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27 Nov 2019

Most of the Sun’s energy comes from the proton-proton chain inwhich four hydrogen nuclei (i.e., protons)
fuse into one helium nucleus.
(a) Calculate how much mass is “lost” in one proton-proton chainreaction.
(b) How much energy is produced in one proton-proton chainreaction? In other words, find a change in
the rest mass energy before and after the reaction.
(c) The total power output of the Sun is 3.85×1026W. Ifall of it comes from the proton-proton chains,
how many kilograms of mass is being converted into energy in theSun in one second?

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Patrina Schowalter
Patrina SchowalterLv2
2 Jun 2019

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

The sun, like all stars, releases energy through nuclear fusion. Inthis problem, you will find the total number of fusion reactionevents that occur inside the sun every second. You will beconsidering the proton-proton chain, in which four hydrogen nucleiare converted into a helium nucleus and two positrons. The netreaction for the proton-proton chain is
4H--->He +2 beta plus

To find the energy released by this reaction, you will need thefollowing mass data:

mass of

and
mass of .

Using the masses of the neutral atoms in your calculation accountsfor the energy released by the annihilation of the positrons withelectrons, so you can work this problem without reference to thepositrons or their rest mass.

What is the total energy released in a single fusion reaction eventfor the equation given in the problem introduction? Use .

The Sun is powered by nuclear fusion. In each chain reaction, four hydrogen nuclei fuse together to become a single helium nucleus. The total combined mass of the individual hydrogen nuclei before the reaction is greater than the mass of the helium nucleus. The mass lost as a result of this chain reaction is turned into energy according to Einstein’s famous equation, E = mc2 (Chapter 39). Consider the first part of the chain reaction in which two hydrogen nuclei (each a single proton) fuse. Figure P8.56A shows the potential energy curve of a two-proton system. The energy in this graph is given in keV, where “eV” is the abbreviation for the unit electron-volt and 1 eV = 1.6 × 10−19 J. When the protons are more than about 2 fm (2 × 10−15 m) apart, the potential energy is positive. When the protons are close together, the potential energy is negative, and the protons are fused. Figure P8.56B shows a close-up of the potential energy curve when the protons are far apart.

  1. a. What is the minimum mechanical energy required for the two protons to fuse? Give your answer in keV.
  2. b. The mechanical energy of an average two-proton system in the Sun is around 2 keV. What is the minimum distance between the protons in such a system?
  3. c. Explain why it seems impossible for fusion to take place in the Sun. Note: Of course, fusion must take place in the Sun. Although it seems impossible according to classical mechanics, quantum mechanics (Part VI) makes fusion possible. According to quantum mechanics, the seemingly impossible is merely improbable, and even events with a low probability of occurrence may still happen. Because there are so many protons in the Sun, there is a good chance that at any moment many of them will fuse.

Chapter 8, Problem 56PQ, The Sun is powered by nuclear fusion. In each chain reaction, four hydrogen nuclei fuse together to

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