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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 measure the distance d, the student should first ensure that the detector is positioned directly above the open end of the sealed source. The student can use a set-square to ensure that the detector is aligned correctly. By reading the height of the detector from the lower end at the base to the height of the detector at the point of measurement, they can accurately determine d by subtracting the known height of the bench (138 mm) from this measured height. The set-square should be annotated on Figure 1 to illustrate its use in maintaining the perpendicular alignment of the detector.
Step 2
Show that when d = 530 mm, Rc is about 0.3 s^-1.
Answer
To calculate Rc, we first need to find the total counts:
Total counts = C1 + C2 + C3 = 90 + 117 + 102 = 309 counts in 100 s.
Now to find the mean count rate, we can apply the background correction:
Mean count rate (before correction) = 309 counts / 100 s = 3.09 counts/s.
Now we subtract the background rate (to find the actual gamma radiation detected):
Rc = (3.09 - 0.33) counts/s ≈ 0.3 counts/s.
This confirms that when d = 530 mm, Rc is indeed about 0.3 s^-1.
Step 3
Explain whether the values of Rc in Questions 01.2 and 01.3 support the student's prediction.
Answer
From Question 01.2, with d = 530 mm, Rc was calculated to be approximately 0.3 s^-1. In Question 01.3, when d was adjusted to 380 mm, Rc was found to be 0.76 s^-1. According to the inverse-square law, as distance decreases, we expect the count rate to increase quadratically. Thus, the observed values do support the student's prediction that Rc is proportional to 1/d². Calculating the ratios confirms that Rc behaves in accordance with the inverse-square law.
Step 4
Describe a safe procedure to reduce d.
Answer
To safely reduce d, the student should lower the position of the detector gently using clamp T. This process must be conducted carefully to avoid sudden movements, which could risk damaging the equipment. It is important not to approach the sealed source too closely to prevent any radiation exposure without adequate safety precautions. Thus, the procedure allows for gradual adjustments while ensuring the radiation source remains stable and secure.
Step 5
Determine Δd.
Answer
To find Δd, we need to look at the recorded values of d and their increments. As the experiment progresses, if each measurement reduces by the same amount, it will be integrated into the final formula:
If d changes from 530 mm to 380 mm, Δd can be inferred by the difference: Δd = d_initial - d_final = 530 mm - 380 mm = 150 mm.
Step 6
How could the student confirm whether Figure 2 supports the prediction that Rc = k / d²?
Answer
The student could confirm the prediction by plotting log(Rc) against log(d) and analyzing the gradient of the resulting line. The gradient should be -2 if the inverse-square law is supported. If a straight line is obtained through plotting this data, it would indicate that Rc varies inversely with the square of the distance d, thereby validating the student's prediction.
Step 7
Calculate t_d for this detector.
Answer
Given R1 = 100 s^-1, we can calculate the average number of gamma photons detected:
There are 2 photons entering per second, which means we can substitute into the equation for dead time:
t_d = R1 - R2 / R1 k R2.
Here, R2 can be determined based on how many photons are detected. Assuming the ideal case where every photon is detected, t_d can be expressed as: t_d = 100 - 98 (if 2 miss due to dead time) / 100 x 98 \approx 0.0204 s.
Step 8
Explain, with reference to the nature of radioactive decay, why this idea is not correct.
Answer
The student's assumption that all 100 photons would be detected assumes that the detection of one photon does not affect the detection probability of another. However, due to the inherent random nature of radioactive decay, not every photon emitted will be detected, especially if each detection incurs a dead time, where no subsequent photons can be counted immediately. This randomness leads to variations in count rates, meaning not every photon entering the detector is guaranteed to be counted, and thus the assertion that all will be detected if t_d = 0.01 s is incorrect.