11.3 Gaussian Distribution Curve
175
95.5%
68.3%
– 2
–
0
+
+ 2
Standard Deviation
Frequency
Fig. 11.2 An ideal Gaussian distribution curve is shown here. Mean value is taken as the zero and
variation of counts with respect to mean values is shown. 68.3% and 95.5% are expected range of
the distribution if there is no other error involved in the counting system and the radioactive material
does not decay during the course of counting
• mean ±1σ 68.3% of total count should fall in this range
• mean ±2σ 95.5% of total count should in this range
• mean ±3σ 99.9% of total count should fall in this range.
However, it will be noticed that the data shown in Table 11.1 and the graph plotted
from these data do not fall in line with the expected Gaussian distribution curve
(Fig. 11.2). As a result of this, even the expected value of mean ±1σ (i.e., 9570 ±
77.92 cpm) contains more than 68.3% of the total data. There could be various
reasons for getting such deviation from the expected result which is discussed in the
next section.
The advantage of this Gaussian distribution analysis is that by plotting a Gaussian
distribution of radioactivity of a long-lived isotope, one can confirm whether the
counting system is operating properly. If the counting system is operating perfectly
and recorded counts are following the Gaussian distribution curve, then a symmetrical
distribution curve is obtained as shown in Fig. 11.3C. But if the curve takes the form
as shown in Fig. 11.3A or B, then one should examine the counting system or even
the counter may be behaving erratically.
There are, however, some practical difficulties in either plotting this curve or
calculating the standard deviation accurately, especially when the radioactive isotope
is either a short-lived one or the activity is very low. In such cases, a single count is
recorded for a duration in which the decrease in the activity due to decay the process
is negligible and the square root of this value is taken as an approximate value of the
standard deviation.
175
95.5%
68.3%
– 2
–
0
+
+ 2
Standard Deviation
Frequency
Fig. 11.2 An ideal Gaussian distribution curve is shown here. Mean value is taken as the zero and
variation of counts with respect to mean values is shown. 68.3% and 95.5% are expected range of
the distribution if there is no other error involved in the counting system and the radioactive material
does not decay during the course of counting
• mean ±1σ 68.3% of total count should fall in this range
• mean ±2σ 95.5% of total count should in this range
• mean ±3σ 99.9% of total count should fall in this range.
However, it will be noticed that the data shown in Table 11.1 and the graph plotted
from these data do not fall in line with the expected Gaussian distribution curve
(Fig. 11.2). As a result of this, even the expected value of mean ±1σ (i.e., 9570 ±
77.92 cpm) contains more than 68.3% of the total data. There could be various
reasons for getting such deviation from the expected result which is discussed in the
next section.
The advantage of this Gaussian distribution analysis is that by plotting a Gaussian
distribution of radioactivity of a long-lived isotope, one can confirm whether the
counting system is operating properly. If the counting system is operating perfectly
and recorded counts are following the Gaussian distribution curve, then a symmetrical
distribution curve is obtained as shown in Fig. 11.3C. But if the curve takes the form
as shown in Fig. 11.3A or B, then one should examine the counting system or even
the counter may be behaving erratically.
There are, however, some practical difficulties in either plotting this curve or
calculating the standard deviation accurately, especially when the radioactive isotope
is either a short-lived one or the activity is very low. In such cases, a single count is
recorded for a duration in which the decrease in the activity due to decay the process
is negligible and the square root of this value is taken as an approximate value of the
standard deviation.