05 nuclear binding energy

8/11/2019 05 Nuclear Binding Energy

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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 Total Energy

EBcXcZmNmZm Nenp .M2A

Z

2

2

2

22

atommass-tsconstituenmass

Z.

c

cXMNmZm

cXMcZmNmmEB

A

ZnH

N

A

Zenp


4/18

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.


5/18

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.

21

1

22

1

12

MM

MM

cXmXS

cmcXcXS

N

A

ZnN

A

Zn

nN

A

ZN

A

Zn

Note we dont have to measure Sndirectly.


6/18

SINGLE PROTON SEPARATION ENERGY

The same clever strategy applies to finding the Single Proton Separation

Energy Sp. But note here there is a differencewe must be careful in

counting electron mass.

22211

2MM cmcmcYcXS epN

A

ZN

A

Zp

21

1

21

1

MM

MM

cXmY

cXmmYS

N

A

ZHN

A

Z

N

A

ZepN

A

Zp

pS [Mass of Final ProductsMass of Initial atom] c

2


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8/18

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.

QMM22

2

4

2

2

cmcYcX NA

ZN

A

Z

He

MM

4

2

4

2

2

2

4

2

BYBXB

cmYXQ

N

A

ZN

A

Z

N

A

ZN

A

Z

Eq 8.2

Eq. 8.3

Eq. 8.4


9/18

U235

92


10/18


11/18

CALCULATION OF BINDING ENERGY

Total Energy Total Energy

EBcXcZmNmZm Nenp .M2A

Z

2

2

2

22


Z.

c

cXMNmZm

cXMcZmNmmEB

A

ZnH

N

A

Zenp


12/18

Mass Defect

Mass defect (M.D) is another way of saying nuclear

B.E. It is simply the nuclear B.E. expressed not asMeV but in mass units (MeV/c2)

M

MZ..

XNmZm

XZmNmmDM

AZnH

N

A

Zenp

2

2

22


M

MZ.

c

cXNmZm

cXcZmNmmEB

A

ZnH

N

A

Zenp

= Mass constituents of atom mass of atom


13/18

Mass Excess

Do not confuse Mass Excess with Mass Defect

(or Binding Energy). Mass Excess is just aCONVENIENT WAYto write down the mass of anucleus in amu (u). 1u = 931.5MeV

AuXNA

ZMThis 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.

2uM cAXAZ MeV

Can either be expressed in u or MeV


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15/18

Mass ExcessExample 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


16/18

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

146

238

92U


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

05 nuclear binding energy

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