Nuclear Physics Nucleus: –nucleons (neutrons and protons) bound together. –Strong Force binds nucleons together over short range (~ m) –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× kg Mass of a proton:  m p = u Mass of a neutron:  m n = u Mass of the electron  m e = 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 c 2 –For a mass loss of 1u, the resulting energy released is: –ΔE = Δm c 2 = (1.66× kg)(2.99×10 8 m) 2 = 1.494× J = 931 MeV So: 1u  931 MeV or 1u = 931 MeV/c 2 (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× u Electrons: 26× u Neutrons: 30× u M Total = u –Mass of the actual atom (most common isotope) M Atom = u –Mass Change: ΔM = M Total - M Atom =.5285 u –Binding Energy: ΔE = Δm c 2 = (.5285 u)(931.5 MeV/ u) = 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/c 2  Conversion: 1μ = 931 MeV/c 2

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”) is Q = (M P - M D – M α )c 2 > 0 (exothermic; reaction occurs.)

Radioactivity (cont’d) Beta Decay- The Weak Force (range ~ m): –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