Elements of Modern Physics
358
(A = 56) where the binding energy per nucleon has a maximum. Here, exothermic
fusion reactions cease. Elements heavier than
56
Fe may be produced by capture
of neutrons produced in some reactions, and subsequent β-decays. Thus,
elements upto and just beyond uranium are produced. Still heavier elements
have short lifetimes and if created would quickly decay either by α-emission or
fission.
9.9 EXAMPLES
Some examples to illustrate the properties and interactions of the nucleus are
considered here.
Example 1
In the early stages of the development of nuclear physics before the neutron
was discovered, one of the models of the nucleus considered was that it was
made up of A protons and (A – Z) electrons. There are several arguments against
this model.
An electron confined to a volume of nuclear dimensions would be highly
relativistic, and its energy would be estimated by the uncertainty principle to be
T ≈ pc ≈
c
x
∆
(9.121)
≈ 100 MeV for ∆x ≈ 2 fm
The confinement of such energetic electrons would require the existence of
very strong forces for which there is no evidence (such potentials would also
create many electron-positron pairs which are not observed). A conclusive
evidence against the proton-electron model of the nucleus is that even A, odd
Z nuclei have integral spin. In the proton-electron picture, such a nucleus would
have A protons and A-Z electrons, i.e. the nucleus has an odd number of fermions,
and hence would be expected to have a half-integral spin. This is contrary to the
experimental observations, e.g.
14
N has I = 1. Finally, the proton-electron picture
would imply the existence of nuclear magnetic moments of the order of 2 e
e
m
whereas the observed moments are much smaller, of the order of 2 p
e
m
.
Example 2
One can estimate the strength of the deuteron potential, by assuming the potential
to be a square well of depth V 0 and radius a.
358
(A = 56) where the binding energy per nucleon has a maximum. Here, exothermic
fusion reactions cease. Elements heavier than
56
Fe may be produced by capture
of neutrons produced in some reactions, and subsequent β-decays. Thus,
elements upto and just beyond uranium are produced. Still heavier elements
have short lifetimes and if created would quickly decay either by α-emission or
fission.
9.9 EXAMPLES
Some examples to illustrate the properties and interactions of the nucleus are
considered here.
Example 1
In the early stages of the development of nuclear physics before the neutron
was discovered, one of the models of the nucleus considered was that it was
made up of A protons and (A – Z) electrons. There are several arguments against
this model.
An electron confined to a volume of nuclear dimensions would be highly
relativistic, and its energy would be estimated by the uncertainty principle to be
T ≈ pc ≈
c
x
∆
(9.121)
≈ 100 MeV for ∆x ≈ 2 fm
The confinement of such energetic electrons would require the existence of
very strong forces for which there is no evidence (such potentials would also
create many electron-positron pairs which are not observed). A conclusive
evidence against the proton-electron model of the nucleus is that even A, odd
Z nuclei have integral spin. In the proton-electron picture, such a nucleus would
have A protons and A-Z electrons, i.e. the nucleus has an odd number of fermions,
and hence would be expected to have a half-integral spin. This is contrary to the
experimental observations, e.g.
14
N has I = 1. Finally, the proton-electron picture
would imply the existence of nuclear magnetic moments of the order of 2 e
e
m
whereas the observed moments are much smaller, of the order of 2 p
e
m
.
Example 2
One can estimate the strength of the deuteron potential, by assuming the potential
to be a square well of depth V 0 and radius a.