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Binding energy

Binding energy. Working out the mass defect and binding energy of He-4. Helium-4 data. The mass of a He-4 atom is 4.002603 u 1 u = 1 atomic mass unit = 1.66054.10 -27 kg A Helium atom includes 2 electrons each 0.000549 u We need the mass of the nucleus

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Binding energy

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  1. Binding energy Working out the mass defect andbinding energy of He-4

  2. Helium-4 data • The mass of a He-4 atom is 4.002603 u • 1 u = 1 atomicmass unit = 1.66054.10-27 kg • A Helium atomincludes 2 electronseach 0.000549 u • We need the mass of the nucleus • Thismass is equalto:4.002603 - (2 x 0.000549) = 4.001505 u • .

  3. The components • The mass of a proton is 1.007276 u • The mass of a neutron is 1.008665 u • Added these 4 particles have a mass of 2 x 1.007276 + 2 x 1.008665 = 4.031882 • .

  4. Time for a comparison • A He-4 nucleus has mass 4.001505 u • 2 protonsand 2 neutrons have mass 4.031882 u • This is weird! • Together, in a nucleus, the mass is smaller. • Sowhenyoucreate a He-4 nucleus from 2 protonsand 2 neutrons somemassdisappears. • This ‘missing mass’ is called the mass-defect • Dm = 4.031882 - 4.001505= 0.030377 u • .

  5. Massand energy are ‘the same’ • The mass–energy equivalence arose originally from special relativity, as developed by Albert Einstein, who proposed this equivalence in 1905 in one of his papers entitled "Does the inertia of an object depend upon its energy content?" • The equivalence of energy E and mass m is described by the famous equation: • DE = Dm.c2 • .

  6. Difficultcalculationthere is a shortcut • The mass defect of He-4 is 0.030377 u • Change thisto kg: 0.030377 x 1.66054.10-27 = 5.044222.10-29 kg • Use E = m.c2tofind the energy equivalent DE = 5.044222.10-29 x (2.997928.108)2 =DE = 4.533531.10-12 J • 1 MeV = 1.602177.10-13 J • DE = 4,533531.10-12 / 1.602177.10-13 = DE = 28.3 MeV • .

  7. Binding energy • The binding energy of He-4 is 28.3 MeV • This energy is neededto separate the 4 particles in the nucleus • This is the energy that is releasedwhen a He-4 nucleus is created • High binding energy= stable nucleus • Massdisappears, energy appears • The binding energy per nucleon of He-4 is28.3 / 4 = 7.1 MeV per nucleon • .

  8. Summary • Step 1 – Find the mass of the nucleus • Step 2 – Find out howmanyprotonsand neutrons youneedtobuild the nucleus andcalculatetheirtotalmass • Step 3 – Calculate the mass-defect • Step 4 – Calculate the binding energy (per nucleon) using 1 u=931.5 MeV • .

  9. Questions?

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