Exponential Decay of Activity
Quantum and Nuclear

Measuring the half-life of protactinium

Practical Activity for 14-16 PRACTICAL PHYISCS


Measuring the half-life of a radioactive isotope brings some of the wonder of radioactive decay into the school laboratory. Students can witness one element turning into another and hear (or see) the decrease in the radiation it gives out as it transmutes.

This demonstration uses a protactinium generator to show the exponential decay of protactinium-234, a grand-daughter of uranium. It has a half-life of just over a minute, which gives students the chance to measure and analyze the decay in a single lesson.

Apparatus and Materials

  • tray
  • Holder for Geiger-Müller tube
  • Geiger-Müller tube, thin window
  • Scaler
  • Stopclock
  • Retort stand, boss, and clamp
  • Ratemeter (OPTIONAL)
  • Protactinium generator

Health & Safety and Technical Notes

See the following guidance note:

Managing radioactive materials in schools

To limit the risk of radioactive liquids being spilt, there should be special instructions in the local rules for handling (and preparing) this source.

Read our standard health & safety guidance

Preparation of the protactinium generator

It is now possible to purchase the chemicals already made up in a sealed bottle. One supplier is TAAB Laboratories Equipment Ltd, 3 Minerva House, Calleva Park, Aldermaston, RG7 8NA. Tel: 0118 9817775. However, you can make your own if you prefer.

These quantities make a total volume of 20 cm3. You can scale them up if you have a larger bottle. (A '30 ml' bottle has a capacity of about 35 ml, so there is still room to shake the solution when the total volume is 30 ml.)

  1. Dissolve 1 g of uranyl nitrate in 3 cm3 of water. Wash it into a small separating funnel or beaker with 7 cm3 of concentrated hydrochloric acid.
  2. To this solution, add 10 cm3 of iso-butyl methyl ketone or amyl acetate.
  3. Shake the mixture together for about five minutes. Then run the liquid into the polypropylene bottle and firmly screw down the cap. It can help to shield the lower half of the bottle with some lead.
  4. Place the bottle in a tray lined with absorbent paper.

Once you have made the protactinium generator, you can store it with other radioactive materials, taking care to follow your school code of practice and local rules: see the Managing radioactive materials in schools guidance note:

Managing radioactive materials in schools

A polypropylene bottle is preferable to polythene because it is somewhat more resistant to attack by the acid and ketone. Nevertheless, polythene bottles can be used, provided no attempt is made to store the liquid in them for more than a few weeks.

The organic layer which separates out contains the protactinium-234. This decays with a half-life of about 70 seconds.

An alternative to protactinium: A new, effective and extremely low hazard system for measuring half-life is available from Cooknell Electronics Ltd, Weymouth, DT4 9TJ. This uses fabric gas mantles designed for camping lights. Each mantle contains a small quantity of radioactive thorium. More details are available on the Cooknell Electronics website:

Cooknell Electronics


  1. Support the Geiger-Muller tube holder in a clamp, so that the tube is facing downwards towards the neck of the bottle.
  2. Allow the bottle to stand for at least ten minutes. Take the background count by running the counter for at least 30 seconds. This is done with the bottle in position, because some of the count will come from the lower layer. You can do this before the experiment or some time after it has finished.
  3. Alternatively, the GM tube can be clamped horizontally with the window close to the upper layer.
  4. Shake the bottle vigorously for about 15 seconds to thoroughly mix the layers.
  5. Place the bottle in the tray.
  6. As soon as the two layers have separated, start the count and start the stop-clock.
  7. Record the time from the beginning of the experiment - i.e. the time of day for the sample.
  8. Record the count every 10 seconds. Or record it for 10 seconds every 30 seconds.
  9. Run the experiment for about five minutes, ample time to reveal the meaning of the term half-life and to illustrate the decay process.
  10. Provided you leave a few minutes between each attempt, you can repeat the experiment. In 5 minutes the activity of the protactinium in the aqueous layer grows to 15/16 of its equilibrium value.
  11. It is possible to record the growth to equilibrium. Do this by moving the GM tube so that the aqueous layer at the bottom of the bottle is immediately above the end window of the GM tube.

Teaching Notes

The chemistry of the experiment:

  • The first stages of the uranium-238 series are involved in this experiment.
  • The aqueous solution (at the bottom of the bottle) contains the uranium-238, its daughter thorium-234 and the short-lived granddaughter protactinium-234.
  • Uranium and protactinium both form anionic chloride complexes but thorium does not. At high hydrogen ion concentrations, these complexes will dissolve in the organic layer (which is floating on top of the aqueous solution).
  • When you shake the bottle, about 95% of the short-lived granddaughter (protactinium) and some of the uranium will be dissolved in the organic layer. The thorium stays in the aqueous layer.
  • Since radioactivity is a property of the innermost nucleus of the atom it is not affected by chemical combination.
  • The granddaughter (in the organic layer) decays without any more being produced by its parent (thorium) all of which is still in the aqueous layer. It emits beta particles which travel through the plastic wall of the bottle. Isolating the protactinium in the top (organic) layer allows it to decay without any top-up from its parent (thorium).
  • The radiation from the thorium and uranium should not interfere with the results, for two reasons:
    1. The counter does not detect the alpha particles from the uranium or the low energy beta particles from the thorium. It only records the high energy (2 MeV) beta particles from the granddaughter (protactinium).
    2. The uranium-238 decays with an extremely long half-life. It yields a meagre, almost constant, stream of low energy alpha particles. Its daughter, thorium-234, decays with a half-life of 24 days. During the length of this experiment the decay rate can be assumed to be constant. If these two isotopes contribute to the count at all, it will be accommodated in the background count. The stockpile of thorium is also constantly topped up in the aqueous layer as long as the protactinium is present with the thorium.

Table of count rate: Get the students to make a table of count rate against time, and correct it for background count. The first 10-second reading should be allocated to a time of zero.

Plot a graph: Get the students to plot a graph of count rate against time. They should draw a smooth curve through the points.

  • First point out the general pattern - that the count rate decreases with time. Then look for an exponential trend - that the best fit curve always takes the same amount of time to halve.
  • Get students to measure the half-life from the curve.
  • Point out the random nature of the points: although the decay follows a pattern, there is an element of randomness and it is not perfectly predictable.

How Science Works extension This experiment provides an opportunity to assess the accuracy of the measured half-life value and how the random nature of decay affects the answer.

The accepted value for the half-life of protactinium is about 70 seconds.

Explore different ways in which a half-life value can be obtained from this apparatus:

  • Amend the procedure described above so that, instead of a scaler (counter), a ratemeter is used. One student just records the time it takes for the count-rate to halve. This will provide a very approximate value.
  • Repeat the experiment with several members of the class timing how long it takes for the count-rate to halve. There is likely to be considerable spread in results across the group and the mean result may differ from the accepted value for half-life. In each case, ask students to identify errors and uncertainties in their measurement(s) and to suggest ways in which these could be reduced.

For example, ask: "how does the random nature of the decay affect the measured count-rate when the count is low, or high, compared the background count?"

  • Either you or your students may suggest a graphical method as an improvement. The procedure described in the main experiment above could then be carried out, and then the accuracy of the half life value assessed and evaluated.

Radioactive materials raise significant safety issues, providing an opportunity to discuss the value and use of secondary data sources.

This experiment was safety-tested in February 2007

Exponential Decay of Activity
can be analysed using the quantity Activity
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