1000 Solved Problems in Modern Physics

436 8 Nuclear Physics – II

8.2.5 Nuclear Stability...................................

8.17 In general only the heavier nuclei tend to show alpha decay. For largeAit is
found thatB/A= 9. 402 − 7. 7 × 10 −^3 A.
Given that the binding energy of alpha particles is 28.3 MeV, show that
alpha decay is energetically possible forA>151.
[University of Wales, Aberystwyth, 2003]

8.18 For the nucleus^16 O the neutron and proton separation energies are 15.7 and
12.2 MeV, respectively. Estimate the radius of this nucleus assuming that the
particles are removed from its surface and that the difference in separation
energies is due to the Coulomb potential energy of the proton.
[University of Wales, Aberystwyth 2004]

8.19 By considering the general conditions of nucleus stability show that the
nucleus^22990 Th will decay and decide whether the decay will take place by
αorβemission.
The atomic mass excesses of the relevant nuclei are:
Element^42 He^22588 Ra^22989 Ac^22990 Th^22991 Pa

Mass excess amu× 10 −^62 ,603 23,528 32,800 31,652 32, 022

8.20 The masses of^6428 Ni,^6429 Cu and^6430 Zn are as tabulated below. It follows that^6429 Cu
is radioactive. Detail the various possible decay modes to the ground state
of the daughter nucleus and give the maximum energy of each component,
ignoring the recoil energy. Compute the recoil energy in one of the cases and
verify that it was justifiable to ignore it.

Nuclide Atomic mass

64

28 Ni 63.927959

64

29 Cu 63.929759

64

30 Zn 63.929145

[University of Bristol 1969]

8.21^2813 Al decays to^2814 Si viaβ− emission withTmax = 2 .865 MeV.^2814 Si is in
the excited state which in turn decays to the ground state viaγ-emission.
Find theγ-ray energy. Take the masses^28 Al = 27 .981908 amu,^28 Si =
27 .976929 amu.

8.22^2211 Na decays to^2210 Ne viaβ+withTmax = 0 .542 MeV followed byγ-decay
with energy 1.277 MeV. If the mass of^22 Ne is 21.991385 amu, determine the
mass of^22 Na in amu.
8.23^74 Be undergoes electron capture and decays to^73 Li. Investigate if it can decay
by the competitive decay mode ofβ+emission. Take masses^74 Be= 7. 016929
amu,^73 Li= 7 .016004 amu.