444
8 Nuclear Physics – II
The reaction above will take place for low energy incident deuterons in a
s-wave state leaving the
12 C nucleus in the ground state.
Given that the deuteron has spin 1 and positive parity while the alpha particle has zero spin and positive parity, estimate the spin of
14 N in the ground
state.
Can the alpha particle come off with orbital angular momentum l = 1?
If the incident kinetic energy of the deuteron is 20 MeV in the laboratory
frame, calculate the laboratory kinetic energy at which α’s should scatter from
12 C to test the principle of detailed balance. What is the expected ratio between
the cross-sections for the direct and inverse reactions? Atomic masses of
14 N,
2 H and
4 He are 14.003074, 2.014102, 4.002603 amu respectively. 1 amu
= 931.44 MeV.
[University of Bristol 1969]
8.74 A beam of 460 MeV deuterons impinges on a target of bismuth. Given the
binding energy of the deuteron is 2.2 MeV, compute the mean energy, spread
in energy and the angle of the cone in which the neutrons are emitted.
[Osmania University 1975]
8.2.14 Fission and Nuclear Reactors
8.75 1.0 g of
23 Na of density 0.97 is placed in a reactor at a region where the thermal flux is 10
11
/cm
2
/s. Set up the equation for the production of
24 Na and
determine the saturation activity that can be produced. The half-life of
24 Na is
15 h, and the activation cross-section of
23 Na is 536 millibarns.
[Osmania University 1964]
8.76 Suppose 100 mg of gold (
197
79 Au) foil are exposed to a thermal neutron flux
of 10
12 neutrons/cm
2
/s in a reactor. Calculate the activity and the number
of atoms of
198 Au in the sample at equilibrium [Thermal neutron activation
cross-section for
197 Au is 98 barns and half-life for
197 Au is 2.7 h]
[Osmania University]
8.77 Estimate the energy released in fission of
238
92 U nucleus, given a c = 0.59 MeV
and a s = 14.0 MeV.
[Osmania University 1962]
8.78 A small container of Ra–Be is embedded in the middle of a sphere of paraffin
wax of a few cm radius so as to form a source of (predominantly) thermal
neutrons. This source is placed at the centre of a very large block of graphite.
Derive an expression for the density of thermal neutrons at a large distance r
from the source in terms of the source strength Q, the diffusion coefficient D
and diffusion length L.
A small BF 3 counter is placed in the graphite at a distance of 3 m from
the above source contains 10
20 atoms of
10 B. The cross-section of
10 B for
the thermal neutron capture follows a 1/v law and has a magnitude of 3,000
8 Nuclear Physics – II
The reaction above will take place for low energy incident deuterons in a
s-wave state leaving the
12 C nucleus in the ground state.
Given that the deuteron has spin 1 and positive parity while the alpha particle has zero spin and positive parity, estimate the spin of
14 N in the ground
state.
Can the alpha particle come off with orbital angular momentum l = 1?
If the incident kinetic energy of the deuteron is 20 MeV in the laboratory
frame, calculate the laboratory kinetic energy at which α’s should scatter from
12 C to test the principle of detailed balance. What is the expected ratio between
the cross-sections for the direct and inverse reactions? Atomic masses of
14 N,
2 H and
4 He are 14.003074, 2.014102, 4.002603 amu respectively. 1 amu
= 931.44 MeV.
[University of Bristol 1969]
8.74 A beam of 460 MeV deuterons impinges on a target of bismuth. Given the
binding energy of the deuteron is 2.2 MeV, compute the mean energy, spread
in energy and the angle of the cone in which the neutrons are emitted.
[Osmania University 1975]
8.2.14 Fission and Nuclear Reactors
8.75 1.0 g of
23 Na of density 0.97 is placed in a reactor at a region where the thermal flux is 10
11
/cm
2
/s. Set up the equation for the production of
24 Na and
determine the saturation activity that can be produced. The half-life of
24 Na is
15 h, and the activation cross-section of
23 Na is 536 millibarns.
[Osmania University 1964]
8.76 Suppose 100 mg of gold (
197
79 Au) foil are exposed to a thermal neutron flux
of 10
12 neutrons/cm
2
/s in a reactor. Calculate the activity and the number
of atoms of
198 Au in the sample at equilibrium [Thermal neutron activation
cross-section for
197 Au is 98 barns and half-life for
197 Au is 2.7 h]
[Osmania University]
8.77 Estimate the energy released in fission of
238
92 U nucleus, given a c = 0.59 MeV
and a s = 14.0 MeV.
[Osmania University 1962]
8.78 A small container of Ra–Be is embedded in the middle of a sphere of paraffin
wax of a few cm radius so as to form a source of (predominantly) thermal
neutrons. This source is placed at the centre of a very large block of graphite.
Derive an expression for the density of thermal neutrons at a large distance r
from the source in terms of the source strength Q, the diffusion coefficient D
and diffusion length L.
A small BF 3 counter is placed in the graphite at a distance of 3 m from
the above source contains 10
20 atoms of
10 B. The cross-section of
10 B for
the thermal neutron capture follows a 1/v law and has a magnitude of 3,000