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Figure 1 shows apparatus used to investigate the inverse-square law for gamma radiation - AQA - A-Level Physics - Question 1 - 2021 - Paper 3
Question 1
Figure 1 shows apparatus used to investigate the inverse-square law for gamma radiation. Figure 1 A sealed source that emits gamma radiation is held in a socket at... show full transcript
Worked Solution & Example Answer:Figure 1 shows apparatus used to investigate the inverse-square law for gamma radiation - AQA - A-Level Physics - Question 1 - 2021 - Paper 3
Step 1
Describe a procedure for the student to find the value of d, the vertical distance between the open end of the source and the bench.
Answer
To determine the vertical distance d, the student should use a set-square to ensure the detector is aligned properly. The following steps could be taken:
- Position the set-square against the base of the bench, ensuring the vertical edge is flush with the surface.
- Measure the height from the bench to the open end of the source using a ruler.
- Subtract the height of the bench (138 mm) from the measured height to find the accurate distance d.
This method allows for a precise measurement while maintaining the stability of the setup.
Step 2
Explain whether the values of Rc in Questions 01.2 and 01.3 support the student's prediction.
Answer
Given that Rc values observed were:
- For d = 530 mm, Rc = 0.33 s⁻¹,
- For d = 380 mm, Rc = 0.76 s⁻¹.
According to the student's prediction, Rc should vary with d². To confirm this, we can calculate the ratio:
For d = 530 mm:
- Rc = 0.33 s⁻¹
For d = 380 mm:
- Rc = 0.76 s⁻¹
Calculating the expected ratio:
d² values:
- (530 mm)² = 280900 mm²
- (380 mm)² = 144400 mm²
Now, calculate the predicted Rc for d = 380 based on the ratio of counts. If we see that the ratio of counts between the two measurements aligns reasonably with the inverse-square law prediction, this would support the student's hypothesis. However, since the values diverge, indicating a non-linear relationship, this suggests the data collected may not fully support the theoretical prediction.
Step 3
Describe a safe procedure to reduce d. Give a reason for your procedure.
Answer
To safely reduce the distance d between the detector and the source without risking instability, the student could lower the position of the detector using clamp T. This involves adjusting the clamp slowly to minimize vibrations or disturbances that could affect the count rate measurements. The reason for this approach is to maximize safety by minimizing handling of the equipment while still allowing accurate results.
Step 4
Determine Δd.
Answer
To determine Δd, examine the changes in the distance d from one measurement to the next as indicated in Figure 2. By calculating the differences between consecutive distance measurements, the value for Δd can be found. Assume the distances are presented accurately in the figure.
Step 5
How the student could confirm whether Figure 2 supports the prediction.
Answer
The student could draw a best-fit line on the graph presented in Figure 2 and check the gradient. If the gradient is approximately -2, as predicted by the relationship Rc = k / d², this would suggest support for the prediction. Additionally, confirming that all data points lie reasonably close to the line will provide further evidence.
Step 6
Calculate t4 for this detector.
Answer
Given R1 = 100 s⁻¹ and the average count of two gamma photons per second:
t4 can be approximated using the formula for dead time: t1 = R1 – R2 / R1 x R2. Substituting in the values: Using R2 approximations accordingly will yield the specific value for t4 based on the conditions defined.
Step 7
Explain, with reference to the nature of radioactive decay, why this idea is not correct.
Answer
The idea that if 100 gamma photons enter a detector in one second and t1 is 0.01 s, all photons would be detected is flawed. Radioactive decay is a random process, and the detection of photons is subject to statistical fluctuations. Some photons may arrive during the dead time, preventing detection. Therefore, even if the detection rate seems high, it does not guarantee that all incoming photons will be captured, due to the inherent nature of radioactive decay and timing constraints.