11.3 Gaussian Distribution Curve
177
work, one should try to measure the activity for the longest possible period so that
the total counts recorded is as high as possible. Certainly, we shall face problems in
recording the large number of counts with either low active materials of long-lived
isotopes or short-lived isotope. Because short-lived isotopes with low activity can
not be counted for a longer duration as it will decay while counting. In such cases,
one has to make a compromise. Similarly, when counting a source of low activity of
long-lived isotopes, one may need several 100 h to counts even 1000 counts. Under
these conditions also one has to make a compromise.
11.3.3 Representation of Activity
The measurement of radioactivity is always expressed by the number of counts per
unit time. Counting is done for a longer duration and the count rate is calculated
by dividing the total count recorded by the time for which counting was done. The
activities of the sample recorded by the counter are also subtracted for the background
count rate to get the true count rate. One may also need to add two or more count
rates together or subtract or divide or multiply one count rate from another count rate
etc., to arrive at required results.
The next question that arises is when counts are to be multiplied, or divided, added
etc., then how can we represent the standard deviation of the final answer? In the
next few sections, we shall devote time to calculate the standard deviation for these
different conditions.
11.4 Sums and Differences of Counts
In radiochemical works, the recorded activities of two samples are either to be subtracted or added to get the final results. The subtraction of background from the
sample is a very common example. In such cases, the standard deviation of final
results is calculated by the Eq. (11.2). It is assumed that the count to be subtracted is
less than the count from which it is to be subtracted, which is also the case with the
background count. Because the background count is normally very low compared to
the actual count rate of the sample. We can define
u = x + y or u = x − y
where x and y are two types of counts (i.e., observed count being x, the background
count being y and net count to be calculated is u). It will be seen that the standard
deviation of the final result (σ u ) is the same, whether the counts are subtracted or
added and is given by Eq. (11.2)
177
work, one should try to measure the activity for the longest possible period so that
the total counts recorded is as high as possible. Certainly, we shall face problems in
recording the large number of counts with either low active materials of long-lived
isotopes or short-lived isotope. Because short-lived isotopes with low activity can
not be counted for a longer duration as it will decay while counting. In such cases,
one has to make a compromise. Similarly, when counting a source of low activity of
long-lived isotopes, one may need several 100 h to counts even 1000 counts. Under
these conditions also one has to make a compromise.
11.3.3 Representation of Activity
The measurement of radioactivity is always expressed by the number of counts per
unit time. Counting is done for a longer duration and the count rate is calculated
by dividing the total count recorded by the time for which counting was done. The
activities of the sample recorded by the counter are also subtracted for the background
count rate to get the true count rate. One may also need to add two or more count
rates together or subtract or divide or multiply one count rate from another count rate
etc., to arrive at required results.
The next question that arises is when counts are to be multiplied, or divided, added
etc., then how can we represent the standard deviation of the final answer? In the
next few sections, we shall devote time to calculate the standard deviation for these
different conditions.
11.4 Sums and Differences of Counts
In radiochemical works, the recorded activities of two samples are either to be subtracted or added to get the final results. The subtraction of background from the
sample is a very common example. In such cases, the standard deviation of final
results is calculated by the Eq. (11.2). It is assumed that the count to be subtracted is
less than the count from which it is to be subtracted, which is also the case with the
background count. Because the background count is normally very low compared to
the actual count rate of the sample. We can define
u = x + y or u = x − y
where x and y are two types of counts (i.e., observed count being x, the background
count being y and net count to be calculated is u). It will be seen that the standard
deviation of the final result (σ u ) is the same, whether the counts are subtracted or
added and is given by Eq. (11.2)