IGCSE Physics / Radiation and half-life
Finding half-life from a decay graph revision notes
Edexcel International GCSE Physics (4PH1), chapter 23: Radiation and half-life, specification point 7.13, M4A. Free lesson.
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A decay graph shows how count rate falls over time, so you can find the half-life by comparing a count rate with half its value. You must use the time between the readings, and account for background count rate where it is present.
How to draw a decay curve
Plot time in minutes along the bottom and corrected count rate in counts per minute up the side. The readings will scatter because radioactive decay is random, so individual counts can be a little high or low. Draw one smooth curve of best fit through the middle of the points. Do not join the points dot to dot. Do not use a ruled straight line.
How to read a half-life
A half-life is the time taken for the count rate to fall to half its value. Read both times from the graph, then subtract the earlier time from the later time. Repeating the method from another starting value gives a check, and the mean of the results is more reliable.
Check that the half-life is consistent
For a count rate starting at 640 counts per minute, half is 320, a quarter is 160, and an eighth is 80. These values occur at 20, 40 and 60 minutes respectively. Each halving takes 20 minutes, which checks that the curve has been read correctly.
How to allow for background
A measured count rate can include background radiation. On the graph, the curve levels off above zero at the background count rate. Halve only the part due to the source, then add the background back before reading the new value from the curve. If the reading starts at 640 counts per minute and the background is 40, the source's part is 600. Half of 600 is 300. Add 40 back, so read the graph at 340 counts per minute. This occurs at 20 minutes. Half of 300 is 150. Add 40 back, so read at 190 counts per minute. This occurs at 40 minutes. The half-life is 20 minutes. Halving the whole…
Remember to subtract the starting time
The half-life is the time between the two readings, not simply the time shown for the later one. For example, 320 counts per minute is at 20 minutes and 160 is at 40 minutes, so the half-life is 40 − 20 = 20 minutes.