8.2 Problems
445
barns for a neutron velocity v = 2, 200 m/s. If the counting rate is 250/min,
calculate the value of Q. Given L = 50 cm; D = 5 × 10
5 cm
2
/s.
[University of Bristol 1959]
8.79 Calculate the thermal utilization factor for a heterogeneous lattice made up of
cylindrical uranium rods of diameter 3 cm and pitch 18 cm in graphite
Take the flux ratio φ m /φ U as 1.6
Densities : Uranium = 18.7 × 10
3 kg m
−3 , Graphite = 1.62 × 10
3 kg m
−3
Absorption cross-sections σ av = 7.68 b; σ am = 4.5 × 10
−3 b.
[University of Durham 1961]
8.80 Calculate approximately, using one-group theory results, the critical size of a
bare spherical reactor, given k ∞ = 1.54 and Migration area M
2
= 250 cm
2 .
8.81 Assuming the energy released per fission of
235 U is 200 MeV, calculate the
amount of
235 U consumed per day in Canada India reactor “Cirus” operating
at 40 MW of power.
8.82 Assuming that the energy released per fission of
235
92 U is 200 MeV, calculate the
number of fission processes that should occur per second in a nuclear reactor
to operate at a power level of 20,000 kW. What is the corresponding rate of
consumption of
235
92 U.
[University of London 1959]
8.83 (a) Assume that in each fission of
235 U, 200 MeV is released. Assuming that
5% of the energy is wasted in neutrinos, calculate the amount of
235 U
burned which would be necessary to supply at 30% efficiency, the whole
annual electricity consumption in Britain 50 × 10
9 kWh
(b) A thermal reactor contains 100 tons of natural uranium (density 19) and
operates at a power of 100 MW (heat). Assuming that the thermal crosssection of
235 U is 550 barns and that the uranium contains 0.7 % of
235 U.
Calculate the neutron flux near the centre of the reactor by neglecting neutron losses from the outside, and assuming flux constant through out the
lattice.
[University of Liverpool 1959]
8.84 If the elastic scattering of neutrons by hydrogen nuclei is isotropic in the centre
of mass system, show that
ln(E 1 /E 2 ) = 1
where E 1 and E 2 are respectively the kinetic energies of a neutron before and
after the collision.
[University of London 1969]
8.85 (a) Estimate the average number of collisions required to reduce fast fission
neutrons of initial energy 2 MeV to thermal energy (0.025 eV) in graphite
moderator.
(b) Calculate the corresponding slowing-down time given that Σ s = 0.385 cm
−1
445
barns for a neutron velocity v = 2, 200 m/s. If the counting rate is 250/min,
calculate the value of Q. Given L = 50 cm; D = 5 × 10
5 cm
2
/s.
[University of Bristol 1959]
8.79 Calculate the thermal utilization factor for a heterogeneous lattice made up of
cylindrical uranium rods of diameter 3 cm and pitch 18 cm in graphite
Take the flux ratio φ m /φ U as 1.6
Densities : Uranium = 18.7 × 10
3 kg m
−3 , Graphite = 1.62 × 10
3 kg m
−3
Absorption cross-sections σ av = 7.68 b; σ am = 4.5 × 10
−3 b.
[University of Durham 1961]
8.80 Calculate approximately, using one-group theory results, the critical size of a
bare spherical reactor, given k ∞ = 1.54 and Migration area M
2
= 250 cm
2 .
8.81 Assuming the energy released per fission of
235 U is 200 MeV, calculate the
amount of
235 U consumed per day in Canada India reactor “Cirus” operating
at 40 MW of power.
8.82 Assuming that the energy released per fission of
235
92 U is 200 MeV, calculate the
number of fission processes that should occur per second in a nuclear reactor
to operate at a power level of 20,000 kW. What is the corresponding rate of
consumption of
235
92 U.
[University of London 1959]
8.83 (a) Assume that in each fission of
235 U, 200 MeV is released. Assuming that
5% of the energy is wasted in neutrinos, calculate the amount of
235 U
burned which would be necessary to supply at 30% efficiency, the whole
annual electricity consumption in Britain 50 × 10
9 kWh
(b) A thermal reactor contains 100 tons of natural uranium (density 19) and
operates at a power of 100 MW (heat). Assuming that the thermal crosssection of
235 U is 550 barns and that the uranium contains 0.7 % of
235 U.
Calculate the neutron flux near the centre of the reactor by neglecting neutron losses from the outside, and assuming flux constant through out the
lattice.
[University of Liverpool 1959]
8.84 If the elastic scattering of neutrons by hydrogen nuclei is isotropic in the centre
of mass system, show that
ln(E 1 /E 2 ) = 1
where E 1 and E 2 are respectively the kinetic energies of a neutron before and
after the collision.
[University of London 1969]
8.85 (a) Estimate the average number of collisions required to reduce fast fission
neutrons of initial energy 2 MeV to thermal energy (0.025 eV) in graphite
moderator.
(b) Calculate the corresponding slowing-down time given that Σ s = 0.385 cm
−1