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Binding energy in atoms and nuclei [Sec. 4.1 Dunlap]

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The binding energy of an atom is the energy released as all the constituent particles (n, p and e) come together FROM INFINITY under both the STRONG force and the EM force. The binding energy is something that is LOST from the atomic system. Thus it is not something that the system possesses. CONCEPT OF BINDING ENERGY

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CALCULATION OF BINDING ENERGY Total Energy

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ANOTHER WAY OF VIEWING BINDING ENERGY + ATOM Constituents at infinity The opposite way of seeing binding energy - is that if B.E. (MeV) is put into the atom then there is just enough energy available to split all the constituents of the atoms apart and get them to rest at infinity.

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SINGLE NEUTRON SEPARATION ENERGY The same method can be used to easily compute the “Single Neutron Separation Energy” – which is the energy required to “pull” a neutron out of the nucleus. Note we don’t have to measure S n directly.

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SINGLE PROTON SEPARATION ENERGY The same clever strategy applies to finding the “Single Proton Separation Energy” S p. But note here there is a difference – we must be careful in counting electron mass. [Mass of Final Products – Mass of Initial atom] c 2

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ALPHA PARTICLE DECAY ENERGY In a nuclear decay energy is given out in the separation of particles. This energy is often referred to as the “Q” of the reaction. Clearly the Q is the negative of the particle separation energy. Eq 8.2 Eq. 8.3 Eq. 8.4

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CALCULATION OF BINDING ENERGY Total Energy

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Mass Defect Mass defect (M.D) is another way of saying nuclear B.E. It is simply the nuclear B.E. expressed not as MeV but in mass units (MeV/c 2 ) = Mass constituents of atom – mass of atom

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Mass Excess Do not confuse Mass Excess with Mass Defect (or Binding Energy). Mass Excess is just a CONVENIENT WAY to write down the mass of a nucleus in amu (u). 1u = 931.5MeV This is just a common sense thing. The mass of a nucleus can get very large if expressed in MeV and will always be approximately equal to Au because it is made up of A nucleons. It is thus convenient to tabulate rather than the whole nuclear mass. MeV Can either be expressed in u or MeV

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Mass Excess – Example on 238 U ( 238 U)=.0507826 u M( 238 U)=238+.0507826 u =238.0507826 u = 238.0507826 x 931.494 MeV/c 2 = 221,742. 875 MeV/c 2 Armed with this information we can work out the B.E. of 238 U

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Mass Deficit + Binding Energy of 92 proton mass = 86,319. 736 MeV /c 2 146 neutron mass = 137,174. 446 MeV /c 2 92 electron mass= 47. 012 MeV /c 2 Mass constituents = 223,541. 194 MeV /c 2 M( 238 U) observed = 221,742. 875 MeV/c 2 Mass Defect = 1,798. 319 MeV/c 2 Binding Energy = 1,798. 319 MeV Electronic B.E =. 795 MeV Nuclear B.E. = 1,797. 52 MeV B.E/nucleon = 1,797.52/238= 7.55MeV

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How much is electronic binding energy? There are two types of binding energy in the atom – Strong Nuclear B.E. and the Electromagnetic B.E. of the electrons to the nucleus.

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THE FAMOUS B/A (binding energy per nucleon) CURVE

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