Isotopes and nuclear radiation

Calculate — 2 marks

A hospital uses Technetium-99m as a tracer to diagnose medical conditions. Technetium-99m has a half-life of 6 hours. A patient is given an initial dose of 800 MBq (megabecquerels) of the radioactive isotope.

Calculate the activity of Technetium-99m remaining in the patient's body after 12 hours. [2 marks]

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{'mark': 1, 'description': 'Correctly identifies that 12 hours = 2 half-lives (or equivalent working showing division of 12 by 6)'}
{'mark': 1, 'description': 'Correctly calculates final activity as 200 MBq (showing either 800 ÷ 2 ÷ 2 or 800 × (1/2)²)'}

Show — 2 marks

Carbon-14 dating is used by archaeologists to determine the age of organic materials. Carbon-14 is a radioactive isotope of carbon that undergoes beta decay. A sample of wood from an ancient artefact contains carbon-14. The half-life of carbon-14 is 5730 years.

Show that after three half-lives, the activity of a carbon-14 sample is reduced to one-eighth of its original activity. [2 marks]

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{'mark': 1, 'description': 'After one half-life, activity = ½ × original activity (or equivalent working for subsequent half-lives)'}
{'mark': 1, 'description': 'After three half-lives, activity = ½ × ½ × ½ × original activity = 1/8 × original activity (or 0.125 × original activity)'}

Calculate — 4 marks

A nuclear physics student is studying a radioactive sample of Carbon-14, which is commonly used in archaeological dating. The sample contains atoms with 6 protons and 8 neutrons. The student needs to identify key properties of this isotope and understand how it differs from a stable Carbon-12 atom (which has 6 protons and 6 neutrons).

(a) Calculate the mass number of the Carbon-14 isotope described in the context. Show your working. [2 marks]
(b) Carbon-14 undergoes beta decay. Calculate the mass number of the nucleus formed after one beta decay event, and identify which element is produced. Explain your answer. [2 marks]

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(a) Correctly identifies that mass number = protons + neutrons
(a) Correctly calculates mass number = 6 + 8 = 14
(b) Correctly states that mass number remains 14 after beta decay (mass number is conserved)
(b) Correctly identifies that atomic number increases by 1 (from 6 to 7) because a neutron converts to a proton, forming Nitrogen-14

Calculate — 2 marks

Show — 2 marks

Calculate — 4 marks

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