10
2 Types of Radiation and Their Properties
undergoes each second. The international unit, the Becquerel (Bq), is the amount of
a radioactive material that undergoes 1 decay in one second. As with other SI units,
modifiers (k, M, m, and so forth) are used to reflect multiples or fractions of a Bq
(e.g. 25,000 Bq = 25 kBq).
In addition to the SI unit, there are places in which the “traditional” unit of the Curie
(Ci) remains in popular, if not in official, use. One Ci is that amount of a radioactive
source that undergoes 37 billion decays in one second, so 1 Ci = 37 GBq.
It is important to note that the amount of radioactivity present in a source is
not necessarily related to the physical size of the source. One gram of Ra-226, for
example, contains about 1 Ci (37 GBq) of activity, one gram of Co-60 contains
over 1000 times as much radioactivity, and one gram of U-238 contains less than a
millionth as much radioactivity. Thus, 1 g of U-238 is radiologically harmless, 1 g
of Ra-226 must be handled with caution, and 1 g of Co-60 can pose a risk to life
and health with only several minutes of exposure. This is why the relative risk posed
by a radioactive source can only be evaluated by making radiation measurements or
through calculation (if sufficient information is available).
If one knows the half-life of a radionuclide and can calculate the number of
radioactive atoms in a sample then it is possible to calculate the amount of radioactivity present in that sample using the law of radioactive decay: A = λN where A
is the number of decays per unit of time and N is the number of atoms. The decay
constant (λ) is the fraction of atoms that decay in a given amount of time and is equal
to
ln(2)
t1/2
where t 1/2 is the nuclide’s half-life. The amount of radioactivity per gram is
referred to as the specific activity.
2.1.6 Radioactive Decay Calculations
When an atom of Co-60 has decayed, the progeny nuclide (Ni-60) is non-radioactive.
This means that radioactive decay reduces the number of radioactive atoms and, as
the number of radioactive atoms decreases so does the decay rate. In other words,
the amount of radioactivity decreases with time. The magnitude of this decrease can
be calculated fairly easily using the equation A t = A 0 × e
−λt where A 0 and A t are
the original and decayed activity (respectively), λ is the decay constant, and t is the
time between A 0 and A t . Decay can also be calculated using the number of elapsed
half-lives: A t = A 0 × 2
−x where x is the number of half-lives that have elapsed.
Example: calculating the specific activity of Co-60
• The number of atoms of Co-60 in one gram is 6.022 × 10
23 atoms per
mole/59.934 g of Co-60 per mole = 1.005 × 10
22 atoms of Co-60 per gram.
• The decay constant for Co-60 = ln(2)/5.27 years = 0.1315 yr
−1 .
• So the decay rate of 1 g of Co-60 = 1.005 × 10
22 atoms of Co-60 ×
0.1315 yr
−1
= 1.32 × 10
21 decays per year.
2 Types of Radiation and Their Properties
undergoes each second. The international unit, the Becquerel (Bq), is the amount of
a radioactive material that undergoes 1 decay in one second. As with other SI units,
modifiers (k, M, m, and so forth) are used to reflect multiples or fractions of a Bq
(e.g. 25,000 Bq = 25 kBq).
In addition to the SI unit, there are places in which the “traditional” unit of the Curie
(Ci) remains in popular, if not in official, use. One Ci is that amount of a radioactive
source that undergoes 37 billion decays in one second, so 1 Ci = 37 GBq.
It is important to note that the amount of radioactivity present in a source is
not necessarily related to the physical size of the source. One gram of Ra-226, for
example, contains about 1 Ci (37 GBq) of activity, one gram of Co-60 contains
over 1000 times as much radioactivity, and one gram of U-238 contains less than a
millionth as much radioactivity. Thus, 1 g of U-238 is radiologically harmless, 1 g
of Ra-226 must be handled with caution, and 1 g of Co-60 can pose a risk to life
and health with only several minutes of exposure. This is why the relative risk posed
by a radioactive source can only be evaluated by making radiation measurements or
through calculation (if sufficient information is available).
If one knows the half-life of a radionuclide and can calculate the number of
radioactive atoms in a sample then it is possible to calculate the amount of radioactivity present in that sample using the law of radioactive decay: A = λN where A
is the number of decays per unit of time and N is the number of atoms. The decay
constant (λ) is the fraction of atoms that decay in a given amount of time and is equal
to
ln(2)
t1/2
where t 1/2 is the nuclide’s half-life. The amount of radioactivity per gram is
referred to as the specific activity.
2.1.6 Radioactive Decay Calculations
When an atom of Co-60 has decayed, the progeny nuclide (Ni-60) is non-radioactive.
This means that radioactive decay reduces the number of radioactive atoms and, as
the number of radioactive atoms decreases so does the decay rate. In other words,
the amount of radioactivity decreases with time. The magnitude of this decrease can
be calculated fairly easily using the equation A t = A 0 × e
−λt where A 0 and A t are
the original and decayed activity (respectively), λ is the decay constant, and t is the
time between A 0 and A t . Decay can also be calculated using the number of elapsed
half-lives: A t = A 0 × 2
−x where x is the number of half-lives that have elapsed.
Example: calculating the specific activity of Co-60
• The number of atoms of Co-60 in one gram is 6.022 × 10
23 atoms per
mole/59.934 g of Co-60 per mole = 1.005 × 10
22 atoms of Co-60 per gram.
• The decay constant for Co-60 = ln(2)/5.27 years = 0.1315 yr
−1 .
• So the decay rate of 1 g of Co-60 = 1.005 × 10
22 atoms of Co-60 ×
0.1315 yr
−1
= 1.32 × 10
21 decays per year.