1000 Solved Problems in Modern Physics

8.2 Problems 443

8.67 Natural Cobalt is irradiated in a reactor with a thermal neutron flux density of
3 × 1012 ncm−^2 s−^1. How long an irradiation will be required to reach 20%
of the maximum activity? GivenT 1 / 2 = 5 .3 years

8.68 In a scattering experiment an aluminum foil of thickness 10μm is placed in
a beam of intensity 8× 1012 particles per second. The differential scattering
cross-section is known to be of the form
dσ
dΩ

=A+Bcos^2 θ

whereA, Bare constants,θis scattering angle andΩis the solid angle.

With a detector of area 0.01 m^2 placed at a distance of 6 m from the foil, it is

found that the mean counting rate is 50 s−^1 whenθis 30◦and 40 s−^1 whenθ

is 60◦. Find the values ofAandB. The mass number of aluminum is 27 and

its density is 2.7g/cm^2.

8.69 A thin target of^48 Ca with 1. 3 × 1019 nuclei per cm^2 is bombarded with a 10 nA
beam ofαparticles. A detector, subtending a solid angle of 2× 10 −^3 steradians,
records 15 protons per second. If the angular distribution is measured to be
isotropic, determine the total cross section for the^48 Ca(α,p) reaction.
[University of Cambridge, Tripos 2004]

8.2.12 Nuclear Reactions via Compound Nucleus.............

8.70 Cadmium has a resonance for neutrons of energy 0.178 eV and the peak value
of the total cross-section is about 7,000 b. Estimate the contribution of scatter-
ing to this resonance.
[Osmania University 1964]

8.71 A nucleus has a neutron resonance at 65 eV and no other resonances nearby.
For this resonance,Γn = 4 .2eV,Γγ = 1 .3 eV andΓα = 2 .7 eV, and all
other partial widths are negligible. Find the cross-section for (n,γ) and (n,α)
reactions at 70 eV.
[Osmania University]

8.72 Neutrons incident on a heavy nucleus with spinJN=0 show a resonance at an
incident energyER=250 eV in the total cross-section with a peak magnitude
of 1,300 barns, the observed width of the peak beingΓ =20 eV. Find the
elastic partial width of the resonance.
[University of Bristol 1970]

8.2.13 DirectReactions...................................

8.73 The reactiond+^14 N→α+^12 C has been used to test the principle of detailed
balance which relates the cross-sectionσabfor a reactiona+x→b+y,to
the cross-section for the inverse reaction and has the form
(2Sa+1) (2Sx+1)Pa^2 σab=(2Sb+1) (2Sy+1)Pb^2 σba