ie-Chemistry

Cosmology Experiment C-2

Synthesis of Elements in Main Sequence Stars

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As noted in the previous section, Edwin Hubble (1889-1953) discovered in 1929 that the universe is currently expanding.  This led George Gamow (1904-1968) about mid-century to realize that the universe was probably once very small and very hot.  As the early universe expanded it cooled allowing nuclear force to form the simplest elements.  But as the universe continued to expand, the average speeds of the particles governed by the cooling temperature soon slowed until the weaker repulsive electric force was able to prevent 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 began to detect tiny acoustic oscillations in the cosmic microwave background radiation.  In 2005 several teams of astronomers analyzing surveys of thousands of distant galaxies reported finding extremely weak acoustic patterns, pressure waves between gravity attraction and radiation repulsion.  The small size of the bell-like ringing observed in both the microwave background and the distribution of galaxies gave further evidence that most of the mass of the universe is invisible dark matter which doesn't interact by electromagnetic forces.  The wave length of the oscillations provides additional 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 Hydrogen and Helium was compressed by gravity, it warmed as described by Clarles' Law.  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).  At these conditions additional 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 to stop the collapse that had previously occurred due to gravitational attraction.  As a result, main sequence stars maintain a relatively constant size for long periods of time.

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, Helium atoms collide too slowly to get close enough to fuse.  To further hamper synthesis, 84Be has a half life of 7 x 10-17 second.  Any Beryllium which might form immediately decays.  As a result main sequence stars make no elements larger than Helium.

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.

Investigation

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!

Procedure

  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.

References

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created 1/17/2005
revised 1/28/2005
by D Trapp
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