Nuclear Spectroscopy

E X P E R I M E N T 11
Potassium 40
INTRODUCTION
Potassium is an element essential for all life, including
human. It is found especially in the muscle tissue. It is
used in fertilizers, and its percent content by weight is
given in the third number of the description of fertilizer.
Fertilizer labeled 30-15-24 has 24% of its total
weight as potassium.
Potassium as an element is 93.3% mass 39, 6.7% mass
41 (giving the atomic weight of 0.933 x 39 + 0.067 x 41
= 39.1), and 0.0117% mass 40. Although 39 K and 41 K
are stable to radioactive decay, 40 K is radioactive with a
half-life of 1.28 x 10 9 years. Radioactivity from the 40 K
in our own bodies accounts for about half of our yearly
exposure to all sources of radiation! It is an important
isotope to study, and it can be purchased at any health
food store by anyone old enough to hold money.
As illustrated in Figure 11.1, 40 K will decay by β −
emission 89.3% of the time to the ground state of 40 Ca
with no gamma emission. 40 K will decay 10.5% of the
time by electron capture to an excited state of 40 Ar,
resulting in a gamma of 1,460.8 keV being emitted. It
is this gamma that you can detect as evidence for 40 K.
A measure of the absolute activity of 40 K will provide a
measure of the total potassium present. It can also
provide a measure of the half-life of 40 K. The activity of
a radioactive sample is the number of decays per
second of that isotope. If it is not being replenished by
some other radioactive process and N(t) represents
the number of parent ( 40 K) atoms at time, t, then the
activity, A(t), for an isotope with decay constant, λ total
(λ= ln2/T 1/2
= 0.693/T 1/2
), and half-life, T 1/2
, is
11.2
0+
40
18 Ar
1461
0
EC,
β
11%
+
4
~0.1%
λtotal = λ + λ
β
+ −
9
1.28x10 y
40
19 K
β
Since N(t) is just 0.0117% of the number of potassium
atoms present at the time of counting, the decay
constant and half-life of potassium can be determined
from a measurement of the present activity. The
relative abundance of 40 K, 0.0117%, is known from
mass-spectrometer measurements.
40
K is found in most soils, building materials, plants
and animals. This will provide a photopeak background
that must be corrected with a background
subtraction. This can be as large as your source strength.
It is important for this chapter’s experiments and
those that follow to increase the shielding around and
under your detector. Any pure metal, such as iron or
lead of a few centimeters’ thickness will significantly
reduce your detected background. Commercial environmental
shields are also available.
89%
β
–
0+ 0
40
20 Ca
Figure 11.1 Schematic energy level diagram of the
radioactive decay of 40 K.
where
11.1
At ()
dN()
t
dt
d
dt N e −λ
( 0)
totalt
= = ( ) =
λ
total
λ t
N( 0) e − total = λ N( t)
total
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