Half-Life
Ages 14–16 · Ages 16–18 · 16–18 extension
counting
Student lab

Measuring a half-life

1The Room

The Room

Step I · 6 min

Predict

With no source anywhere near the tube, what will ten counts of 30 s show?

  1. In the classroom, with a count time of 30 s, write down ten counts.
  2. Work out the mean, and the background count rate in counts per second with its uncertainty, √N ÷ t.
  3. Repeat in the basement. Say what is different and why.
countclassroom: counts in 30 sbasement: counts in 30 s
2The Source

The Source

Step II · 8 min

Predict

Sketch the count in each 10 s against time, for ten minutes.

  1. Write down the count in the 10 s that starts at each time in the table.
  2. Take off the background you measured in the room, in counts per 10 s.
  3. Plot both columns against time, with error bars of ±√N. Mark where each curve ends up.
t / scount in 10 s± √countcount − background
3Half-Life

Half-Life

Step III · 10 min

  1. Sample A: with the background taken off, read the time for the count to halve, then to halve again. Average the two, enter it and check it.
  2. Do the same for sample C.
  3. Extension: on the ln graph the gradient is −λ. Work out T½ = ln 2 ÷ λ, and its uncertainty from the steepest and shallowest lines through the error bars.
samplefirst halving / ssecond halving / smean T½ / schecked T½ / s
Exit

A source gives 250 counts per minute where the background is 26 counts per minute. Its half-life is 3 hours. What will the counter read 9 hours later, and why?

4Data Question

Data Question

Step IV · 15 min

  1. Print the question, or copy the table and the graph. Answer every part on paper, showing your working and your uncertainties.
  2. Check each part in Step IV, and mark it against the marking points.
  3. Take a new set of readings and do it again, faster.
The modelEach nucleus has the same chance of decaying in every second, whatever has happened before. The counter records a fixed share of the particles from the source, set by how far away it is, and never misses one while it recovers from the last. The background rates are typical values; real ones differ from room to room.
The samplesProtactinium-234m (half-life 1.16 min), radon-220 (55.6 s) and barium-137m (2.55 min) are the short-lived sources schools use to measure a half-life in one lesson.
HistoryIn 1900 Ernest Rutherford found that the radioactivity of the gas given off by thorium halves in about a minute, however much of the gas there is. The Geiger–Müller tube, still the usual school detector, was made by Hans Geiger and Walther Müller in 1928.
UnitsTime in s. Count rates in counts per second (s−1), or as the counts in a stated time. Activity in becquerels (Bq): decays per second.