Half-Life (Cambridge O Level Physics)

• It is impossible to know when a particular unstable nucleus will decay
• But the rate at which the activity of a sample decreases can be known
  • This is known as the half-life
• Half-life is defined as:

The time taken for half the nuclei of that isotope in any sample to decay

• In other words, the time it takes for the activity of a sample to fall to half its original level
• Different isotopes have different half-lives and half-lives can vary from a fraction of a second to billions of years in length
• Half-life can be determined from an activity–time graph

How to Determine Half-Life

The graph shows how the activity of a radioactive sample changes over time. Each time the original activity halves, another half-life has passed

• The time it takes for the activity of the sample to decrease from 100 % to 50 % is the half-life
  • It is the same length of time as it would take to decrease from 50 % activity to 25 % activity
  • The half-life is constant for a particular isotope

• The table below shows that
  • As the number of half-lives increases by 1, the proportion of the isotope remaining halves

Relationship between the number of half-lives to the proportion of isotope remaining

Number of half-lives	Proportion of isotope remaining
0	1
1
2
3
4

• The isotope carbon-14 is commonly used in radioactive dating due to its abundance in living tissue
• Carbon-14 forms when a high-energy cosmic ray knocks a neutron out of a nucleus, which then collides with a nitrogen nucleus in the air
• This process can be represented by the equation:

• 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 an organism dies, 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 measuring the current amount of carbon-14 it contains and comparing this to the initial amount (which is based on the current ratio of carbon-14 to carbon-12)
  • The proportion of carbon-14 a sample contains can therefore provide an approximate age for the sample 

Reliability of Carbon Dating

• Carbon dating is a highly reliable ageing method for samples ranging from around 1000 to 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:

Decay Curve for 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