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Problem 14 Easy Difficulty

The proton-proton cycle responsible for the Sun's $3.84 \times 10^{26} \mathrm{W}$ power output yields about 26.7 $\mathrm{MeV}$ of energy for every four protons that are fused into a helium nucleus. Determine (a) the energy in joules released during each proton-proton cycle fusion reaction, (b) the number of proton-proton cycles occurring per second in the sun, and (c) the change in the Sun's mass each second due to this energy release.

Answer

$4.27\times 10^9 \mathrm{kg}$

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Top Physics 103 Educators
Elyse G.

Cornell University

Marshall S.

University of Washington

Farnaz M.

Other Schools

Meghan M.

McMaster University

Video Transcript

So this question we're looking at a put on proton cycle their suffering the sun argument that each off this fusion reaction energy releases 26.7 MTV and the first part requires us to accommodation to juice. So the commission factor is 1.6 time sent poll minus 13 juice for MTV. So this will keep us in tops off juice. Putting into co creator. We should get 4.27 times 10 to post minus chose jobs. Now, to find out how many erections are taking place, you'll need to look at the total power that is actually producing this. Son, you're assuming that all of this power is produced by this particular reaction. So each of the reaction will give us this mount of energy and the total amount of energy released by Sun E Toto put a second is close to the power right, which is 3.4 times 10 politan six juice. Right. So this is the moment energy the sun produces per second. So the number off reactions in each second equals 2.4 times 10 poll 26 divided by the energy released. Poor reaction. We should get 8.99 times 10 depart the seven. So this is normal reactions for a second to find out what is the mess that the sun lose us. As a result, this process we use Einstein's equation which release e the energy to mess by equals two empty square. So these energy must come from the mass of the sun. So we know that the mess that is being converted because to be over c squared, there will be 3.4. I understand part six juice divided by the speed off like squid. And now and so be in terms off kg Yes, I units, which is 4.27 time stand up all night programs.

National University of Singapore
Top Physics 103 Educators
Elyse G.

Cornell University

Marshall S.

University of Washington

Farnaz M.

Other Schools

Meghan M.

McMaster University