Purpose:
The purpose of this experiment is to determine the decay constant and resulting
halflife of the radioactive element
137m
56
Ba.
Introduction
:
In the last decade of the 19
th
century, it was discovered that certain
materials spontaneously gave off penetrating rays of energy. This process was named
radioactivity by Marie Curie and subsequent investigations proved the rays were actually
of three types. Called Alpha (α) which consisted of a helium nucleus (two protons and
two neutrons), Beta (β) which consisted of an emitted electron and Gamma (γ) for
convenience, it was found the first two were composed of electrically charged particles
and could be stopped by the thinnest sheets of paper. The last type, Gamma, was a highly
penetrating form of electromagnetic radiation. The atom from which the radiation is
emitted is in an unstable state, and by the emission, tries to lower its energy to a ground
state.
Since the parent atom is transformed into a new element, the number of original
atoms No, is seen to drop according to the formula:
N=N
o
e
λt
Equation (1)
where N is the population of atoms at a particular time t, and lambda, λ, is the
decay constant of the parent atom with the units of time
1
. To find the decay constant, the
natural log of both sides of Equation 1 is taken and the terms rearranged as shown below
in Equation (2).
ln N/N
o
=λt
Equation (2)
A plot of this equation will yield a straight line. The slope of the line is the decay
constant, λ.
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A quantity related to the decay constant is the halflife with the symbol. This is
the time required for onehalf of the original element to under go radioactive decay. The
halflife for a radioactive material is found from its decay constant by the following
formula.
t
½
= 0.693/λ
Equation (3)
Using the Spectech Counter with the GeigerMuller Probe, we will be able to
count the number of radioactive decays within a preset time window over a period of
time. For today’s lab, we will be determining the decay constant for an isotope of
Barium,
137m
56
Ba.
137m
56
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 Fall '08
 Fedorchak
 Radioactive Decay, Background radiation, sample holder, radiation counter

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