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10 Identification of Radioactive Isotopes
techniques, one is normally interested in short-lived nuclides, whose rate of decay
could be at least measured within a span of few minutes to few days.
It is observed that decay of radioactive isotope follows the law of first order kinetic
i.e.,
N = N 0 exp(−λ × t)
(10.5)
where
N = count rate at time “t”
N 0 = count rate at zero time or the time when first count was measured with respect
to time “t”
λ = decay constant.
If we take log of Eq. (10.5), we have
log e (N ) = log e N 0 − λ × t
(10.6)
If
N =
N 0
2
which is the condition when “t” = half-life i.e., t 0.5 . Then the Eq. (10.6) becomes
t 0.5 =
0.693
λ
(10.7)
Therefore, when ln(count rate) is plotted versus time, a linear graph is obtained with
a slope of (1/λ) and if log e is converted to log 10 then the slope becomes 0.693/λ.
This method is applicable if the activity is measured for only one type of radioactive isotope and observations are extended over several half-lives (at least 1.5 times of
the half-life of the isotope). However, when a sample contains two types of radioactive isotopes having sufficiently different half-lives, it is possible to determine the
half-life of each species with reasonable accuracy. In such cases, the plot of log of
activity versus time will appear as a curve (Fig. 10.4). For determining the half-life of
long-lived isotope, the linear tail of the curve is extrapolated to zero time. This linear
curve is taken as the activity due to long-lived isotope. Examination of this linear
graph gives half-life for the long-lived isotope. The half-life of the short-lived isotope
is determined by subtracting the activity of long-lived isotope from total observed
count rate for the respective time. Plotting the decay curve from this subtracted data
gives the correct decay curve for short-lived isotope. Examination of this linear graph
gives the half-life of the short-lived isotope.
For plotting such a graph, experimentally count rate is measured with an appropriate instrument, at a number of suitable successive intervals of time. Then the
logarithm of the count rate is plotted against time. A linear graph is obtained if the
sample is not contaminated with another isotope of a different half-life. Half-life is
found out by inspection. However, care is needed while assigning the time for which
10 Identification of Radioactive Isotopes
techniques, one is normally interested in short-lived nuclides, whose rate of decay
could be at least measured within a span of few minutes to few days.
It is observed that decay of radioactive isotope follows the law of first order kinetic
i.e.,
N = N 0 exp(−λ × t)
(10.5)
where
N = count rate at time “t”
N 0 = count rate at zero time or the time when first count was measured with respect
to time “t”
λ = decay constant.
If we take log of Eq. (10.5), we have
log e (N ) = log e N 0 − λ × t
(10.6)
If
N =
N 0
2
which is the condition when “t” = half-life i.e., t 0.5 . Then the Eq. (10.6) becomes
t 0.5 =
0.693
λ
(10.7)
Therefore, when ln(count rate) is plotted versus time, a linear graph is obtained with
a slope of (1/λ) and if log e is converted to log 10 then the slope becomes 0.693/λ.
This method is applicable if the activity is measured for only one type of radioactive isotope and observations are extended over several half-lives (at least 1.5 times of
the half-life of the isotope). However, when a sample contains two types of radioactive isotopes having sufficiently different half-lives, it is possible to determine the
half-life of each species with reasonable accuracy. In such cases, the plot of log of
activity versus time will appear as a curve (Fig. 10.4). For determining the half-life of
long-lived isotope, the linear tail of the curve is extrapolated to zero time. This linear
curve is taken as the activity due to long-lived isotope. Examination of this linear
graph gives half-life for the long-lived isotope. The half-life of the short-lived isotope
is determined by subtracting the activity of long-lived isotope from total observed
count rate for the respective time. Plotting the decay curve from this subtracted data
gives the correct decay curve for short-lived isotope. Examination of this linear graph
gives the half-life of the short-lived isotope.
For plotting such a graph, experimentally count rate is measured with an appropriate instrument, at a number of suitable successive intervals of time. Then the
logarithm of the count rate is plotted against time. A linear graph is obtained if the
sample is not contaminated with another isotope of a different half-life. Half-life is
found out by inspection. However, care is needed while assigning the time for which