The nuclear reaction that powers the sun is the fusion of...

The nuclear reaction that powers the sun is the fusion of four protons into a helium nucleus. The process involves several steps, but the net reaction is simply $4 p \rightarrow{ }^{4}$ He $+$ energy. The mass of a helium nucleus is known to be $6.64 \times 10^{-27} \mathrm{kg}$ a. How much energy is released in each fusion? b. What fraction of the initial rest mass energy is this energy?

Transcript

00:01 Hello students in this question we are given that the fusion reaction takes place like four protons reacts or fuse to form one helium atom plus some energy is given out so we have to find in the a part how much energy is released in each fusion so the a part for finding the amount of energy released we will firstly calculate the total initial mass so it is equals to mass of four protons so it will be equals to 4 .002603 multiplied with 1 .67 multiplied by 10 to minus 27 so it will come out equals to 6 .68 4 3 multiplied with 10 to the power minus 27 kg and the final mass of the helium atom is 6 .64 multiplied with 10 to the power minus 27 kg so the amount of energy released is equal to delta m multiplied by c square delta m is the mass defect so it will be 6 .68 4 3 minus 6 .64 whole multiplied with 10 to the power minus 27 multiplied with 3 multiplied with 10 to the power 8 whole square so the energy reduced approximately per fusion reaction is 4 multiplied with 10 to the power minus 12 joules now in the b part we have to calculate the fraction of the initial rest mass energy is this energy so we have to calculate what fraction of this energy is the total energy so we can calculate it by calculating the total initial mass if it is converted into energy so ei will be equals to total initial mass which is 6 .68 4 3 multiplied by 10 to titha minus 27 multiplied by c square which is 3 multiplied with 10 to the power 8 whole square so it is 6 .0157 multiplied with 10 to the power minus 10 joules so the fraction will be equals to the energy which we get which is 4 multiplied with 10 to the power minus 12 over 6 .0 1587 multiplied with 10 to the power minus 10 so this fraction comes out to be 0 .66%.

03:16 So now let us write our answer.

03:20 Our answer to the question is for the part a is 4 multiplied with 10 to the power minus 12 joules...

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