Biomedical Engineering Reference
In-Depth Information
would give the smallest standard deviation of the net count
rate?
32.
A certain counter has an efficiency of 35%. A background
measurement gives 367 counts in 100 min. When a long-lived
sample is placed in the counter, 48 gross counts are registered
in 10 min.
(a)
Estimate the standard deviation of the sample activity in Bq.
(b)
For optimum statistical accuracy, how should the total time
of 110 min be apportioned between taking background and
gross counts?
33.
A sample containing a short-lived radionuclide is placed in a
counter, which registers 57,912 counts before the activity
disappears completely. Background is zero.
(a)
If the counter efficiency is 28%, how many atoms of the
radionuclide were present at the beginning of the counting
period?
(b)
What is the standard deviation of the number?
34.
Repeat the last problem for an efficiency of (a) 45% and
(b) 80%.
35.
What value
<1
of the counter efficiency maximizes the
standard deviation of the count number, Eq. (11.62)? Interpret
your answer.
36.
Describe an experiment for obtaining the half-life of a
radionuclide when its activity decreases noticeably during the
time an observation is made. Include a provision for
background counts. How can one minimize the statistical
uncertainty in the half-life determination? (See R. D. Evans,
The
Atomic Nucleus
, pp. 812-816, cited in Section 11.14.)
37.
How are Eqs. (11.58)-(11.62) affected when background is
taken into account?
38.
Show that Eq. (11.68) follows from (11.67).
39.
Show that Eqs. (11.69) and (11.70) follow from (11.67) when
t
g
=
t
b
.
40.
A sample is to be placed in a counter and a gross count taken
for 10 min. The maximum acceptable risk for making a type-I
error is 0.050. The efficiency of the counter is such that 3.5
disintegrations in a sample result in one net count. A 20-min
background measurement yields 820 counts. Under these
conditions, what is the minimum significant measured activity
in Bq, as inferred from a 10-min gross count?
41.
At a certain facility, gross and background counts are made for
the same length of time, and
α
=
0.025
.The
background is not accurately known beforehand. Calibration at
the facility shows that one net count corresponds to a sample
activity of 260 Bq. The minimum significant measured activity
0.050
and
β
=
