Atomic and Nuclear Physics
DOE-HDBK-1019/1-93
RADIOACTIVITY
Rev. 0
Page 31
NP-01
The activity (A) of a sample is the rate of decay of that sample. This rate of decay is usually
measured in the number of disintegrations that occur per second. For a sample containing
millions of atoms, the activity is the product of the decay constant and the number of atoms
present in the sample.
The relationship between the activity, number of atoms, and decay constant is shown in
Equation (1-3).
A =
N
(1-3)
where:
A =
Activity of the nuclide (disintegrations/second)
=
decay constant of the nuclide (second )
-1
N =
Number of atoms of the nuclide in the sample
Since is a constant, the activity and the number of atoms are always proportional.
Units of Measurement for Radioactivity
Two common units to measure the activity of a substance are the curie (Ci) and becquerel (Bq).
A curie is a unit of measure of the rate of radioactive decay equal to 3.7 x 10 disintegrations
10
per second. This is approximately equivalent to the number of disintegrations that one gram of
radium-226 will undergo in one second. A becquerel is a more fundamental unit of measure of
radioactive decay that is equal to 1 disintegration per second. Currently, the curie is more
widely used in the United States, but usage of the becquerel can be expected to broaden as the
metric system slowly comes into wider use. The conversion between curies and becquerels is
shown below.
1 curie = 3.7 x 10 becquerels
10
Variation of Radioactivity Over Time
The rate at which a given radionuclide sample decays is stated in Equation (1-3) as being equal
to the product of the number of atoms and the decay constant. From this basic relationship it
is possible to use calculus to derive an expression which can be used to calculate how the
number of atoms present will change over time. The derivation is beyond the scope of this text,
but Equation (1-4) is the useful result.
(1-4)
where:
N
=
number of atoms present at time t
N
=
number of atoms initially present
o
=
decay constant (time )
-1
t
=
time
