CHAPTER 8 | THE SUN 151
Hydrogen Fusion
Th e sun fuses together four hydrogen nuclei to make one helium
nucleus. Because one helium nucleus has 0.7 percent less mass
than four hydrogen nuclei, it seems that some mass vanishes in
the process. To see this, subtract the mass of a helium nucleus
from the mass of four hydrogen nuclei:
4 hydrogen nuclei 6.693 10 ^27 kg
1 helium nucleus 6.645 10 ^27 kg
Diff erence in mass 0.048 10 ^27 kg
Th is small amount of mass does not actually disappear but is
converted to energy according to Einstein’s famous equation:
E mc^2
(0.048 10 ^27 kg) (3.0 108 m/s)^2
0.43 10 ^11 J
You can symbolize the fusion reactions in the sun with a
simple nuclear reaction:
4 1 H → 4 He energy
In this equation,^1 H represents a proton, the nucleus of a
hydrogen atom, and^4 He represents the nucleus of a helium
atom. Th e superscripts indicate the approximate weight of the
nuclei (the number of protons plus the number of neutrons). Th e
actual steps in the process are more complicated than this conve-
nient summary suggests. Instead of waiting for four hydrogen
nuclei to collide simultaneously, a highly unlikely event, the
process normally proceeds step by step in a chain of reactions—
the proton–proton chain.
Th e proton–proton chain is a series of three nuclear reac-
tions that builds a helium nucleus by adding together protons.
Th is process can only happen at temperatures
above about 4 million K, and is effi cient above
10 million K. Th e sun makes over 90 percent of
its energy in this way.
Th e three steps in the proton–proton chain
entail these reactions:
(^1) H 1 H → 2 H e (^)
(^2) H 1 H → 3 He γ
(^3) He 3 He → 4 He 1 H 1 H
In the fi rst reaction, two hydrogen nuclei
(two protons) combine and emit a particle called
a positron, e^ (a positively charged electron),
and a neutrino, (a subatomic particle having
an extremely low mass and a velocity nearly
equal to the velocity of light). Th e emission of
the positively charged positron results from the
conversion of one of the protons into a neutron,
and that forms a heavy hydrogen nucleus called
deuterium, which contains a proton and a neu-
tron. In the second reaction, the heavy hydrogen
nucleus absorbs another proton and, with the
emission of a gamma ray, γ, becomes a lightweight helium
nucleus. Finally, two lightweight helium nuclei combine to form
a nucleus of normal helium and two hydrogen nuclei. Because
the last reaction needs two^3 He nuclei, the fi rst and second reac-
tions must occur twice (■ Figure 8-9). Th e net result of this chain
reaction is the transformation of four hydrogen nuclei into one
helium nucleus plus energy.
Th e energy appears in the form of gamma rays, positrons,
neutrinos and the energy of motion of all the particles. Th e
gamma rays are photons that are absorbed by the surrounding
gas before they can travel more than a fraction of a millimeter.
Th is heats the gas. Th e positrons produced in the fi rst reaction
combine with free electrons, and both particles vanish, convert-
ing their mass into gamma rays, which are absorbed and also help
keep the gas hot. In addition, when fusion produces new nuclei,
they fl y apart at high velocity and collide with other particles.
Th is energy of motion helps raise the temperature of the gas. Th e
neutrinos, on the other hand, don’t heat the gas. Neutrinos are
particles that almost never interact with other particles. Th e aver-
age neutrino could pass unhindered through a lead wall a light-
year thick. Consequently, the neutrinos do not warm the gas but
race out of the sun at nearly the speed of light, carrying away
roughly 2 percent of the energy produced.
ν
γ
γ
γ
ν
ν
Gamma ray
Proton
Neutron
Neutrino Positron
(^1) H
(^1) H
(^1) H
(^1) H
(^1) H
(^1) H
(^1) H
(^2) H
(^1) H
(^4) He
(^2) H
(^3) He
(^3) He
■ Figure 8-9
The proton–proton chain combines four protons (at far left) to produce one
helium nucleus (at right). Energy is produced mostly as gamma rays and as
positrons, which combine with electrons and convert their mass into energy.
Neutrinos escape, carrying away about 2 percent of the energy produced.