Nuclear Spectroscopy

E X P E R I M E N T 8
Multichannel Scaling and Half-life
INTRODUCTION
The memory locations (channel numbers) used to
store the gamma data can be used in a different
manner, called multichannel scaling (MCS). Selecting
and starting the MCS option will result in the
computer storing the total number of gammas counted
in the selected time period (called the dwell time),
starting with channel 0 and proceeding through all
the channels in order. This allows you to record the
gamma intensity as a function of time. This will be
quite useful for determining the half-life of 137m Ba.
The m following the mass number indicates that the
isotope is an excited state with a half-life of seconds to
years. This is an isomeric state to the ground state of
the isotope.
Early in this century, Soddy and Rutherford discovered
that radioactive elements decay away in an exponential
manner. Since things that decrease at a fixed
rate, λ , decrease exponentially, the rate is a representative
measure of the decay. In the case of radioactivity,
the half-life, T 1/2
, was chosen as the measure of the
time for decay. The half-life is related to the rate by
8.1
ln 2 0.
693
λ = =
T T
1 2
1 2
The half-life is the amount of time necessary for the
activity of the sample (the number of decays per
second) to decrease to half of the initial value. This
can be determined from a graph of the number of
gammas counted per (dwell) time interval as a function
of time. The graph of the logarithm of the activity
as a function of the time will be a straight line. Just
such a graph is shown in Figure 8.1. The decay rate, λ,
is the slope of that straight line, and the half-life is
calculated from equation 8.1.
OBJECTIVE
137
Cs beta (minus) decays into an excited state of 137 Ba,
which decays by gamma emission to the ground state
of 137 Ba, the lowest energy state. The excited state of
barium, 137m Ba, has a half-life of a few minutes and can
be easily measured with this equipment. Measure this
half-life. Later there will be an opportunity in the 40 K
lab to measure a much longer half-life, about a million,
billion times longer!
SUPPLIES
•NaI(Tl) detector with MCA
•Radioactive sources: 54 Mn, 65 Zn, 137 Cs cow
SUGGESTED EXPERIMENTAL PROCEDURES
1. Have the detector and the MCA operating in the
usual manner. After Experiment 7 you will need
to recalibrate, as in Experiment 1.
2. Set the lower level discriminator (LLD) to an
energy near 100 keV, and set the upper level
discriminator (ULD) near 750 keV. (See the
boxed note at the end of this chapter.)
3. Select multichannel scaling (MCS) under the
mode menu; select a dwell time of 4 seconds.
4. Run a background spectrum in the background
buffer.
5. Have your instructor “milk” the 137 Cs cow for the
137m
Ba into a planchet. Be careful not to spill this
liquid, especially on yourself or your clothing.
6. Carefully place the planchet on a shelf underneath
and close to the detector for counting. Run
a MCS spectrum in the main memory.
7. Save both the background and the 137 Cs decay data
files as spectrum (*.SPE)files and as spreadsheet
(*.TSV) files. For the Macintosh, select ‘Save’ or
‘Save Data Text Only’ from the EDIT menu and
paste your data into a spreadsheet as it is needed.
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