Transparency Temperature

At temperatures higher than about 3000 K where the average kinetic energy of particles is about 0.26 electron volts, the formation of stable atoms is hindered. Above that temperature, matter exists in a plasma state of ionized atoms, which strongly absorbs electromagnetic radiation of all wavelengths, i.e., the plasma is opaque.

When the plasma cools below about 3000K, it is cool enough for hydrogen and helium nuclei to collect electrons and become stable atoms. The electrons in stable atoms exist in specific quantum energy states that are characteristic of those atoms. They will absorb only radiation of the specific frequencies (specific photon energies) that will cause an electron to jump to a higher quantum state in that atom, unless the photon energy of the incoming radiation is high enough to take the electron all the way out of the atom (ionize the atom). This means that the cooling gas cloud of the expanding universe has a point at which it forms stable atoms and becomes transparent to almost all wavelengths, at least for photons with quantum energy less than the ionization energy of the atoms.

Hydrogen


Helium

At this stage of the universe, almost all the ordinary matter was hydrogen and helium (>99%).

To illustrate the idea of transparency, consider a range of the hydrogen emission spectrum and the helium emission spectrum in the visible wavelengths. The three frequencies of light emitted represent transitions between the quantum levels of the hydrogen atom. The emitted wavelengths from hot hydrogen gas are also the frequencies that could be absorbed by cool hydrogen, so if you illuminated the hydrogen gas with all of the wavelengths in this range, it would be transparent to most of them - only those three narrow energy bands would be absorbed. So the stable hydrogen gas is transparent to most wavelengths. The helium would have more absorbable frequencies, but for both hydrogen and helium, most wavelengths would pass through without absorption.

This transparency point is a crucial concept in the modeling of the expanding universe and in the modeling of star formation. Key information about it is provided by the 3 K background radiation.

Neutrino transparency
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Radiation Pressure

Stars can maintain fairly stable sizes because of the radiation pressure exerted by the radiation coming from the hot core. This radiation pressure comes into play in a major way at point during the stellar evolution where the collapsing gas cloud becomes opaque to electromagnetic radiation. Striking this opaque ionized region, the radiation is said to "scatter" off the ions, exerting a net outward pressure which halts the gravitational collapse.

There is a strong connection between the transparency point and radiation pressure. Trefil makes the analogy to the air in a tire - the pressure exists because the molecules bounce back from the tire "the tire remains inflated because the rubber walls are very efficient at scattering air molecules." Before the transparency point of the "big bang", the ions and electrons of the plasma were efficient scatterers of light, but after they condense into atoms, they are very inefficient scatterers of light - you can easily see 100 miles through air on a clear day.

Arthur Eddington is credited with calculating a radiation pressure of some 25 million atmosperes for a model star and with calculating that for a star of more than about a hundred solar masses the radiation pressure alone would tear it apart.

Calculation of Radiation Pressure
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