A star initially has $$3$$×$$1020$$ deuterons. It produces energy via the process $$1H2+1H2$$→$$1H3+p$$ and $$1H2+1H3$$→$$2He4+n$$ . Find the total energy released during the deuteron supply of star is exhausted (mass$$ of $$2He4=4.001amu$$, $$1H1=1.007amu$$, $$1H2=2.014amu$$, $$0n1=1.008amu$$ $$)

Question

A star initially has $$3$$×$$1020$$  deuterons. It produces energy via the process   $$1H2+1H2$$→$$1H3+p$$ and  $$1H2+1H3$$→$$2He4+n$$ . Find the total energy released during the deuteron supply of star is exhausted (mass$$ of  $$2He4=4.001amu$$, $$1H1=1.007amu$$, $$1H2=2.014amu$$, $$0n1=1.008amu$$ $$)

Infinity Learn · Accepted Answer

$$1H2+1H2$$→$$1H3+pplus$$ $$1H2+1H3$$→$$2He4+ngives31H2$$→$$2He4+n+pMass$$ defect $$=$$Δ$$M=mass$$  of   $$2He4+n+P$$−mass $$31H2$$ ⇒Δ$$M=4.001+1.008+1.007$$−$$32.014$$⇒Δ$$M=$$−$$0.026$$ amu∴Energy released $$=$$Δ$$E=$$Δ$$M931MeV=0.026$$×$$931$$×$$106$$×$$1.6$$×$$10$$−$$19J$$ $$=3.87$$×$$10$$−$$12J$$ No. of reactions $$=N3=3$$×$$10203=1020$$∴Total energy released $$=E=N3$$Δ$$E=3.87$$×$$10$$−$$12$$×$$1020=3.87$$×$$108J$$

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A star initially has 3×1020 deuterons. It produces energy via the process 1H2+1H2→1H3+p and 1H2+1H3→2He4+n . Find the total energy released during the deuteron supply of star is exhausted (mass of 2He4=4.001amu, 1H1=1.007amu, 1H2=2.014amu, 0n1=1.008amu )

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