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A patient is going to have a PET scan - AQA - A-Level Physics - Question 3 - 2017 - Paper 5

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A patient is going to have a PET scan. A small amount of radioisotope is injected into the patient's bloodstream and the patient is left to relax. The patient then l... show full transcript

Worked Solution & Example Answer:A patient is going to have a PET scan - AQA - A-Level Physics - Question 3 - 2017 - Paper 5

Step 1

State what is meant by a radioisotope.

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Answer

A radioisotope is a material with nuclei that are unstable and decay, emitting radiation in the form of particles or electromagnetic waves.

Step 2

Show that the effective half-life of the radionuclide in the body is about 70 minutes.

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Answer

The effective half-life (TeT_e) can be calculated using the formula:

1Te=1Th+1Tb\frac{1}{T_e} = \frac{1}{T_{h}} + \frac{1}{T_{b}} where:

  • ThT_{h} is the physical half-life (110 minutes)
  • TbT_{b} is the biological half-life (185 minutes)

Calculating:

1Te=1110+1185\frac{1}{T_e} = \frac{1}{110} + \frac{1}{185}

This results in:

Te68.98 minutes70 minutesT_e \approx 68.98 \text{ minutes} \approx 70 \text{ minutes}

Step 3

Discuss what might be a suitable length of time for the patient to relax between injecting the radionuclide and moving the patient into the PET scanner.

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Answer

A suitable length of time for the patient to relax could range from 10 to 70 minutes. This allows the radioisotope to circulate and localize in the body while ensuring the patient is comfortable and adequately prepared for the scan.

Step 4

Explain the process in which the gamma photons are created.

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Answer

When a positron emitted from the decay of the radionuclide collides with an electron in the body, they annihilate each other, resulting in the release of energy in the form of two gamma photons. These photons are emitted in opposite directions, in accordance with the conservation of momentum. This process is integral to the detection mechanism in PET scanning.

Step 5

Discuss the range of values of Δt that the scanner must measure to perform a PET scan on the head.

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Answer

The scanner must account for the distance the gamma photons travel and the speed of light. Given that the head is 0.2 m across, the time interval (rianglet riangle t) can be calculated:

Using the speed of light (c=3imes108extm/sc = 3 imes 10^8 ext{ m/s}), the time taken to travel across the head would be:

rianglet=0.2 m3×108extm/s=6.67×1010 s riangle t = \frac{0.2 \text{ m}}{3 \times 10^8 ext{ m/s}} = 6.67 \times 10^{-10} \text{ s}

The range for the scanner could be adjusted from this value to account for measurement precision and timing variations, thus ensuring accurate positioning information.

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