22.01 Introduction to Ionizing Radiation
Fall 2003
Problem Set #5
Due Date: Wednesday, October 15, 2003
Show all work. Provide units on all answers.
1. For 10-MeV photons, the mass attenuation coefficient for air is 0.204. The
average energy transferred (Etr) is 7.37 MeV. The average energy absorbed (Eab) is
4
7.10 MeV. Assuming a fluence of 10 photons traverse a volume of air of “thickness”
2
1.5 g/cm , compute the number of scattering events, the energy appearing as kinetic
energy of electrons in the medium, the energy removed from the incident beam, and
the amount of the original incident energy that reappears as bremsstrahlung.
24
3
2. Natural boron has a density of 0.128 x 10 at/cm . The capture cross section σc =
764 b and the scattering cross section σs = 4 b at an energy of E = 0.025 eV.
a) Calculate the macroscopic cross sections at 0.025 eV for capture, scattering and
total interaction.
b) What fractional attenuation will a 0.025-eV neutron beam experience when
traveling through 1 mm of the boron? 1 cm?
c) Assuming the capture cross section is "one-over-υ" in energy, calculate the
macroscopic cross sections for boron for neutrons of 0.0025-eV and 100-eV energies.
d) What thickness of boron is required to absorb 50 percent of a 100-eV neutron
beam?
3. A beam of fast neutrons includes two energy groups. One group, of 1-MeV
neutrons, includes 99% of the total neutron flux. The remaining 1% of the neutrons
have an energy of 10 MeV.
(a) What will be the relative proportions of the two groups after passing through 25
cm of water?
(b) What would be the relative proportion of the two groups after passing through a
slab of lead of the same density thickness?
The removal cross sections (in barns) are as follows:
H
O
Pb
1 MeV
10 MeV
4.2 barns
0.95
8
1.5
5.5
5.1
4. A sample containing an unknown quantity of chromium is irradiated for 1 week
11
2
51
in a thermal neutron flux of 10 n/cm /s. The resulting Cr gamma rays give a
counting rate of 600 counts per minute in a scintillation counter whose overall
efficiency is 10%. How many grams of chromium were there in the original sample?
The reaction in this case is
50
Cr +
1
0
 51Cr + 
n
50
50
The thermal neutron activation cross section for Cr is 13.5 barns, and Cr forms
4.31% by number of the naturally occurring chromium atoms. Chromium 51 decays
by orbital electron capture with a half-life of 27.8 days and emits a 0.323-MeV
gamma-ray in 9.8% of the decays. The atomic weight of Cr is 52.01.
5. In an experiment designed to measure the total cross section of lead for 10 MeV
neutrons, it was found that a 1-cm-thick lead absorber attenuated the neutron flux
to 84.5% of its initial value. The atomic weight of lead is 207.21, and its density is
3
11.4 g/cm . Calculate the total cross section from these data.
24
6. What is the saturation activity of Na that can be induced in a 400 g sample of
10
-2
–1
NaCl with a constant thermal-neutron fluence rate of 5 x 10 cm sec ? The isotope
23
Na is 100% abundant and has a thermal-neutron capture cross section of 0.53
barns.
7. If the G value for the OH radicals produced by 20 keV electrons is 1.10, how
many of them are produced, on the average, when a 20 keV electron stops in water?
3
8. A 50 cm sample of water is given a dose of 2 Gy from 2 MeV protons. If the
yield of OH radicals is G = 1.44 per 100 eV, how many OH radicals are produced in
the sample?
-6
9. How far can a hydroxyl radical and a hydrogen radical diffuse in 10 sec?
10. Estimate the average time it takes for an OH radical to diffuse 400 Å in water.