Question

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?

Answer 1

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`