Cosmology Experiment C-2

Synthesis of Elements in Main Sequence Stars


As noted in the previous section, Edwin Hubble (1889-1953) discovered in 1929 that the universe is currently expanding.  This expansion led George Gamow (1904-1968) about mid-century to propose that the universe essentially exploded from what was probably once very tiny and extremely hot.  The early universe cooled as a consequence of the expansion, eventually allowing the nuclear force to assemble the smallest elements.  As the universe continued to expand and cool, the average speeds of the particles slowed until the weaker repulsive electric force prevented further formation of elements.  These ideas have now been strongly verified by a large number of independent investigations.

One of the remaining challenges has been to explain why the early universe was not uniform in composition.  Evidence from very early indicates that even then the universe was lumpy.  In 1999 researchers studying the very uniform microwave radiation that pervades the cosmos in every direction were able to detect extremely tiny, acoustic-like oscillating variations in this radiation.  In 2005 several teams of astronomers analyzing surveys of thousands of distant galaxies also found extremely weak acoustic patterns, perhaps caused by pressure waves between their gravitational attraction and repulsion by their emitted radiation.  The small size of the bell-like ringing observed in both the microwave background and the distribution of galaxies gave additional evidence that most of the mass of the universe is a dark matter, invisible because it doesn't interact with electromagnetic forces.  The wave length of the detected oscillations also provides evidence of an acceleration of the universe's expansion due to what has been named dark energy.

Those regions with sufficient mass density created enough gravitational attraction to eventually locally stop the expansion and pull the matter back into clumps.  As that mixture of mostly dark matter, Hydrogen and Helium was attracted together and compressed by gravity, the Hydrogen and Helium warmed as described according to Clarles' Law.  The formation of lumps we call stars is still not well understood.  The larger clumps with mass greater than 0.1 that of the Sun warmed enough to become what astronomers classify as main sequence stars.  About 90% of the stars in the sky are main sequence stars.  The nearby star we call our Sun is such a star.  The temperature of the cores of these stars depends on the mass, but generally is about 15 000 000 K.  (This compares with about 300 K on he surface of the earth.)  The density of such stars is about 100 g/cm3 (which compares to Lead having a density of 11 g/cm3 but a nucleus in an atom having a density of about 1014 g/cm3).  The nuclear processes that occur at these temperatures are relatively well understood.  At these conditions Hydrogen can fuse together to form Helium in a sequential process proposed by Hans Bethe and C. von Weisacker in 1938.

11H + 11H ⇒ 21H + 01β     (1)

21H + 11H ⇒ 32He     (2)

32He + 32He ⇒ 42He + 2 11H;     (3)

4 11H ⇒ 42He + 2 01β     (combination of above)

The energy released by these reactions further warms a star's core, creating sufficient pressure (due to electromagnetic repulsion) to stop the collapse which had previously been occurring due to the gravitational attraction.  As a result, main sequence stars maintain a relatively constant size for long periods of time (until they deplete their Hydrogen).

Synthesis of larger atoms requires significantly higher temperatures than occurs in main sequence stars.  This is because the nuclei of Helium atoms contain two positively charged protons and thus experience double the electrical repulsion of Hydrogen atoms.  So at the maximum temperature in main sequence stars, nearly all Helium atoms collide too slowly to get close enough to fuse.  Further hampering synthesis, 84Be has a half life of 7 x 10-17 second.  The small amounts of Beryllium and similar isotopes which might form immediately decay.  As a result main sequence stars make no elements larger than Helium.

(After Einstein suggested E=mc2, physicists realized that the stability of a particular isotope can be determined by calculating missing mass.  The nuclear bonding forces between the protons and neutrons may be thought of as the nucleons caught in an energy well of depth due to dissipation of the energy equivalent to the missing mass.  This missing mass is calculated by comparing the mass of an isotope to either the sum of the masses of the constituent protons, neutrons and electrons or other possible components such as alpha particles.  Thus a nucleus such as 84Be which has nearly identical missing mass as two alpha particles is very unstable, especially in the environment inside a star where collisions and radiation absorption can provide additional energy for somwhat endothermic decays. )

At distances away from a star's core, the pressure and temperature are less.  As a result only the Hydrogen near the core is hot enough to fuse, and then only to Helium.  The surrounding bulk of the star absorbs energy radiating from the core then a moment later readmits it.  The light travels a very short distance before it is again reabsorbed.  Thus the light eventually shining from the star's surface originated from fusion at the core at a considerable time earlier.


In 1905, out of a consideration of Maxwell's equations for electric and magnetism from various moving perspectives, Albert Einstein (1879-1955) connected mass with energy.  Based on his famous equation, E = mc2, Einstein wrote the mass of a body is a measure of its energy content.  This equation was valuable for calculating the energy involved in nuclear reactions such as those in stars.  By comparing the masses of the initial materials with those remaining at the end, it was possible to determine if a reaction is exothermic (emitting energy) and the amount.

atom     mass (u)
11H 1.007 825
21H 2.014 102
32He 3.016 030
42He 4.002 428
01β 0.000 539
The following procedure has been found to be immensely valuable for understanding what occurs both at the scale of cosmology and the scale of nuclei.  Learn it well!


  1. For each reaction in a main sequence star, add the masses of reactants

  2. For each reaction add the masses of products

  3. Subtract the sun of the masses of the reactants from the sum of the masses of the products

  4. Multiply the loss in mass by 931.5 MeV/u.  (If mass for Einstein's equation is measured in kilograms, the speed of light, c, is 3.0 x 108 m/sec providing energy in units of Joules.  However those units are inconvenient for single atoms.  Chemists prefer to measure mass in atomic mass units, Daltons, u and energy in electron volts, eV.  Using those units, c2 = 931.5 million electron volts per Dalton.)

Communicating technical information such as observations and findings is a skill used by scientists but useful for most others.  If you need course credit, use your observations in your journal to construct a formal report.



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created 17 January 2005
revised 11 March 2012
by D Trapp
Mac made