The Sun radiates isotropically with luminosity

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Astrophysics & Cosmology · Relativistic dynamics and fields in flat spacetime

Relativity and Gravitation, Ch Mass as energy: binding, defect and annihilation

Problem

L_\odot = 3.828 \times 10^{26}\ \mathrm{W}

. The net effect of the proton-proton chain in its core is that four hydrogen atoms are replaced by one helium-4 atom. Take the atomic masses

m(^1\mathrm{H}) = 1.007825\ \mathrm{u}

and

m(^4\mathrm{He}) = 4.002603\ \mathrm{u}

, and assume that all the energy released is eventually radiated away (the small fraction carried off by neutrinos is ignored). Use

1\ \mathrm{u} = 1.660539 \times 10^{-27}\ \mathrm{kg} = 931.494\ \mathrm{MeV}/c^2

and

c = 2.998 \times 10^8\ \mathrm{m\,s^{-1}}

. ((a)) Estimate the mass difference of the net reaction in

\mathrm{u}

and the energy it releases in MeV. ((b)) Estimate the rate at which the Sun's mass decreases, in

\mathrm{kg\,s^{-1}}

. ((c)) Estimate how many helium-4 nuclei the Sun must form each second.

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