436
8 Nuclear Physics – II
8.2.5 Nuclear Stability
8.17 In general only the heavier nuclei tend to show alpha decay. For large A it is
found that B/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 for A > 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
229
90 Th will decay and decide whether the decay will take place by
α or β emission.
The atomic mass excesses of the relevant nuclei are:
Element
4
2 He
225
88 Ra
229
89 Ac
229
90 Th
229
91 Pa
Mass excess amu ×10
−6
2,603 23,528 32,800 31,652 32,022
8.20 The masses of
64
28 Ni,
64
29 Cu and
64
30 Zn are as tabulated below. It follows that
64
29 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
28
13 Al decays to
28
14 Si via β
− emission with T max = 2.865 MeV.
28
14 Si is in
the excited state which in turn decays to the ground state via γ -emission.
Find the γ -ray energy. Take the masses
28 Al = 27.981908 amu,
28 Si =
27.976929 amu.
8.22
22
11 Na decays to
22
10 Ne via β
+ with T max = 0.542 MeV followed by γ -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
7
4 Be undergoes electron capture and decays to
7
3 Li. Investigate if it can decay
by the competitive decay mode of β
+ emission. Take masses
7
4 Be = 7.016929
amu,
7
3 Li = 7.016004 amu.
8 Nuclear Physics – II
8.2.5 Nuclear Stability
8.17 In general only the heavier nuclei tend to show alpha decay. For large A it is
found that B/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 for A > 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
229
90 Th will decay and decide whether the decay will take place by
α or β emission.
The atomic mass excesses of the relevant nuclei are:
Element
4
2 He
225
88 Ra
229
89 Ac
229
90 Th
229
91 Pa
Mass excess amu ×10
−6
2,603 23,528 32,800 31,652 32,022
8.20 The masses of
64
28 Ni,
64
29 Cu and
64
30 Zn are as tabulated below. It follows that
64
29 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
28
13 Al decays to
28
14 Si via β
− emission with T max = 2.865 MeV.
28
14 Si is in
the excited state which in turn decays to the ground state via γ -emission.
Find the γ -ray energy. Take the masses
28 Al = 27.981908 amu,
28 Si =
27.976929 amu.
8.22
22
11 Na decays to
22
10 Ne via β
+ with T max = 0.542 MeV followed by γ -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
7
4 Be undergoes electron capture and decays to
7
3 Li. Investigate if it can decay
by the competitive decay mode of β
+ emission. Take masses
7
4 Be = 7.016929
amu,
7
3 Li = 7.016004 amu.