Unit 10: Applications of Radioactivity
Exploring the beneficial uses of radioactive isotopes in science, medicine, and industry.
10.17 Carbon-Dating (Principles & Calculations)
Radiocarbon dating is a method for determining the age of an object containing organic material by using the properties of radiocarbon ($^{14}C$), a radioactive isotope of carbon.
The Principle:
- Cosmic rays in the upper atmosphere create a small, steady amount of radioactive carbon-14.
- Living organisms (plants and animals) are constantly exchanging carbon with the atmosphere, so they maintain the same ratio of $^{14}C$ to stable $^{12}C$ as the atmosphere.
- When an organism dies, it stops taking in new carbon. The $^{14}C$ it contained at the
time of death begins to decay via beta emission with a known half-life of
approximately 5,730 years.
$$^{14}_{6}C \rightarrow ^{14}_{7}N + ^0_{-1}\beta$$ - By measuring the remaining ratio of $^{14}C$ to $^{12}C$ in an ancient sample and comparing it to the ratio in living organisms, we can calculate how many half-lives have passed and thus determine the age of the sample.
This method is effective for dating objects up to about 50,000 years old.
Solved Examples:
- What radioactive isotope is used in carbon
dating?
Solution: Carbon-14 ($^{14}C$). - What is the half-life of carbon-14?
Solution: Approximately 5,730 years. - Why does carbon dating only work on organic
materials?
Solution: Because it relies on measuring the decay of carbon that was incorporated into the material when it was part of a living organism. - A fossilised bone is found to have 25% of the carbon-14 activity of a modern
bone. How old is the fossil?
Solution: 25% remaining means two half-lives have passed (100% → 50% → 25%). Age = 2 × 5,730 years = 11,460 years. - When does the "clock" for carbon dating
start?
Solution: At the moment the organism dies and stops exchanging carbon with its environment. - What type of decay does carbon-14
undergo?
Solution: Beta decay. - Why is carbon dating not suitable for determining the age of a dinosaur
fossil?
Solution: Dinosaurs lived over 65 million years ago. After so many half-lives, the amount of remaining carbon-14 would be too small to measure accurately. - An ancient wooden tool is found to have 1/8th the carbon-14 concentration of
a living tree. Estimate its age.
Solution: 1/8th remaining means three half-lives have passed (1/2 → 1/4 → 1/8). Age = 3 × 5,730 years = 17,190 years. - How is carbon-14 naturally produced in the
atmosphere?
Solution: It is formed when cosmic rays strike nitrogen-14 atoms. - What is the daughter nucleus produced when carbon-14
decays?
Solution: Nitrogen-14 ($^{14}N$).
10.18 Radioactive Tracers (Industry, Agriculture, Medicine)
A radioactive tracer is a radioactive isotope that is added to a substance to monitor its movement. Since the chemical properties of a radioisotope are identical to its stable isotopes, it will follow the same biological or industrial pathways. Its presence can be easily detected by a device like a Geiger counter.
Applications:
- Medicine: Tracers can be used to diagnose medical conditions. For example, iodine-131 is absorbed by the thyroid gland. By injecting a small amount and measuring the radiation it emits, doctors can assess thyroid function. Technetium-99m is widely used to image blood flow and detect tumours.
- Industry: Tracers can be added to oil or gas pipelines to detect leaks. A detector is moved along the pipe, and an increase in radioactivity indicates the location of the leak. They can also be used to monitor engine wear.
- Agriculture: Tracers can be used to study how plants absorb fertilisers. By incorporating a radioactive isotope like phosphorus-32 into a fertiliser, scientists can track how and where the plant uses the nutrient.
Isotopes used as tracers are chosen to have a short half-life, so they decay quickly and do not remain a long-term hazard.
Solved Examples:
- What is a radioactive tracer?
Solution: A radioactive isotope used to follow the path of a substance through a system. - Why are radioisotopes effective as
tracers?
Solution: They behave chemically just like their stable isotopes but can be easily detected by the radiation they emit. - How can a tracer be used to find a leak in an underground
pipe?
Solution: A gamma-emitting tracer is added to the fluid in the pipe. A radiation detector is passed over the ground above the pipe. A high reading indicates a spot where the radioactive fluid has leaked out. - What property is desirable for a medical
tracer?
Solution: It should have a short half-life to minimise the radiation dose to the patient, and it should emit gamma rays so it can be detected outside the body. - Which isotope is used to study the function of the thyroid
gland?
Solution: Iodine-131. - How can farmers use tracers to study fertiliser
uptake?
