228 The Poetry of Physics and The Physics of Poetry
total mass of the bound state is less than the sum of the masses of the
individual particles composing the system. The reason for this is that the
potential energy of the bound particles is negative. If one wished to
separate the two particles, one would have to supply energy to do work
against the attractive force, hence the negative potential energy. The rest
mass energy of the bound state is less than that of the sum of the rest
mass energies of the individual components making up the bound state
because of the negative potential energy and because as Einstein
discovered mass and energy are equivalent. In fact the attenuation of
nuclear mass due to binding energy formed one of the basic tests of
Einstein’s hypothesis of the equivalence of mass and energy.
The binding energy of the electron in the hydrogen atom is only 13.6
electron volts (eV). An eV is a unit of energy equal to the energy an
electron gains when accelerated through a one volt potential. The eV is
the commonest unit of energy in nuclear and elementary particle physics.
Rest mass energies are also measured in electron volts or eVs. Since
mass and energy are equivalent, one can specify the mass of a particle by
specifying the energy of the particle’s rest mass, which is equal to mc^2
and is measured in eVs or MeVs (million electron volts). The rest mass
energy of the electron is approximately 0.5 MeV and the rest mass
energy of the proton approximately 940 MeV. The rest mass energy of
the hydrogen atom is 13.6 eV less than the sum of the rest mass energies
of the proton and the electron. The binding energy hardly affects the
mass of the hydrogen atom. Nuclear binding energies are much greater
than atomic binding energies and involve rest mass energies in the MeV
range.
The reason the nuclear binding energies are greater is because the
nuclear force is stronger than the electric force and also the separation of
the particles involved is much smaller. Let us consider the binding
energy of one of the simplest nuclei known, the deuteron. The deuteron,
an isotope of hydrogen, is a bound state of a proton and a neutron. The
difference in mass between the deuteron and the sum of the masses
of the proton and the neutron is just equal to the nuclear binding energy
of the deuteron. The rest mass energy of the proton is 938.27 MeV,
of the neutron 939.56 MeV and of the deuteron 1877.7 MeV. The
binding energy of the deuteron in MeV is therefore 938.27 + 939.56 –
1875.61 = 2.22 MeV.
If we would want to separate the neutron and the proton in the
deuteron we would be obliged to supply an energy of at least 2.22 MeV.