12.3 The Sun's Energy Source
(Discovering the Universe, 5th ed., §9.7)
- The source of the Sun's energy was not understood until this
It was known that familiar sources of energy could not
For example, if the Sun was made of oil, to produce the observed
luminosity its mass would be burned up in a few thousand years,
and the Earth was known to be much, much older than that.
- Einstein's Theory
of Special Relativity provided the key when it showed that
and mass are convertible:
E = mc2
- Because c is so large, a small amount of mass can
provide a huge amount of energy.
The only question then was how this conversion from mass to energy
- The subsequent development of nuclear physics provided the
necessary understanding: thermonuclear fusion of hydrogen
Basically, this is nuclear
fusion at a very high temperature, which is necessary to
overcome the nuclei's electrostatic
- Recall that the positive charge on hydrogen nuclei (protons)
ordinarily keeps them far apart.
The proton's electric potential energy increases as they get
closer together, so they will slow down, stop, and begin to separate
This is like trying to roll a ball up a hill; with too little
energy, it will turn around and roll back down.
- If the protons are hot enough, however, they will have enough
energy that that they can get quite close together.
- At short (nuclear) distances, the strong
nuclear force will dominate the electric force, so that the
protons are now attracted to each other, and they can fuse together
into a new nucleus.
This would be like a ball with enough energy to roll up and over
the top of a hill, and down the other side.
- The energy required for protons to overcome their electric
repulsion corresponds to a temperature of 8.5 MK.
Since the Sun's core has a temperature of 15.5 MK, it can easily
sustain hydrogen fusion, and in fact burns hydrogen faster than
it would at a lower temperature.
- The actual process by which hydrogen fusion occurs is somewhat involved and is called the proton-proton cycle, summarized by the equation:
This equation says that four hydrogen atoms (with one nucleon each) are combined to produce a helium atom (with four nucleons).
In addition, the fusion produces four photons (represented by the Greek letter gamma, because they are gamma radiation), two neutrinos (represented by the Greek letter nu), and energy.
- According to Einstein, the proton-proton cycle must conserve
mass + energy.
In particular, because
the overall reaction begins with more mass than it ends up with,
and the difference is converted into other forms of energy.
Question: what other forms
of energy might result from this fusion?
Note that in the above reaction, the hydrogen on the left has
four protons, while the helium on the right has two
protons and two neutrons.
The weak nuclear force governs the reaction which turns protons into neutrons, resulting in the neutrinos:
Question: where did we previously see a similar process? how did it differ?
Question: why does this reaction require energy to occur? (Hint: consider the masses involved.)
- In addition to a neutrino, this reaction produces a positron,
which is a positive electron.
The positron ensures conservation
of electric charge by carrying away the proton's positive
Positrons are a form of antimatter, particles which have
the same mass as regular matter but the opposite electric charge.
Antimatter does not normally exist in nature, because it will
usually quickly collide with matter and be destroyed in a process
called pair annihilation:
Note that here mass is now converted completely back into energy
in the form electromagnetic radiation.
- The proton-neutron conversion occurs when two protons ("ordinary"
hydrogen) fuse into a nucleus of deuterium ("heavy"
Deuterium is an isotope
of hydrogen, 2H, with one proton
and one neutron.
The energy to convert the proton into a neutron comes from a net mass loss in the conversion from two protons to deuterium.
- The deuterium quickly fuses with another proton to form an
isotope of helium, 3He, which
has only one neutron:
Another photon of gamma radiation is released in this process.
- Finally, two "light" helium nuclei fuse together,
producing "ordinary" helium, and two protons:
- The fusions (1) and (2) occur twice, and together with fusion
(3) the result is:
Note that two protons are "recycled" for use in later
fusions, which is how the proton-proton cycle gets its name.
The entire series of reactions is displayed at the right.
- The energy resulting from thermonuclear fusion is distributed
in several ways:
- kinetic energy of 4He and
the two "recycled" protons: 91%
- electromagnetic energy of the photons: 8%
- kinetic energy of the neutrinos: 1%
- To produce the Sun's luminosity, 600 million tons of H must
be burned by this process every second.
Because the Sun is so massive, though, it will last for another
5 billion years!