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Relationship between Energy and Mass

Nuclear fusion involves the formation of larger nuclei from smaller nuclei. During fusion, mass is converted to energy according to Einstein’s equation:

ΔE=(Δm)c2

where ΔE is the energy produced in joules, Δmis the change in mass in kilograms, and c is the speed of light (3.00×108m/s). In the core of the Earth’s sun, fusion involves hydrogen atoms (11H) forming helium atoms (42He) accompanied by the release of tremendous amounts of energy. The mass of our sun is about 2×1030 kg. About80% of this mass is hydrogen, and about 25% of the hydrogen is located in the sun’s core, where it is available for fusion.

Spectroscopic studies have shown that the fusion reaction in the sun’s core proceeds by a complicated mechanism.  One proposed overall equation for the solar fusion reaction is

411H+2 0−1e→42He

which is also accompanied by the release of “massless” neutrinos and photons in addition to energy. Precise masses of the reactants and product are given below.

 

Species 11H   0−1e 42He
Mass (amu) 1.007825 0.000549 4.002603

The sun produces energy via nuclear fusion at the rate of 4×1026J/s . Based on the proposed overall fusion equation, how long will the sun shine in years before it exhausts its hydrogen fuel? (Assume that there are 365 days in the average year.)

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Posted on October 3, 2013, in Question and tagged , , , , . Bookmark the permalink. 1 Comment.

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