Most of the Sun’s energy comes from the proton-proton chain in which four hydrog

Question

Most of the Sun’s energy comes from the proton-proton chain in which four hydrogen nuclei (i.e., protons)
fuse into one helium nucleus.
(a) Calculate how much mass is “lost” in one proton-proton chain reaction.
(b) How much energy is produced in one proton-proton chain reaction? 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. If all of it comes from the proton-proton chains,
how many kilograms of mass is being converted into energy in the Sun in one second?

Explanation / Answer

The proton-proton chain include the fusion of 4 protons(11H) into Helium nucleus(42He) a) Mass of the proton is mp = 1.00727 u Mass of Helium nucleus mHe = 4.00260 u The 'lost' mass in each chain reaction will be m = 4*mp - mHe m = 4(1.00727 u)-(4.00260 u) m = 0.02648 u m = 4(1.00727 u)-(4.00260 u) m = 0.02648 u m = 4.395*10-29 kg b) The rest mass energy of the four protons before reaction is Ei = 4*mpc2 c is the speed of llight in vacuum Ei = 4*(1.00727 u)(931.46 MeV/c2)c2 Ei = 3.752927*103 MeV The rest mass energy of the Helium nucleus after reaction is Ef = mHec2 c is the speed of llight in vacuum Ef = (4.00260 u)(931.46 MeV/c2)c2 Ef = 3.728261*103 MeV Ei = 3.752927*103 MeV The rest mass energy of the Helium nucleus after reaction is Ef = mHec2 c is the speed of llight in vacuum Ef = (4.00260 u)(931.46 MeV/c2)c2 Ef = 3.728261*103 MeV The rest mass energy of the Helium nucleus after reaction is Ef = mHec2 c is the speed of llight in vacuum Ef = (4.00260 u)(931.46 MeV/c2)c2 Ef = 3.728261*103 MeV Ef = 3.728261*103 MeV The energy produced in the reaction is E = Ef - Ei E = 24.67 MeV c) The power output of the Sun is P = 3.85*1026 W The energy produced by the Sun in one second id E = 3.85*1026 J The mass being converted to energy is m = E/c2 m = 3.85*1026 J / (3*108 m/s)2 m = 4.28*109 kg m = 4.28*109 kg

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