Solution: They can use fertiliser containing a radioisotope (like phosphorus-32) and measure the radioactivity in different parts of the plant over time. - Why are gamma emitters preferred for medical
imaging?
Solution: Because gamma rays are highly penetrating and can easily pass out of the body to be detected by an external scanner. - What is the most widely used radioisotope in
medicine?
Solution: Technetium-99m. - A tracer with a half-life of 2 years is used to find a leak in a pipe. Is
this a good choice?
Solution: No, the half-life is too long. The area around the pipe would remain contaminated for a long time. An isotope with a half-life of a few hours would be better. - Does the tracer change the chemical process it is
monitoring?
Solution: No, because chemically it is identical to the non-radioactive atoms in the substance.
10.19 Radiation in Cancer Treatment (Radiotherapy)
While radiation can cause cancer, it can also be used to treat it. The field of medicine that uses radiation to treat cancer is called radiotherapy. The principle is that ionising radiation damages and kills cells. Cancer cells are particularly vulnerable because they divide rapidly and are less able to repair radiation-induced damage than healthy cells.
Methods of Radiotherapy:
- External Radiotherapy: A focused beam of high-energy gamma rays (often from a cobalt-60 source) is directed at the cancerous tumour from outside the body. The beam is rotated around the patient to maximise the dose to the tumour while minimising the dose to the surrounding healthy tissue.
- Internal Radiotherapy (Brachytherapy): A radioactive source is placed inside the body, on or near the tumour. This can involve implanting small radioactive "seeds" (e.g., iodine-125) directly into a tumour, or using a liquid radioisotope that is naturally absorbed by the cancerous organ (e.g., iodine-131 to treat thyroid cancer).
The goal of all radiotherapy is to deliver a lethal dose of radiation to the cancer cells while sparing healthy tissue as much as possible.
Solved Examples:
- What is the basic principle of
radiotherapy?
Solution: To use ionising radiation to kill cancer cells or stop them from dividing. - Why are cancer cells more susceptible to radiation than healthy
cells?
Solution: Because they divide rapidly and are less effective at repairing the DNA damage caused by radiation. - What is external radiotherapy?
Solution: Treatment where a beam of radiation from a machine outside the body is aimed at the tumour. - What type of radiation is typically used in external radiotherapy?
Why?
Solution: Gamma rays, because they are highly penetrating and can reach tumours deep inside the body. - What is a common radioisotope used as a source for external
radiotherapy?
Solution: Cobalt-60. - How is damage to healthy tissue minimised during external
radiotherapy?
Solution: By using multiple beams from different angles that all converge on the tumour, or by rotating the beam around the patient. - What is internal radiotherapy?
Solution: Treatment where a radioactive source is placed inside the body. - How can iodine-131 be used to treat thyroid
cancer?
Solution: The thyroid gland naturally absorbs iodine. When a patient ingests radioactive iodine-131, it concentrates in the thyroid and the emitted beta and gamma radiation kills the cancer cells. - What kind of radiation would be best for an implanted "seed" to treat a
localised tumour?
Solution: Alpha or beta emitters would be effective, as their low penetrating power means they deliver a high dose of radiation to the tumour with very little damage to surrounding tissues. - What is the overall goal of
radiotherapy?
Solution: To destroy the cancer cells while causing as little damage as possible to healthy cells.
Knowledge Check (20 Questions)
Answer: ~5,730 years.
Answer: A radioisotope used to follow
the path of a substance through a system.
Answer: Radiotherapy.
Answer: Approximately 11,460 years old
(2 half-lives).
Answer: Gamma radiation.
Answer: Because cancer cells divide
rapidly and are less able to repair radiation damage than healthy cells.
Answer: After about 50,000 years, the
amount of remaining C-14 is too small to measure accurately.
Answer: The tracer leaks out with the
fluid, and the radiation can be detected at the surface.
Answer: External radiotherapy.
Answer: When the organism dies.
Answer: It should be short (e.g., hours
or days).
Answer: Cobalt-60.
Answer: No, because the sword is not
made of organic material. (However, a wooden handle could be dated).
Answer: Treatment where the radioactive
source is placed inside the body.
Answer: By using a fertiliser
containing a radioactive tracer like phosphorus-32.
Answer: Nitrogen-14.
Answer: Because the thyroid gland
naturally absorbs and concentrates iodine from the bloodstream.
Answer: 2 counts/min (after 3
half-lives: 16 -> 8 -> 4 -> 2).
Answer: So they follow the exact same
biological or industrial pathway.
Answer: By rotating the radiation beam
or using multiple beams that converge on the tumour.