446 8 Nuclear Physics – II8.86 Show that a homogeneous, natural uranium-graphite moderated assembly can
not become critical. Use the following data:
400 moles of graphite per mole of uraniumNatural uranium Graphite
σa(U)= 7 .68 b σa(M)= 0 .0032 b
σs(U)= 8 .3b σs(M)= 4 .8b
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 × 1023 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 emit-
tingQneutrons/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:
σa(C)= 0 .003 b,ρc= 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:
Σa= 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.^03 xlaw wherexis 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]