8.2.4 Applications of Radioactivity

• The isotope carbon-14 is commonly used in radioactive dating
• It forms as a result of cosmic rays knocking out neutrons from nuclei, which then collide with nitrogen nuclei in the air:

¹n + ¹⁴N → ¹⁴C + ¹p

• Plants take in carbon dioxide from the atmosphere for photosynthesis, including the radioactive isotope carbon-14
• Animals and humans take in carbon-14 by eating the plants
  • Therefore, all living organisms absorb carbon-14, but after they die they do not absorb any more

• The proportion of carbon-14 is constant in living organisms as carbon is constantly being replaced during the period they are alive
• When they die, the activity of carbon-14 in the organic matter starts to fall, with a half-life of around 5730 years
• Samples of living material can be tested by comparing the current amount of carbon-14 in them and compared to the initial amount (which is based on the current ratio of carbon-14 to carbon-12), and hence they can be dated

Reliability of Carbon Dating

• Carbon dating is a highly reliable ageing method for samples ranging from around 1000 years old up to a limit of around 40 000 years old
  • Therefore, for very young, or very old samples, carbon dating is not the most reliable method to use

• This can be explained by looking at the decay curve of carbon-14:

Carbon-14 decay curve used for carbon dating

• If the sample is less than 1000 years old:
  • The activity of the sample will be too high
  • So, it is difficult to accurately measure the small change in activity
  • Therefore, the ratio of carbon-14 to carbon-12 will be too high to determine an accurate age

• If the sample is more than 40 000 years old:
  • The activity will be too small and have a count rate similar to that of background radiation
  • So, there will be very few carbon-14 atoms remaining, hence very few decays will occur
  • Therefore, the ratio of carbon-14 to carbon-12 will be too small to determine an accurate age

• Carbon dating uses the currently known ratio of carbon-14 to carbon-12, however, scientists cannot know the level of carbon-14 in the biosphere thousands of years ago
• Therefore, this makes it difficult to age samples which are very old

Potassium-Argon Dating

• Ancient rocks contain trapped argon gas as a result of the decay of the radioactive isotope of potassium-40
• This happens when a potassium nucleus captures an inner shell electron, also known as electron capture

⁴⁰K + e^– → ⁴⁰Ar + v_e

• The potassium isotope can also decay by β^– emission to form calcium-40

⁴⁰K → ⁴⁰Ca + β^– + vₑ

• The half-life of the potassium-40 is 1.25 billion years
• The age of the rock (when it solidified) can be calculated by measuring the proportion of argon-40 to potassium-40
• This method is accurate for dating rocks up to 100 million years old

Uranium-Lead Dating

• While the potassium-argon method is best for ageing younger rocks, the uranium-lead method has been critical in dating geologic events more than 100 million years old

Uranium atoms decay whilst the number of lead atoms increases

• Initially, there is only uranium in the rock, but over time, the uranium decays via a decay chain which ends with lead-206, which is a stable isotope
• Uranium has a half-life of 4.5 billion years and over time, the ratio of lead-206 atoms to uranium-238 atoms increases
  • This ratio may be used to determine the age of a sample of rock

• Uranium is so well studied that its decay constant is much better known than other isotopes, such as potassium, making the uranium-lead dating technique the most accurate available

Uranium-238 decay chain

Storage of Radioactive Waste

• Radioactive substances can be dangerous and some substances have very long half-lives (even billions of years)
  • This means that they will be emitting harmful radiation well above background radiation for a very long time

• Waste products from nuclear power stations need to be appropriately stored for the remaining time that they are radioactive
• Common methods are water tanks or sealed underground 
  • This is to prevent damage to people and the environment now and for many years into the future
  • Sealing them underground means they are less likely to be dislodged or released due to natural disasters