The Sun generates energy by fusing four hydrogen nuclei into one helium nucleus;
ID: 2268982 • Letter: T
Question
The Sun generates energy by fusing four hydrogen nuclei into one helium nucleus; during this process, a tiny fraction of mass is lost and converted to pure energy.
1. The Sun’s luminosity tells us how quickly the Sun radiates energy. If the Sun will eventually release the total amount of energy you calculated above, but it can only release energy as quickly as its present luminosity indicates, how long will it take for the Sun to release all of its energy? Convert your answer to years, and write it out in standard notation (not scientific).
2. Your previous answer is an estimate of the maximum lifetime of the Sun. Astronomers believe the Sun will only live 10 billion years before fusion ceases. Explain why this lifespan is shorter than the maximum estimate you just calculated.
Explanation / Answer
fusoin of hydrogen on sun is termed as proton proton chain reaction
total energy released sue to mass deficit per 2 Hydrogen atoms as reactants is 0.42 MeV
hence
0.42 MeV per 2*1.00794*1.66*10^-27 kg
mass of sun = M = 1.989*10^30 kg
hence
total energy which can be released by sun assuming it is 100% hydrogen right now
E = 0.42 MeV * 1.989*10^30 /2*1.00794*1.66*10^-27
E = 2.496*10^62 eV = 3.994*10^43 J
now,
1. current power radiated from sun = P
P = 3.828×10^26 W
hence time taken to release energy E at constant power = t
E/t = P
t = E/P = 104342049488694392.8 s = 1739034158144906.54 min = 28983902635748.44 hrs = 1207662609822.851 days = 3306400026.893 years = 33064. million years = 33.06 billion years
2. suns estimated life is about 10 billion years, less that this estimate, because as sun swells up, its rate of reaction will increase once the heaveier elements start fusing and there is more radiance of energy per unit time. hence the sun will live leser than what we calculates using constant power output from the sun
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