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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. A sealed source that emits gamma radiation is held in a socket attached to ... 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 find the value of d, the student can use a ruler or measuring tape to measure the distance from the bottom edge of the radiation detector to the bench. Specifically, they should place the detector vertically above the source and align the lower edge of the detector in a straight line with the source. After obtaining the height measurement, the distance d can be calculated by subtracting the fixed height of the bench (138 mm) from the measured height of the detector's lower edge.
In Figure 1, a set-square can be utilized to ensure that the detector is perfectly vertical by aligning one edge against the base and the other edge against the side of the detector.
Step 2
Explain whether the values of R_c in Questions 01.2 and 01.3 support the student's prediction.
Answer
To evaluate whether the values of R_c support the student's prediction that R_c is proportional to rac{1}{d^2}, we can compare the calculated mean count rates. For d = 530 mm, R_c was determined to be approximately 0.33 s^{-1}, and for d = 380 mm, R_c increased to 0.76 s^{-1}. To verify the prediction, we can calculate the expected values using the inverse-square law:
Assuming R_c is directly proportional to rac{1}{d^2}, the ratio of R_c values can be calculated as follows:
decreased distance ratio = rac{(530 mm)^2}{(380 mm)^2} ightarrow ext{Calculate this value}
If the calculated value aligns with the ratio of the measured R_c values, it supports the student's prediction.
Step 3
Describe a safe procedure to reduce d. Give a reason for your procedure.
Answer
To safely reduce d, the student should first ensure that the apparatus is turned off to avoid any gamma radiation exposure. The student should use a long ruler or measuring tape from a safe distance, adjusting the clamp T to lower the detector carefully. Additionally, they should minimize movement near the source to prevent disturbance of the experimental setup. This procedure is essential to ensure safety while maintaining accuracy in measuring the radiation levels.
Step 4
Step 5
How the student could confirm whether Figure 2 supports the prediction: R_c = k rac{1}{d^2}.
Answer
To confirm whether Figure 2 supports the prediction, the student should plot the measured values of R_c against the corresponding values of d on a graph. A linear relationship on a logarithmic scale would validate the prediction. They should then calculate the gradient of the resultant line:
If the gradient equals -2, it confirms that R_c is indeed proportional to rac{1}{d^2} as suggested by the student. However, if the gradient deviates significantly from -2, it indicates that the prediction might not hold.
Step 6
Calculate t_{dead} for this detector.
Answer
To calculate t_{dead} using the formula provided:
Substituting the count rates:
- R_s is 100 s^{-1}
- R_c can be calculated as 100 - (the background counts from previous measurements)
Using the values, the calculation will yield a specific dead time for the detector.
Step 7
Explain, with reference to the nature of radioactive decay, why this idea is not correct.
Answer
The student’s assertion that all photons should be detected if 100 gamma photons enter in one second is incorrect due to the nature of radioactive decay. Gamma decay is a random process, and particles emitted may not arrive at the detector simultaneously. In reality, there will be instances where the detector is unable to register new photons during t_{dead}. Therefore, some of these photons will be missed during this interval, leading to a non-unity detection efficiency.