Nuclear Physics• Nucleus:

–nucleons (neutrons and protons) bound together.–Strong Force binds nucleons together over short range (~10-15m)–Nuclide: term for a specific nucleus described by

• Z = number of protons. Determines the identity of the element. (Also called the “atomic number”)• A = mass number = number of nucleons = number of protons + number of neutrons• N = A-Z = number of neutrons.• Z also equals the number of electrons for a neutral atom.

–Isotopes: Nuclei of the same element having different numbers of neutrons.

Symbols For Nuclides and Particles• For Nuclides

• For Particles

These symbols are used in writing nuclear reactions in much the same way that chemical reactions are written.Subscripts are used to conserve charge.

Atomic Mass Units

• A unit of mass used for nuclear calculation:1u = (1/12) the mass of a C12 nucleus (definition)1u = 1.66×10-27 kg

• Mass of a proton: mp= 1.007276 u

• Mass of a neutron:mn= 1.008665 u

• Mass of the electronme= .0005486 u

Binding Energy and Nuclear Forces

• When nucleons come together to form a nucleus (mass of nucleus) < (mass of separated nucleons)

• The mass lost in creating the nucleus – is equivalent to energy lost in its formation– This is the binding energy of the nucleus – Add it to the nucleus and you’ll split it apart.

• If mass is not lost in creating the nucleus; it is not stable.• Mass Energy Equivalency

– ΔE = Δm c2

– For a mass loss of 1u, the resulting energy released is:– ΔE = Δm c2 = (1.66×10-27 kg)(2.99×108m)2

= 1.494×10-10J = 931 MeV

• So: 1u 931 MeV or 1u = 931 MeV/c2 (unit conversion)

Example 1: What is the Binding Energy for Iron?

• For Iron: A=56, Z=26:– What particles are in iron?

• 26 protons, 30 neutrons, 26 electrons

– Add up the masses of the separate constituents:• Protons: 26×1.007276 u• Electrons: 26×.0005486 u• Neutrons: 30×1.008665 u• MTotal = 56.4634 u

– Mass of the actual atom (most common isotope)• MAtom= 55.9349 u

– Mass Change: ΔM = MTotal - MAtom = .5285 u– Binding Energy: ΔE = Δm c2 = (.5285 u)(931.5 MeV/ u) = 492.3 MeV

Example: What is the Binding Energy for Iron?(cont’d)

• The “binding energy per nucleon” is a measure of the relative stability of a nucleus. For iron:– (ΔE/A) = (492.3 MeV/56 nucleons) = 8.8 MeV/nucleon

IRON is the peak of stability:Smaller nuclei may undergo fusion towards it. (e.g. in Stars)Larger nuclei may undergo fission towards it. (e.g. Radioactive Decay)

Binding Energy of Helium Nucleus

Nuclear Reactions

• Nuclei undergo nuclear reactions:– Radioactivity (Alpha, Beta, and Gamma Decay)

• Parent nucleus emits a particle or photon turning into a different “daughter” nucleus.

– Fission (ex: nuclear reactors, A-bombs)

• Parent nucleus is split into smaller daughter nuclei.

– Fusion (ex: Stars, H-bombs)

• Smaller nuclei are fused into larger nuclei.

– There are many other types of reactions

• Transmutation – the act of one element turning into another due to nuclear reaction.

Nuclear Reactions (cont’d)

• Nuclear Reactions– Conserve mass number (A)– Conserve charge– Conserve mass-energy (now interrelated)– Conserve momentum – Conserve angular momentum

• In a Reaction

(Reactants) (Products) + Q (Energy) Energy Released is the K.E. of the products. Energy released represents a mass loss: Δm=Q/c2

Conversion: 1μ = 931 MeV/c2

Example 2

We have to balance the reaction:

Some Problems (pg 194)

More Problems (pg 195)

Radioactivity

• Alpha Decay– Electric Repulsion overpowers the Strong Force in large

nuclei. Helium Nuclei (very stable) are then emitted:

Energy Released (“Disintegration Energy” or “Q-value”) isQ = (MP - MD – Mα)c2 > 0 (exothermic; reaction occurs.)

Radioactivity (cont’d)

• Beta Decay- The Weak Force (range ~ 10-18m):– Nucleus gives off a

high speed electron and a neutron becomes a proton. (β- decay)

– Nucleus gives off a high speed positron and a proton becomes a neutron.(β+ decay)

Radioactivity (cont’d)• Electron Capture (or “K-Capture”) - Nucleus of an

atom captures an electron from K-shell (innermost shell). Higher energy electrons jump down emitting x-rays.

• Gamma Decay – A nucleus in an excited state (X*) (due to its “spin angular momentum” drops to a lower energy state emitting γ-rays

Example 3

Hints: • Conserve Momentum for part (b)• The energy released in a reaction goes into the kinetic energy of the products (part c).

Example 4