Half-Life (SQA National 5 Chemistry): Revision Note

Half-life of isotopes

What is half-life?

• Radioactive decay is the process where the nuclei of unstable atoms (radioisotopes) break down to become more stable

• Half-life is a measure of how quickly this happens for a particular radioisotope

• It is defined as:

"the time taken for half of the nuclei in a sample of a particular isotope to decay"

• It is given the symbol, t_1/2

• Half-life is constant

  • So, after each half-life, the amount of the radioisotope remaining is halved:

100% 50% 25% 12.5% 6.25%

• For example, for 250g of an isotope with a half-life of 30 years:

• Half-life is unaffected by conditions

  • It is a nuclear property

  • So, it is not changed by:

    • Physical conditions like temperature or pressure

    • Chemical conditions, such as the compound that the isotope is part of

• Half-life is used for dating

  • The known, constant half-life of radioisotopes, like carbon-14, can be used by scientists to determine the age of ancient materials and artefacts

Half-life calculations

• The two main skills for half-life problems are:

  1. Determining half-life from a decay curve (graph)

  2. Performing calculations with given data

1. Determining half-life from a decay curve

• A decay curve is a graph that shows how the mass or activity of a radioisotope decreases over time

• The half-life (t_1/2) is the time it takes for the mass or percentage of the sample to fall to half of its original value

• After a second half-life, it will have fallen to a quarter of its original value

How to find the half-life from a decay curve:

1. Read the initial value on the y-axis (at time = 0)

2. Divide this value by two to find the half-way point

3. Find this half-way value on the y-axis and draw a line across to the curve

4. Then, draw another line straight down to the x-axis

5. Read the time off the x-axis to get the half-life

2. Performing half-life calculations

• These questions involve the relationship between:

  • The starting amount

  • The final amount

  • The number of half-lives

  • The total time

The "arrow method"

• An easy and reliable way to solve half-life problems is to use the "arrow method"

• This method tracks the decay process

• Each arrow represents one half-life passing

  • During this time, the amount of the radioisotope is halved

• For example, tracking the decay of an 80g sample

80 g 40 g 20 g 10 g 5 g

• By counting the arrows, you can find out how many half-lives have passed to get from the start amount to the end amount