FNT13 - FNT #13: Nuclear physics Damien Martin December 2,...

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FNT #13: Nuclear physics Damien Martin December 2, 2006 1 The binding energy of Lithium: 6 3 Li What is the binding energy of 6 3 Li based on the masses given in DL# 13? Solution: Based oﬀ the table in activity 3.5.2, the mass of 6 3 Li is 6.015121 atomic mass units. Looking at the mass of the constituents of Lithium gives 3 m proton + 3 m neutron + 3 m elec = 3 × (1 . 00728 amu) + 3 × (1 . 00866 amu) + 3 × (0 . 00055 amu) = 6 . 04947 amu The sum of the masses of the parts of 6 3 Li is heavier than 6 3 Li itself. When 6 3 Li is formed, energy is released as Δ E mass decreases. The amount of mass change in forming a 6 3 Li nucleus is Δ m = m f - m i = 6 . 015121 amu - 6 . 04947 amu = - 0 . 034349 amu Converting this into kilograms gives Δ m = - (0 . 034349 amu) × 1 . 661 × 10 - 27 kg 1 amu = - 5 . 71 × 10 - 29 kg This gives a binding energy of E bind = | Δ m | c 2 = (5 . 71 × 10 - 29 kg)(3 × 10 8 m/s) 2 = 5 . 13 × 10 - 12 J Converting this into MeV (1 MeV = 1 . 602 × 10 - 13 J) gives E bind = 32 . 08 MeV. 1

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2 Fusion Consider the fusion of deuterium and tritium by the following reaction: 3 1 H + 2 1 H 4 2 He + 1 0 n + energy Binding energies (i.e. the energy for the inﬁnitely separated nucleons - the energy for the bound nucleus) are given by 3 1 H = 8.48 MeV, 2 1 H=2.22 MeV and 4 2 He=28.3 MeV. a) How much energy is released in this reaction? Instead of binding energy, consider bond energy instead. The bond energy of each of these nuclei is - E bind . Our initial and ﬁnal conditions are E bond, initial = ( - 8 . 48 MeV) + ( - 2 . 22 MeV) = - 10 . 7 MeV E bond, ﬁnal = - 28 . 3 MeV Δ E bond = - 17 . 6 MeV This process corresponds to the following energy-interaction diagram: ' \$ % E bond E bond,i = - 10 . 7 MeV E bond,f = - 28 . 3 MeV Δ E bond = Q - | Q | The heat is therefore Q = - 17 . 6 MeV, the negative sign telling us that it is leaving the system. Therefore the heat released is (+) 17.6 MeV in this
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This note was uploaded on 07/31/2008 for the course PHY 7A taught by Professor Pardini during the Winter '08 term at UC Davis.

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FNT13 - FNT #13: Nuclear physics Damien Martin December 2,...

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