# 5.2.4 Half-Life

### Half-Life Basics

• As an isotope decays, the number of nuclei of that isotope that remain will decrease
• As a consequence of this, the activity of that isotope will also decrease over time
• The half-life of an isotope is the time taken for the activity of that isotope (or the number of original nuclei) to drop to half of its initial value
• Every time one half-life passes, the activity (and the number of nuclei) will fall by half Graph showing the change in activity of an isotope over time and its radioactive half-life

• Different isotopes have different half-lives and half-lives can vary from a fraction of a second to billions of years in length
• As mentioned above, every time one half-life passes the activity (and number of nuclei remaining) halves
However, the activity (and number of nuclei) will never quite drop to zero ### Measuring Half-Life

To find the half-life of an isotope:

• If given some data showing how the activity (or number of nuclei) changes over time:
• Plot a graph of this data (with time on the x-axis)
• Add a smooth best fit curve (the curve should get closer to, but never quite reach, the x-axis)
• Look at the original activity (where the line crosses the y-axis) and halve it
• Go across from the halved value (on the y-axis) to the best fit curve, and then straight down to the x-axis
(It’s a good idea to draw lines showing this on your graph)
• The point where you reach the x-axis should be the half-life Use graphs like the one above to work out the half-life of an isotope

• IF you are given just two pieces of data (along with a time) – say the initial and final activity of an isotope:
• Start by figuring out how many times you have to halve the initial activity to get to the final activity
• This number will be the number of half-lives that have passed
• Divide the time by the number of half-lives to figure out the value of one half-life

Example:

An isotope has an initial activity of 120 Bq.
6 days later it’s activity is 15 Bg.

The number of half-lives that have passed is:

120/2 = 60

60/2 = 30

30/2 = 15

We had to halve 120 three times to get to 15, and so three half-lives have passed.

Therefore each half-life must be:

6 days/3  =  2 days

Extended Only

• 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 ### Author: Jenna

Jenna studied at Cardiff University before training to become a science teacher at the University of Bath specialising in Biology (although she loves teaching all three sciences at GCSE level!). Teaching is her passion, and with 10 years experience teaching across a wide range of specifications – from GCSE and A Level Biology in the UK to IGCSE and IB Biology internationally – she knows what is required to pass those Biology exams.
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