446
8 Nuclear Physics – II
8.86 Show that a homogeneous, natural uranium-graphite moderated assembly can
not become critical. Use the following data:
400 moles of graphite per mole of uranium
Natural uranium
Graphite
σ a (U) = 7.68 b
σ a (M) = 0.0032 b
σ s (U) = 8.3 b
σ s (M) = 4.8 b
ε = 1.0; η = 1.34
ξ = 0.158
[Osmania University 1964]
8.87 A point source of thermal neutrons is placed at the centre of a large sphere of
beryllium.
Deduce the spatial distribution of neutron density in the sphere. Estimate
what its radius must be if less than 1% of the neutrons are to escape through
the surface. Find also the neutron density near the surface in this case in terms
of the source strength.
At. Wt of beryllium = 9
Density of beryllium = 1.85 g/cc
Avagadro number = 6 × 10
23 atoms/g atom
Thermal neutron scattering cross-section on beryllium = 5.6 barns
Thermal neutron capture cross-section on beryllium = 10 mb (at velocity
v = 2,200 m/s)
[University of Bristol 1961]
8.88 Calculate the steady state neutron flux distribution about a plane source emitting Q neutrons/s/cm
2 in an infinite homogeneous diffusion medium. Assume
that neutrons are not produced in any region of interest.
8.89 Calculate the thermal diffusion time for graphite. Use the data:
σ a (C) = 0.003 b, ρ c = 1.62 g cm
−3
. Average thermal neutron speed
= 2,200 m/s.
8.90 Estimate the generation time for neutrons in a critical reactor employing
235 U
and graphite. Use the following data:
Σ
a
= 0.0006 cm
−1 ; B
2
= 0.0003; L
2
= 870 cm
2 ; < v >= 2200 ms.
8.91 The spatial distribution of thermal neutrons from a plane neutron source kept
at a face of a semi-infinite medium of graphite was determined and found to
fit e
−0.03x law where x is the distance along the normal to the plane of the
source. If the only impurity in the graphite is boron, calculate the number of
atoms of boron per cm
3 in the graphite if the mean free path for scattering
and absorption in graphite are 2.7 and 2,700 cm, respectively. The absorption
cross-section of boron is 755 barns.
[Osmania University 1964]
8 Nuclear Physics – II
8.86 Show that a homogeneous, natural uranium-graphite moderated assembly can
not become critical. Use the following data:
400 moles of graphite per mole of uranium
Natural uranium
Graphite
σ a (U) = 7.68 b
σ a (M) = 0.0032 b
σ s (U) = 8.3 b
σ s (M) = 4.8 b
ε = 1.0; η = 1.34
ξ = 0.158
[Osmania University 1964]
8.87 A point source of thermal neutrons is placed at the centre of a large sphere of
beryllium.
Deduce the spatial distribution of neutron density in the sphere. Estimate
what its radius must be if less than 1% of the neutrons are to escape through
the surface. Find also the neutron density near the surface in this case in terms
of the source strength.
At. Wt of beryllium = 9
Density of beryllium = 1.85 g/cc
Avagadro number = 6 × 10
23 atoms/g atom
Thermal neutron scattering cross-section on beryllium = 5.6 barns
Thermal neutron capture cross-section on beryllium = 10 mb (at velocity
v = 2,200 m/s)
[University of Bristol 1961]
8.88 Calculate the steady state neutron flux distribution about a plane source emitting Q neutrons/s/cm
2 in an infinite homogeneous diffusion medium. Assume
that neutrons are not produced in any region of interest.
8.89 Calculate the thermal diffusion time for graphite. Use the data:
σ a (C) = 0.003 b, ρ c = 1.62 g cm
−3
. Average thermal neutron speed
= 2,200 m/s.
8.90 Estimate the generation time for neutrons in a critical reactor employing
235 U
and graphite. Use the following data:
Σ
a
= 0.0006 cm
−1 ; B
2
= 0.0003; L
2
= 870 cm
2 ; < v >= 2200 ms.
8.91 The spatial distribution of thermal neutrons from a plane neutron source kept
at a face of a semi-infinite medium of graphite was determined and found to
fit e
−0.03x law where x is the distance along the normal to the plane of the
source. If the only impurity in the graphite is boron, calculate the number of
atoms of boron per cm
3 in the graphite if the mean free path for scattering
and absorption in graphite are 2.7 and 2,700 cm, respectively. The absorption
cross-section of boron is 755 barns.
[Osmania University 1964]