Nuclear Spectroscopy

Exercise 11.2
Potassium in Fertilizer
Exercise 11.3
Stoichiometry
OBJECTIVE
Measure the 40 K activity of a sample of concentrated,
water soluble fertilizer. From this measurement and
the known half life of 40 K, the number of 40 K atoms,
and therefore the mass of all the potassium in the
sample can be determined. The potassium fractional
content of the fertilizer can be calculated and compared
with the manufacturer’s estimate.
OBJECTIVE
Measure the activities of equal volume samples of
various potassium compounds, such as potassium nitrate
(KNO 3
), potassium chloride (KCl), potassium
iodide (KI), or anhydrous potassium fluoride (KF).
The measured activities should scale with the fraction
of potassium in each sample, as conveniently calculated
from the chemical formula.
SUPPLIES
•Standard 50 ml beaker
•Radioactive sources: 22 Na, 137 Cs
•Chemicals: Miracle Grow water-soluable fertilizer or
a commercially-available equivalent fertilizer.
SUGGESTED EXPERIMENTAL PROCEDURE
1. Follow the same procedures as in Experiment
11.1.
DATA ANALYSIS
From your data of photopeak counts and live time
calculate the net count rate and the statistical error
for each measurement made. Subtract the background
net count rate from the sample’s and calculate
the statistical error of this difference. Correct this
count rate for the detector efficiency and gamma
decay fraction, as was done in Exercise 11.1.
Using your measured activity and the known half-life
(decay constant), determine the number of 40 K atoms
in your sample. From the known abundance of 40 K,
calculate the number of potassium atoms and then
the mass of those atoms in your sample. What percentage
of the total fertilizer weight is the potassium?
How do your results compare to the manufacturer’s
values? Did the manufacturer quote the fractional
weight of the potassium or the potassium oxide (KO 2
)?
SUPPLIES
•Standard 50 ml beaker
•Radioactive sources: 22 Na, 137 Cs
•Chemicals: 40 ml of KF (100 g), 40 ml of KCl (80 g),
40 ml of potassium sulfate (110 g), 40 ml of
potassium nitrate (90 g), and 40 ml of potassium
iodide (130 g).
SUGGESTED EXPERIMENTAL PROCEDURE
1. Follow the procedures of Exercise 11.2 for each
sample. The background measurement needs to
be made only once.
DATA ANALYSIS
From your data of photopeak counts and live time
calculate the net count rate and the statistical error for
each measurement made. Subtract the background
net count rate from the sample’s and calculate the
statistical error of the difference. Detector efficiency
and gamma decay fraction corrections need not be
made with these data. Calculate the ratio of activities
between pairs of observed samples.
Using the chemical masses of the elements from the
Periodic Table, calculate the molecular masses of each
compound and the fractional mass of potassium in
each compound. The ratios of these fractional masses
should agree with the observed ratio of activities.
Can you take a pure, but unknown compound of
potassium and determine the relative abundance of
potassium atoms in its molecular structure? Try it.
34