HW4-9 - 4-5 9. What is the net energy released (in MeV) for...

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Unformatted text preview: 4-5 9. What is the net energy released (in MeV) for each of the following fusion reactions? (a) ~H + ~H --+ ~He+ Anand (b) ~H+ iH --+ ~He+ An Solution: (a) The energy releasedis the Q-value of the reactions. Q = {2M(~H) -M(~He) -mn} C2 = {2 x 2.0141018-3.0160293 -1.0086649} (u) x 931.5 (MeV /u) = 3.27 MeV (b) Similarly Q = {M(~H) + M(~H) -M(~He) -mn} C2 x 931.5 = {2.0141018 + 3.0160493 -4.0026032 -1.0086649} = 17.59 MeV 10. Calculate the Q-values for the following two beta radioactive decays. (a) ~~Na --+ ~~Ne+ +~e+ v and (b) ~~Cl --+ ~~Ar+ _~e+ v. Solution: Becausein beta and positron decaythe number of protons in the parent and daughter are different from the number of electrons in neutral atoms of the parent and daughter are different. This change in electron number must be accounted for in the decayreactions. (a) This positron reaction, in terms of neutral atoms, is written as ~~Na~ ~~Ne+ _~e+ +~e+ v. The Q-value is then Q = {M(~~Na) -M(~~Ne) -2me} c2 = {21.994437-21.991386 -2 x O.OOO5486} x 931.5 (MeV lu) (u) = 1.820 MeV (b) This beta minus reaction, in terms of neutral atoms, is written as ~~CI+ _~e --t ~~Ar+ _~e+ v. The Q-value is then Q = {M(~~CI) -M(~~Ar)} C2 = {37.968011 37.962732} (u) x 931.5 (MeV lu) 4.917 MeV July 24, 2002 ...
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