## Experiment N-4

In Experiment N-4 we studied a short lived nucleus.  We found that in a certain period of time called the half life the intensity of radiation decreased to half.  The radioactive material seems to have had no memory of when it started.  So in every identical period of time, the intensity of radiation drops in half, no matter when that half life started.

For a short lived substance, it is not difficult to wait around and measure the half life.  But for more stable substances, one's life could end before the intensity decreased in half.  So an alternate procedure will be necessary.  At the end of the previous experiment it was noted that the rate radiation is emitted is given by

R = 0.693 N / t1/2

where N is the number of nuclei of that type present, and R is the rate of decay (using the same time unites as the half life, t1/2).  That can be reversed to solved for the half life:

t1/2 = 0.693 N / R

So if we carefully measure (or calculate) all radiation coming for a known number of atoms, we can calculate very long half lives.

### Experiment

The purpose of this experiment is to determine the half life of Potassium-40.

1. Potassium is a reactive metal that commonly exists in salts such as KCl.  One hundredth of one percent (1.0 x 10-4) of the potassium in nature has a radioactive nucleus: .  To start the experiment a sample of the salt KCl is found to weigh 7.6g.  Using the molecular weight of KCl, Avogadro's number, and the fraction that is 19K40, calculate the number of 19K40 atoms present.  That will be the N in our equation.

2. Next we will need to measure how radioactivity comes from the sample.  Count the Geiger counter clicks due to the KCl (use aiff file, mp3 file, or visual graph) for the two minutes and calculate the counts per minute.  100KB; downloading may take patience.

3. Count the Geiger counter clicks caused by the background radiation (use aiff file, mp3 file, or visual graph) for the two minutes and calculate the counts per minute.  100KB

4. But there are two shortcomings with the previous measurements.  The Geiger counter doesn't surround the sample but only catches the radiation coming in the direction of the counter.  An furthermore, some γ radiation passes completely through the Geiger-Muller tube without ever colliding with a single atom and getting counted.  We may correct for both causes of missed radiation by counting and comparing another substance known to emit a known intensity of γ radiation.  The minigenerator used in Experiment N-3 (the blue cylinder shown at a distance in this diagram) emits 1.4 x 106 per minute of γ radiation.  But even though most of this is missed by our counter, the radiation still comes too fast to count.  To make the signal slow enough to count, it was electronically filtered inside the Geiger counter to remove 9/10 of the pulses.  Count the clicks from the minigenerator (use aiff file, mp3 file, or visual graph).  52KB download  To find the actual radiation intensity multiple your count by 10.

5. After correcting all counts for background, multiply the ratio of (known minigenerator radiation / your minigenerator count) times the KCl count to get R for the half-life equation.

6. Substitute your data into the equation above to find t1/2, the half-life of 19K40.  How many years is this?

Finally, a word about worries over the hazards of radiation.  In earlier experiments it was noted that radiation is know to be hazardous to living tissue.  That hazard can be minimized by increasing the distance from the source, or in the case of short-lived isotopes, storing them away from living cells until the isotope has naturally decayed over time to less hazardous material.  But isotopes such as K-40 have very long half-lives.  Some people worry about the radiation hazards from such materials.  It should be remembered that when a material has a very long half-life, the rate of radiation emitted in very low.  For example, the K-40 sample measured in this experiment was only slightly above background radiation intensity.  So such long-lived isotopes pose only a trivial risk to living creatures because the radiation intensity is so tiny.  Much greater radiation exposures occur when we choose to spend a few hours outdoors or take a single airline flight.  Thus there is no reason for concern for the Potassium-40 which exists naturally in our food and in our own bodies.  Based on this understanding, consider the radiation risks to society from the portion of nuclear reactor wastes which also have extremely long half-lives.

Communicating technical information such as observations and findings is a skill used by scientists but useful for most others.  If you need course credit, use your observations in your journal to construct a formal report.

created 11/17/2002
revised 5/19/2005
by D Trapp