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

To determine whether the values of R_c support the prediction that R_c = k/d^2, we will compare the results.

For d = 530 mm:

• The corrected count rate R_c was found to be approximately 0.3 s^-1.

For d = 380 mm:

• The corrected count rate R_c was found to be 0.76 s^-1.

Calculating the expected ratios:

Using the equation R_c = k/d^2 and evaluating:

• For d = 530 mm,
  R_c = k/ (530^2) o ext{expected to fit relation.}
• For d = 380 mm,
  R_c = k/ (380^2) o ext{verified that it retains consistent decrease.}

Thus, the values do suggest a consistent behavior that supports the inverse-square law.

One safe procedure to reduce d is to:

1. Adjust the Position of the Detector: Carefully lower the position of the radiation detector (clamp T) closer to the source without disturbing other apparatus.

2. Maintain Stability: Ensure that clamps are tightened properly to avoid accidental movement.

3. Monitoring: Continuously check the distance using the vertical meter ruler while moving the detector downwards.

The reason for this procedure is to maximize the distance between the source and the radiation detector safely while minimizing any vibrations or movements that could affect the measurements.

To determine Δd, we first note how the distance d is adjusted for each measurement. We look at the two given values in the experiments, d when d = 530 mm and d when d = 380 mm.

The difference here is:

Δd = 530 mm - 380 mm = 150 mm.

To confirm whether Figure 2 supports the prediction R_c = k/d^2, the student could:

1. Plot the Data: Draw a graph with log(R_c) on the y-axis and log(d) on the x-axis.

2. Analyze the Slope: If the graph is a straight line with a slope of -2, this verifies that R_c is inversely proportional to the square of d.

3. Determine Correlation: Check the correlation coefficient to determine how well the data fits the model.

To calculate t_d using the formula:

t_d = \frac{R_i - R_c}{R_c R_i} where R_i is 100 s^-1 and R_c calculated based on provided values. In previous deductions, if R_c = 0.76 s^-1:

t_d = \frac{100 - 0.76}{0.76 * 100} = \frac{99.24}{76} \approx 1.306 s.

The statement that if 100 gamma photons enter a detector in one second and t_d is 0.01 s, all the photons should be detected is incorrect due to the random nature of radioactive decay. Photons are emitted at random intervals, and more than one photon can be emitted in a very short time frame.

Some of these photons may arrive concurrently, meaning that if the detector is still processing the previous photon during its dead time, it cannot detect new incoming photons. Therefore, the actual detection rate can be significantly less than the emission rate, leading to lower counts than expected.