The oxygen in the universe formed through nuclear fusion reactions in stars acco
ID: 2077681 • Letter: T
Question
The oxygen in the universe formed through nuclear fusion reactions in stars according to the process given below, (a) What is the Q for the reaction? (b) If a star consists of a mixture of equal numbers of helium and carbon atoms, and if the total mass of the star is 4.0 times 10^30 kg helium, how much mass energy would be produced if all the helium and carbon react to form oxygen? (d) If the total power output of the star is 1.0 times 10^30 W, how many years would the helium to carbon fusion process last?Explanation / Answer
2. (a) mass on the left side
m1 = 4.002603 + 12.000000 = 16.002603 u
mass on the right side = 15.994915 u
mass difference = m1 - m2 = 7.688 x 10^-3 u
Q = 7.688 x 10^-3 x 931.5 MeV = 7.16 MeV ........Ans
(B) moles of helium = (4 x 10^30 kg) / (4 x 10^-3 kg / mol)
= 1 x 10^33 mol
total number of atoms = 1 x 10^33 x 6.022 x 10^23
= 6.022 x 10^56 atoms
total energy produced = 6.022 x 10^56 x 7.16 MeV
= 4.311 x 10^57 MeV
energy (in Joule) = (4.311 x 10^57)(10^6 x 1.6 x 10^-19)
= 6.90 x 10^44 J
(d) time = total energy / power
= (6.90 x 10^44) / (1 x 10^30)
= 6.90 x 10^14 sec
time (In years) = 6.90 x 10^14 / (3600 x 24 x 365)
= 2.19 x 10^7 years
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