Nuclear Spectroscopy

Exercise 11.1
Half-Life of 40 K
OBJECTIVE
Measure the activity of a sample of either potassium
chloride (KCl) or anhydrous potassium fluoride (KF)
to estimate the half-life of 40 K. This is more a good
estimate than a precise determination, because the
geometry of the source violates the assumption of a
point source.
SUPPLIES
•Standard 50 ml beaker
•Radioactive sources: 22 Na, 137 Cs
•Chemicals: 40 ml of KF (100 g)and 40 ml of KCl
(80 g)
SUGGESTED EXPERIMENTAL PROCEDURE
1. Have the detector and the MCA operating in the
usual manner.
2. Check the energy scale using the 22 Na source to
be certain that peaks out to 1,600 keV can be
observed.
3. Measure the mass of a 50 ml beaker.
4. Fill the 50 ml beaker with a potassium compound
compressed to the 40 ml level and remeasure the
mass. Place it on the holder in the sixth source
position. Your source material will be approximately
in the fourth position.
5. Acquire a spectrum for up to 10,000 seconds. To
reduce the room background, surround the detector
assembly with bags of lead shot or iron
bricks. Record the live time, net counts and gross
counts in the photopeak at 1,461 keV. Figure
11.2 is a sample spectrum from a potassium
sample.
6. Remove the potassium sample and count the
background for up to 10,000 seconds. Record the
live time, net counts and gross counts in the
photopeak at 1,461 keV.
DATA ANALYSIS
10000
1000
100
10
1
0 200 400 600 800 1000 1200
Channel Number
Figure 11.2 The gamma spectrum from a 1 kg potassium
sample. The 40 K photopeak is near channel 280.
the background’s net count rate from the sample’s
and calculate the statistical error of the difference.
Correct this count rate for the detector efficiency and
gamma decay fraction, as was done in Experiment
#10. The solid angle increases by about a factor of
three if we consider the source to be effectively at
position 4. You need to increase your effective detector
efficiency from Figure 10.1 by this factor.
Using the mass of the potassium sample, determine
the number of 40 K atoms in your sample. Using the
relationship, equation 11.1, between the measured
activity and the number of 40 K atoms, calculate the
half-life of 40 K. How do your results compare to the
accepted value?
Considering that self-shielding has been neglected
and you are using the source position as shelf #4, your
result is probably too good. Self-shielding and source
position can be improved by diminishing the amount
of source material used. Of course this diminishes the
signal at the same time, requiring longer counting
times. Cutting the material in half, and then half
again will allow you to systematically study these
effects. It may provide a limiting sequence of halflives
that appear to converge. Try this only if there is
enough time.
From your data of 40 K photopeak counts and the live
time, calculate the net count rate and the statistical
error in that rate for each spectrum taken. Subtract
33