Exponential Decay

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There are many processes in nature that produce a decay that is exponential in nature. Common examples are radioactive decay (Protactinium or Thoron/Radon {modern version uses a Thorium doped gas mantle as source of Radon}), capacitive discharge, dice returning "6", the envelope of a decaying pendulum.
Often modelling exponential decay is requested using some other source of data.
One idea, that illustrates how widespread the curve is in nature, is to use the head on beer as a source of data. (Not that technicians are aware of such matters), observers have noticed that the head (frothy bit) of a badly poured pint -or if you're lucky-a good stout, gradually sinks to a stable thickness.
Another is the contents of a vessel holding water with a small hole.
A third is the cooling curve of a temperature probe.
And finally the output of a transformer (based on two coils on a iron based core) varies with the separation in an exponential manner.

Suggestions for the apparatus are made as follows:

Head on a beer.
A can of beer (ideally one with a “widget”) is poured into 100ml measuring cylinder. A 440ml can should be enough for about six stations. A 30 cm rule and stopwatch are also required. The depth of head is then measured for about ten minutes. An alternative is to have a single measuring cylinder and video the experiment. The disadvantage of this is that the technician may have to dispose of more beer.

Liquid dripping from a vessel
Burrettes are suggested using distilled water. Slow rates are essential so that the tap should only be partially opened.

The temperature probe cooling
Essentially a datalogging practical. The probe is heated in near boiling water for several minutes. The probe is then removed , immediately wiped with a dry cloth or paper and the recording started. A good curve should be produced within 3 minutes.

Transformer investigation
Two demountable transformer coils 60-60 or 120-120 are ideal. Steel retort stand and 2Vac source. DMM (or ac voltmeter) and rule.

To test the graph for an exponential curve it is necessary to take the natural log of the quantitity that is varying (the dependant) and plot it against the quantity that is not subject to derived changes (the independent variable) this is usually time. When this is done, an exponential curve will lead to a straight line graph.

A double exponential decay is frequently encountered in radioactivity. In this case a parent isotope decays to an unstable daughter product which also decays. In the process Mo99 decaying to Tc99m the source is called a Molybdenum Cow. This may be covered in medical physics courses.

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