A Look at Nuclear Science and Technology

Larry Foulke

2.2 Atomic and Nuclear Physics The Einstein Connection Binding Energy and Nuclear Glue

The Nucleus

Protons each carry a positive charge, so how is it possible to hold so many protons together in such a small volume?

Answer:

The (Strong) Nuclear Force Image Source: See Note 1

Neutrons

Prot

ons

(Strong) Nuclear Force (Strong) Nuclear

Force Force between nucleons

(protons and neutrons).

Extremely attractive force at ranges up to 210-15 m ( 2 nucleon diameters).

Force drops to zero beyond 210-15 m.

Force acts equally on protons and neutrons.

3

p p Coulomb Forces

repulsive

p n no effect p e

attractive

p p Nuclear Force

attractive

p n

no effect p e

Nuclear Stability Nuclear Stability

The attractive nuclear force and repulsive coulomb force exactly balance in a stable nucleus.

Any change in the nuclear composition will change the balance of forces.

Lots of potential energy in the nucleus.

4

p

n

p

p

n

n n

Nuclear Force (Attractive) Coulomb Force (Repulsive)

Lithium-7 Nucleus

Nuclear Binding Energy

When bound, each nucleon turns a small fraction of its mass into energy, which is typically radiated from the nucleus.

This binding energy must be added to the nucleus to remove (unbind) a nucleon.

5

E=mc2

Due to the structure of the nucleus and the balance of forces, nucleons bound in a nucleus are more stable (have a lower energy) than free nucleons.

Image Source: See Note 2

Nuclear Binding Energy

Constituents may be individual nucleons or two (or more) nuclei. Example: 6Li + 6Li = 12C

Mass Energy Equivalence:

Binding Energy:

6

Mass Defect = Massconstituents - Massbound nucleus

E=m c2

Binding Energy = [ Massconstituents - Massbound nucleus ] c2

u = abbreviation for amu

Nuclear Binding Energy The binding

energy can be seen as a mass defect between the weight of the nucleus and the individual (unbound) weights of its constituent nucleons.

E=mc2 Lots of energy for a very small mass defect

Energy Released from mass defect worth 28.3 MeV (0.030407amy)(931.5MeV/amu)=28.3 Mev

Montessori Muddle by Montessori Muddle is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License.

p p

n n

2 protons = 2 x 1.007276 u = 2.014552 u

2 neutrons = 2 x 1.008665 u = 2.017330 u

Total mass of individual particles = 4.031882 u

n n p p

Total mass of bound nucleus = 4.001475 u

Mass loss = 0.030407 u

Conversion Factors Mass

1 amu = 1 u = 1.661 10-27 kg

Energy

1 eV = 1.602 10-19 Joule

1 Joule = 1 kg m2 / s2

Velocity (Speed of Light)

c = 2.998 108 m / s Mass to Energy Conversion (E=mc2)

1 amu = 931.50 MeV

8

Binding Energy Tips Nuclei are more stable than free nucleons. The binding energy provides a measure of how tightly

bound a nucleus is. Nuclei with larger binding energies require more

energy to break apart.

Binding Energy Per Nucleon Gives a measure of the forces acting on each

nucleon in the nucleus.

Amount of energy (average) required to rip a single nucleon out of the nucleus.

9

Binding Energy Per Nucleon

10 Image Source: See Note 3

Binding Energy Per Nucleon

11

Most Tightly Bound (Nickel-62)

Dec

reas

ing

N

ucle

ar S

treng

th

Dec

reas

ing

N

ucle

ar S

treng

th

Image Source: See Note 3

Binding Energy Example

12

236 118 2 8.5 118

= 2006 MeV 7.5 236 = 1770 MeV

Change in binding energy per nucleon

Tighter bound nuclei = Lower energy state BE118 > BE235

Reaction: 2118 236, Add 236 MeV (endothermic) Reaction: 236 2118, Remove 236 MeV (exothermic)

Image Source: See Note 3

Binding Energy Example

13

4 (Helium)

2 (Deuterium)

3 3 = 9 MeV

4 7 = 28 MeV

Cha

nge

in

bind

ing

ener

gy

per n

ucle

on BE4 > BE2 + BE3

Reaction: 2 + 3 4 (9+2)-(28)=-17 Remove 17 MeV (exothermic) Reaction: 4 2 + 3 (28)-(9+2)=17 Add 17 MeV (endothermic)

3 (Tritium)

2 1 = 2 MeV

D-T Fusion

Image Source: See Note 3

1. Creative Commons: http://en.wikipedia.org/wiki/File:Helium_atom_QM.svg

2. Public domain: http://en.wikipedia.org/wiki/File:Einstein-formal_portrait-35.jpg

3. Background graph in public domain. Source: https://commons.wikimedia.org/wiki/File:Binding_energy_curve_-_common_isotopes.svg; Overlay reprinted with permission from the American Nuclear Society. Nuclear Engineering Theory and Technology of Commercial Nuclear Power by Ronald Allen Knief, 2nd Edition. Copyright 2008 by the American Nuclear Society, La Grange Park, Illinois. Figure 2-1.

Image Source Notes

Slide Number 1The Nucleus(Strong) Nuclear ForceNuclear StabilityNuclear Binding EnergyNuclear Binding EnergyNuclear Binding EnergyConversion FactorsBinding Energy TipsBinding Energy Per NucleonBinding Energy Per NucleonBinding Energy ExampleBinding Energy ExampleSlide Number 14Slide Number 15Slide Number 16Binding Energy - ExampleBinding Energy ExampleSlide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24Slide Number 25Nuclear Binding EnergyNuclear Binding Energy