Half-Life (CIE IGCSE 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

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

• Half-life can also be represented on a table
  • As the number of half life increases, the proportion of the isotope remaining halves

Table For Number of Half Lives to Proportion of Isotope

• To calculate the half-life of a sample from a graph:
  • Check the original activity (where the line crosses the y-axies), A₀
  • Halve this value and look for this activity
  • Go across from the halved value (on the y-axis) to the best fit curve, and then straight down to the x-axis 
  • The point where you reach the x-axis should be the half-life
• The time taken for the activity to decrease to half its original value is the half-life

Background Radiation

• Background radiation is radiation that is always present in the environment around us
• As a consequence, whenever an experiment involving radiation is carried out, some of the radiation that is detected will be background radiation
• When carrying out experiments to measure half-life, the presence of background radiation must be taken into account

When measuring radioactive emissions, some of the detected radiation will be background

 

• To do this you must:
  • Start by measuring background radiation (with no sources present) – this is called your background count
  • Then carry out your experiment
  • Subtract the background count from each of your readings, in order to give a corrected count
  • The corrected count is your best estimate of the radiation emitted from the source, and should be used to measure its half-life

Step 1: Draw lines on the graph to determine the time it takes for technetium to drop to half of its original activity

Step 2: Read the half-life from the graph

• • In the diagram above the initial activity, A₀, is 8 × 10⁷ Bq
  • The time taken to decrease to 4 × 10⁷ Bq, or ½ A₀, is 6 hours
  • The time taken to decrease to 2 × 10⁷ Bq is 6 more hours
  • The time taken to decrease to 1 × 10⁷ Bq is 6 more hours
  • Therefore, the half-life of this isotope is 6 hours

Step 1: Calculate how many times the number of un-decayed atoms has halved

• • There were 2 000 000 atoms to start with
  • 1 000 000 atoms would remain after 1 half-life
  • 500 000 atoms would remain after 2 half-lives
  • Therefore, the sample has undergone 2 half-lives

Step 2: Divide the time period by the number of half-lives

• • The time period is a year
  • The number of half-lives is 2
  • 1 year divided by 2 is half a year or 6 months
  • Therefore, the half-life is 6 months