Nuclear Structure 391
properties of isotopes may very more dramatically with mass number: tritium is radioac-
tive, for instance, whereas ordinary hydrogen and deuterium are not.N
uclide masses are always very close to being integral multiples of the mass of the hydro-
gen atom, as we can see in Table 11.2. Before the discovery of the neutron, it was tempt-
ing to regard all nuclei as consisting of protons together with enough electrons to neutralize the
positive charge of some of them. This hypothesis is buttressed by the fact that certain radioac-
tive nuclei spontaneously emit electrons, a phenomenon called beta decay. However, there are
some strong arguments against the idea of nuclear electrons.
1 Nuclear size. In Example 3.7 we saw that an electron confined to a box of nuclear dimensions
must have an energy of more than 20 MeV, whereas electrons emitted during beta decay have
energies of only 2 or 3 MeV, an order of magnitude smaller. A similar calculation for protons
gives a minimum energy of around 0.2 MeV, which is entirely plausible.
2 Nuclear spin. Protons and electrons are fermions with spins (that is, spin quantum numbers)
of ^12 . Thus nuclei with an even number of protons plus electrons should have 0 or integral spin,
those with an odd number of protons plus electrons should have half-integral spins. This pre-
diction is not obeyed. For instance, if a deuterium nucleus,^21 H, consisted of two protons and
an electron, its nuclear spin should be 2 ^1 or ^32 , but in fact is observed to be 1.
3 Magnetic moment. The proton has a magnetic moment only about 0.15 percent that of the
electron. If electrons are part of a nucleus, its magnetic moment ought to be of the order of mag-
nitude of that of the electron. However, observed nuclear magnetic moments are comparable
with that of the proton, not with that of the electron.
4 Electron-nuclear interaction. The forces that hold the constituents of a nucleus together lead
to typical binding energies of around 8 MeV per particle. If some electrons can bind this strongly
to protons in the nucleus of an atom, how can the other electrons in the atom remain outside
the nucleus? Furthermore, when fast electrons are scattered by nuclei, they behave as though
acted upon solely by electric forces, whereas the scattering of fast protons shows that a differ-
ent force also acts on them.
Despite these difficulties, the hypothesis of nuclear electrons was not universally abandoned
untill the discovery of the neutron in 1932. When he wrote a book on nuclear physics pub-
lished the year before, George Gamow felt so uneasy about the accepted proton-electron model
of the nucleus that he marked each section dealing with nuclear electrons with a skull and cross-
bones. When the publisher objected, Gamow replied that “It has never been my intention to
scare the poor readers more than the text itself will undoubtedly do,” and replaced the skull and
crossbones with a less dramatic symbol.Nuclear Electrons
Table 11.2The Isotopes of Hydrogen and Chlorine Found in NatureProperties of
Element Properties of Isotope
Average Protons Neutrons Atomic Relative
Atomic Atomic in in Mass Mass, Abundance,
Element Number Mass, u Nucleus Nucleus Number u Percent
Hydrogen 1 1.008 1 0 1 1.008 99.985
1 1 2 2.014 0.015
1 2 3 3.016 Very small
Chlorine 17 35.46 17 18 35 34.97 75.53
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