Biomedical Engineering Reference
In-Depth Information
The
W
value for silicon is 3.6 eV ip
-1
at 77 K. Calculate the
Poisson energy resolution (FWHM in keV) for the absorption
of 5.3-MeV alpha particles.
52.
The
W
value for Ge is 3.0 eV ip
-1
at 77 K. Based on Poisson
statistics, calculate the expected energy resolution (FWHM) of
an HPGe detector for 0.662-MeV photons from
137
Cs. Assume
that charge collection is complete and that electronic noise is
negligible.
53.
54.
The resolution of a certain HPGe spectrometer
(
W
=
3.0
eV ip
-1
)
for 662-keV
137
Cs photons is found to be
0.50%. Assume that variations in pulse height are due entirely
to statistical fluctuations in the number of ions produced by an
absorbed photon. What is the resolution for the 1.332-MeV
gamma ray from
60
Co?
55.
Using Poisson statistics, calculate the energy resolution
(percent) of both detectors for the 4-MeV alpha particles in
Problem 26 of the last chapter. How would the resolution of the
two compare if the alpha-particle energy were 6 MeV?
56.
A 30-keV beta particle is absorbed in a scintillator having an
efficiency of 8%. The average scintillation photon energy is
3.4 eV. If 21% of the photons are counted, what is the
resolution for the measured beta-particle energy? What would
be the resolution in a semiconductor detector (
W
3
eV ip
-1
)?
=
57.
What are the pros and cons of using Nal scintillators vs. HPGe
detectors for gamma-ray spectroscopy?
58.
Give an argument that, because of energy conservation alone,
the Fano factor cannot be unity.
59.
From the definition (11.90) of the Fano factor, show that the
resolution of a counter can be expressed as
R
=
)
1/2
.
FWHM/
µ
=
2.35(
F
/
µ
60.
The resolution for 360-keV photons with a certain gas
proportional counter (
W
=
30
eV ip
-1
) is observed to be 0.80%.
Determine the Fano factor.
61.
Show that Eq. (11.97) leads to (11.93) when
r
t
τ
1
.
62.
A nonparalyzable counter with a source in place registers
128,639 counts in 2.5 s. An identical source is added, and
210,649 counts are recorded in 2.5 s. Background is zero, and
self-absorption in the sources is negligible. What is the dead
time of the counter?
63.
Show that the maximum count rate obtainable with a
paralyzable system having a dead time
τ
is
1/
e
τ
.
64.
If the maximum count rate attainable with a paralyzable
counter is 64,100 s
-1
, what is the dead time?
65.
The mass attenuation coefficient for 600-keV photons in
aluminum is 0.080 cm
2
g
-1
.
