the above, it will yield the dead time period.

The statement made by the student reflects a misunderstanding of radioactive decay. In radioactive decay:

1. Random Emission: The emission of gamma photons is inherently random. This means that not every incoming photon leads to a detection due to the probabilistic nature of interactions with the detector.
2. Dead Time Effect: The concept of dead time implies that after a photon is detected, there is a brief period during which the detector cannot register another photon. Thus, there is always a chance that some photons will not be detected during this time, regardless of their flux.
3. Detection Limit: This results in a lower than expected number of detected photons, emphasizing that higher rates do not guarantee full detection due to these timing limitations.