Binding energy in atoms and nuclei

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Binding energy in atoms and nuclei

• Sec. 4.1 Dunlap

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CONCEPT OF BINDING ENERGY
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.
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CALCULATION OF BINDING ENERGY
Total Energy
Total Energy
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ANOTHER WAY OF VIEWING BINDING ENERGY

Constituents at infinity
ATOM
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 dont have to measure Sn directly.
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SINGLE PROTON SEPARATION ENERGY
The same clever strategy applies to finding the
Single Proton Separation Energy Sp. But note
here there is a difference we must be careful
in counting electron mass.
Mass of Final Products Mass of Initial atom c2
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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
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/c2)

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 238U
?(238U) .0507826 u M(238U)238 .0507826 u
238.0507826 u 238.0507826 x
931.494 MeV/c2 221,742 . 875 MeV/c2
Armed with this information we can work out the
B.E. of 238U
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Mass Deficit Binding Energy of
92 proton mass 86,319 . 736 MeV /c2
146 neutron mass 137,174 . 446 MeV /c2
92 electron mass 47 . 012 MeV /c2 Mass
constituents 223,541 . 194 MeV /c2
M(238U) observed 221,742 . 875 MeV/c2 Mass
Defect 1,798 . 319
MeV/c2 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