Stellar Processes - Hydrogen-Helium
General astronomy texts often cite the "mass lost" from
nuclear fusion in the Sun is the difference between the (heavier) helium
nucleus and the (lighter) four hydrogen nuclei. However, the mass of a
neutron is (slightly) greater than the mass of a proton. So how can the
product of nuclear fusion (a helium nucleus with 2 protons and 2
neutrons) be LIGHTER than the reactants (four protons)? Also, how can
the neutron be heavier than the proton, if in the first step of the
proton-proton chain a proton seems to cast off a positron (with the mass
of an electron) and a )practically massless neutrino) to turn into a
neutron? It seems that by conservation of mass this new neutron should
have less mass than the proton that it used to be. I am confused!
This is a very good question, and one that had me looking up proton and
neutron masses. But really, if we look at any nuclear transformation (if
we write a balanced nuclear equation) we note that all the nucleons are
accounted for, that is, the number of protons and neutrons (and emitted
sub-atomic particles) balance out.
So what we really need to consider are two things: (1) nuclear binding
energy, and (2) mass defect. Both of these concepts come from empirical
measurements that showed that the masses of nuclei are always less than
the mass of the nucleons. Thus, "nuclear binding energy" represents the
mass that has been converted to energy in the nuclear transformation, and
the "mass defect" is the difference between the mass of the atom and the
sum of the atom parts (protons, neutrons, electrons).
With this concept then, it is not fair to compare the mass of a hydrogen
(1 proton) to a deuterium (1 proton + 1 neutron) and expect that the
difference between the two atoms is exactly the mass of 1 neutron. We need
to account for the mass defect or nuclear binding energy. Same goes for
comparing the mass of hydrogen to helium or deuterium to helium.
Greg (Roberto Gregorius)
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Update: June 2012