2.6 Decay Scheme
25
The γ -ray emission will depend upon the amount of excess mass (i.e., whether the
mass of the isotope is equal to the mass of the stable isotope) remaining with the
daughter isotope after each decay. Thus, we see that the decay process of an isotope
can be very complex. The decay of
90 Sr to either ground state
90 Sr via various other
excited states (
90 Y is the best example to illustrate this process (Fig. 2.7C). There
are, of course, many other decay schemes both simple and extremely complex.
2.6.1 Rate of Decay
Unstable nuclides can approach stability by a suitable mode of decay, but none of
these decay processes are instantaneous. The unstable nuclei may require a millionth
of a second or millions of years to decay to a more stable one. The rate of decay can
be expressed using the differential form:
d N
dt
∝ N = −λN
(2.3)
in which “N ” is the number of radioactive atoms d N is the change in the number of
atoms and dt is the change in time. By introducing a proportionality constant λ, and
indicating a decrease in activity with a negative sign, this equation becomes equal to
the product of λN . In other words, radioactive decay follows the law of first-order
kinetics. Integration of Eq. (2.3) gives the following solution:
N = N 0 e
−λt
(2.4)
in which N 0 is the number of radioactive atoms at some reference time, “N ” the
number of radioactive atoms at time “t”, and λ is the decay constant. λ is a fundamental constant for each nucleus and has the dimension of reciprocal time. It is a
measure of the probability that a given single nucleus will decay within unit time.
It may not always be possible to measure absolute values of N or N 0 . However,
each atom of the radioactive isotope emits one radiation per decay of the atom. If
the radiations emitted by atoms could be measured for some period and the value is
converted to a unit “number of radiations recorded per unit time”, i.e., activity
(expressed in terms of disintegration rate or counting rate), the Eq. (2.4) can then be
expressed as
A = A 0 e
−λt
(2.5)
in which “A” is the activity at time “t” (i.e., counts per unit time) and A 0 is activity
at some reference time (i.e., counts per unit time). This relationship can be used to
determine the half-life of the radioactive isotope.
25
The γ -ray emission will depend upon the amount of excess mass (i.e., whether the
mass of the isotope is equal to the mass of the stable isotope) remaining with the
daughter isotope after each decay. Thus, we see that the decay process of an isotope
can be very complex. The decay of
90 Sr to either ground state
90 Sr via various other
excited states (
90 Y is the best example to illustrate this process (Fig. 2.7C). There
are, of course, many other decay schemes both simple and extremely complex.
2.6.1 Rate of Decay
Unstable nuclides can approach stability by a suitable mode of decay, but none of
these decay processes are instantaneous. The unstable nuclei may require a millionth
of a second or millions of years to decay to a more stable one. The rate of decay can
be expressed using the differential form:
d N
dt
∝ N = −λN
(2.3)
in which “N ” is the number of radioactive atoms d N is the change in the number of
atoms and dt is the change in time. By introducing a proportionality constant λ, and
indicating a decrease in activity with a negative sign, this equation becomes equal to
the product of λN . In other words, radioactive decay follows the law of first-order
kinetics. Integration of Eq. (2.3) gives the following solution:
N = N 0 e
−λt
(2.4)
in which N 0 is the number of radioactive atoms at some reference time, “N ” the
number of radioactive atoms at time “t”, and λ is the decay constant. λ is a fundamental constant for each nucleus and has the dimension of reciprocal time. It is a
measure of the probability that a given single nucleus will decay within unit time.
It may not always be possible to measure absolute values of N or N 0 . However,
each atom of the radioactive isotope emits one radiation per decay of the atom. If
the radiations emitted by atoms could be measured for some period and the value is
converted to a unit “number of radiations recorded per unit time”, i.e., activity
(expressed in terms of disintegration rate or counting rate), the Eq. (2.4) can then be
expressed as
A = A 0 e
−λt
(2.5)
in which “A” is the activity at time “t” (i.e., counts per unit time) and A 0 is activity
at some reference time (i.e., counts per unit time). This relationship can be used to
determine the half-life of the radioactive isotope.