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A star converts all its hydrogen to helium, achieving 100% helium composition. It then converts the helium to carbon via the reaction `._2He^4 + ._2He^4+ ._2He^4 to._6C^(12)+7.27MeV` The mass of the star is `5.0xx10^(32)kg` and it generates energy at the rate of `5xx10^(30)kg` watt. How long will it take to convert all the helium to carbon at this rate? |
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Answer» Mass of star `=5.0xx10^(32)kg=5.0xx10^(35)g` Number of atoms in 4grams of He `=6.023xx10^(23)` `:.` Number of atoms in `5.0xx10^(35)` gram of He `=(6.023xx10^(23)xx5.0xx10^(35))/4=7.529xx10^(58)` As each fusion reaction consumed 3 helium atoms to produce 7.27MeV energy. `:.` Total energy produced by fusion of `5.0xx10^(35)` gram of He `7.27/3xx7.529xx10^(58)MeV` `=(7.27xx7.529xx10^(58)xx1.6xx10^(-13))/3J` `=29.191473xx10^(45)J` As power `=5xx10^(30)"watt" =5xx10^(30)"joule"//sec`. `:.` Time required `= (29.191473xx10^(45))/(5xx10^(30))sec`. `=(29.191473xx10^(15))/(5xx60xx60xx24xx365) years` `t=1.85xx10^8 years` |
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