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Explore how the Sun's energy is derived from nuclear reactions, enabling it to emit light for billions of years. Understand the difference between fusion and fission reactions and how mass is converted into energy as per Einstein's famous equation. Learn about the Sun's internal structure and apply the age concept to other stars. Validate the accuracy of solar models through solar oscillation and neutrino measurements.
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ASTR 1102-0022008 Fall Semester Joel E. Tohline, Alumni Professor Office: 247 Nicholson Hall [Slides from Lecture09]
A Problem with Time Scales! • Kelvin-Helmholtz contraction explains how the Sun’s interior could stay hot (even as it radiates copious amounts of heat from its surface) for hundreds of thousands of years. • But geological and fossil records show that the Earth is far older than this (the Earth-Moon system is about 4.6 billion years old!).
A Problem with Time Scales! • Perhaps the Sun’s interior remains hot because the Sun is burning fuel in a manner similar to the way we humans burn fuel (for example, wood or coal) to generate heat/energy. • This type of “burning” involves building or breaking chemical bonds. • This won’t work because, in practice, relatively little energy is released through chemical burning processes. • To generate the Sun’s luminosity via chemical burning, the entire Sun would be consumed in about 10,000 years!
Is there a Solution? • Is there some other source of energy that can be called upon to explain how the Sun’s structure can remain virtually unchanged for billions of years? • The answer is…the Sun “burns” its fuel (hydrogen) via nuclear reactions, rather than via chemical reactions. • Energy is released when the nuclei of hydrogen atoms are fused together to produce helium.
Nuclear Reactions • Two basic types of nuclear reactions: • Fusion = the nuclei of two or more elements “fuse” together to create the nucleus of a heavier element • Fission = the nucleus of one element breaks apart to form nuclei of two or more lighter elements • Some reactions generate heat/energy (exothermic); other reactions absorb heat/energy (endothermic) • Rule of thumb: The dividing line falls within the Fe-Ni (iron-nickel) group of elements • Energy/heat generated via fusion when elements lighter than the Fe-Ni group are involved in the reaction • Energy/heat generated via fission when elements heavier than the Fe-Ni group are involved in the reaction
Chemical Elements & Their Isotopes Courtesy of:http://atom.kaeri.re.kr/
Chemical Elements & Their Isotopes Hydrogen
Chart of Nuclides 14 C 6 + 8 = 14
How is Energy Generated?(and how much energy?) • Mass is converted into energy! • The total mass of the nuclei (or nucleus) produced by a reaction, Moutput, is less than the total mass of the nuclei (or nucleus) that start(s) the reaction, Minput. • E = (DM)c2 • Here, the quantity, DM = (Minput – Moutput) • Example: When 4 hydrogen nuclei fuse to form 1 helium nucleus, 0.7% of Minput is converted into energy/heat
Is there a Solution? • Via nuclear fusion reactions (so-called, nuclear burning), the Sun can “live” for approximately 10 billion years and only use up approximately 10% of its total fuel supply! • We can express this mathematically: • tage = fMc2/L • For M = Msun, L = Lsun, and f = 0.7% x 10%, tage = 10 billion years
Sun’s Internal Structure Figure 16-4
Apply the “Age” Concept to Other Stars • How long can other stars live? • tage = fMc2/L • (tage /1010 years) = (M/Msun)/(L/Lsun)
Checking Accuracy of Solar Model • Solar Oscillation measurements • Solar Neutrino measurements
