Nuclear notation and Binding energy Contents: Atomic notation Isotopes Whiteboard Binding Energy AMU Making an atom Calculating binding energy Whiteboards The curve of binding energy and the strong nuclear force (or why there is a limit to the periodic table)The curve of binding energy and the strong nuclear force (or why there is a limit to the periodic table)

Atomic notation X A Z X = Symbol (C, Au) A = Atomic Mass Number = #nucleons (Protons + Neutrons) Z = Atomic Number = #protons C 12 6 Carbon A = 12, Z = 6. #neutrons? TOC

Isotopes Carbon 12 has 6 Neutrons TOC C 12 6 C 14 6 Carbon 14 has 8 Neutrons Carbon 14 is an isotope of Carbon Chemically the same Nuclear-lly different (it’s unstable)

Whiteboards: Atomic Notation 11 | 2 | 3 | 4 | TOC

W Hydrogen has a Z = 1, A = 1 p + 2 n = 3 What is the Atomic notation for tritium? (tritium is an isotope of Hydrogen with 2 neutrons) 3/1 H

22/10 Ne Z = 10, A = = 22, element 10 is Ne 10 protons, 12 neutrons. What is its atomic notation? W

143 U is element = 143 neutrons How many neutrons in U 235? (235 = A) (1) W

126 Pb is element = 126 neutrons How many neutrons in Pb 208? (208 = A) (1) W

42 Kr is element = 42 neutrons How many neutrons in Kr 78? (1) W

Binding energy - the energy to take an atom apart TOC Unified Mass Units: (u) C 12 (neutral atom) = u (defined) 1 u = x kg = MeV Electron = u (not useful) Proton = u (not useful) H (neutral atom) = u (very useful) Neutron = u (very useful)

Binding energy - the energy to take an atom apart TOC To take an atom apart: C 12 can be taken apart into: 6 H atoms:6( u) (i.e. 6 p + 6 e) 6 Neutrons:6( u) Total “taken apart” mass = 6( u) + 6( u) Total “taken apart” mass = u Mass “defect” = u u = u u - Represents energy needed to take atom apart Binding energy = ( u)(931.5 MeV/u) = MeV H (neutral atom) = u (very useful) Neutron = u (very useful) 1 u = MeV

Binding energy - the energy to take an atom apart TOC Binding energy in general 1.Look neutral atom mass in Appendix F (p 1064) 2.Break atom into H and n 3.Subtract neutral atom mass from taken apart mass 4.Multiply mass defect by Mev/u H (neutral atom) = u (very useful) Neutron = u (very useful) 1 u = MeV

Whiteboards: Binding Energy 11 | 2 | 323 TOC

W Atom mass = H + 6n = 7( u) +6( u) = u Binding energy = ( )931.5 MeV/u = MeV What is the binding energy for Nitrogen 13? (Z = 7) N 13 mass = u H = u Neutron = u 1 u = MeV MeV

W What is the binding energy for Carbon 14? (Z = 6) C 14 mass = u H = u Neutron = u 1 u = MeV MeV Atom mass = H + 8n = 6( u) +8( u) = u Binding energy = ( )931.5 MeV/u = MeV Binding energy per nucleon: C 12: 92.16/12 = 7.68 MeV/nucleon C 14: 105.3/14 = 7.52 MeV/nucleon (less)

W What is the binding energy for Carbon 10? (Z = 6) C 10 mass = u H = u Neutron = u 1 u = MeV Atom mass = H + 4n = 6( u) +4( u) = u Binding energy = ( )931.5 MeV/u = MeV (Carbon 10 does not exist)

The curve of binding energy TOC Binding energy per nucleon Going to more tightly bound releases energy Fission - splitting nuclei Fusion - joining nuclei Most tightly boundFission releases energy Fusion releases energy

Nuclear Stability TOC p p p p n n n Coulombic force tries to tear apart nucleus Strong Nuclear force holds it together (force between nucleons) Strong Nuclear is very short range As nucleus gets bigger Strong nuclear gets weaker Coulombic gets stronger Neutrons add strong force, don’t repel Trend with heavier elements At some point neutrons don’t cut it The crazy man at UMn