PHYS219 Fall semester 2014 Lecture 27: Nuclear Structure Dimitrios Giannios Purdue University PHYS 219 Final Exam Thursday; December 18, PM-3 PM PHYS 112 Topics covered in Chapters24, 25, 28, 29, 30 Please, respond to the Course Evaluation Survey

Source: OSMIAC- Oxygen, Silicon, Magnesium, Iron, Aluminum, and Calcium Number of chemical elements: 118 elements have been identified. Most abundant on earth: 6 elements account for 99% of the earth’s mass: oxygen, silicon, magnesium, iron, aluminum, and calcium How do you measure the size of the nucleus????

Measuring the Size of the Nucleus Two Limiting Scenarios: Result A: Box is filled with soft, fluffy material Result B: Box is filled with hard, rigid material Scattering Experiments: The Basic Idea B A What’s inside the box? KEY QUESTION: We know the foil is made of (gold) atoms that are electrically neutral. But how are the + and - charges distributed?

Evidence for a Massive Nucleus: Rutherford’s Scattering Experiments - (Rutherford 1911) Conservation of energy and momentum imply the presence of small “heavy objects”. Rutherford concludes that the “heavy objects” are roughly ~10,000 times smaller than an atom!! A few of the particles are backscattered! 4,000 3,000 2,000 1, N u m b e r o f E v e n ts Typical Rutherford Scattering (172,000 events) x10 Scattering angle (+)

Rutherford Computer Simulation

Bohr’s orbits Atom (diameter  0.2 nm) Rutherford’s “heavy objects” Nucleus (diameter  3 fm) electrons protons Neutrons 1 fm = 1× m Composition and Approximate Dimensions of an Atom

Also written as: A = mass number = Z+N Z = number of protons = atomic number N= A-Z = number of neutrons Examples: ~ m X=Chemical Element Nucleons – the basic building blocks of the nucleus

Isotopes - same element but different mass More than 2000 isotopes have been identified! About 400 are considered stable; about 1600 of them undergo radioactive decay Hydrogen Stable Deuterium (1/6000) Stable Tritium (1 in ) decays-12.3 yrs U-235(0.72%) decays-700Myrs 92 U-238 (99.27%) decays-5Gyrs protonsneutronselectrons

Notes: 1 C = 1 Coulomb; m p + m e = x kg Diagram not to scale Electrically Neutral Atom Atom diam. ~ 0.2 nm (or 2 x m) e-e- e-e- e-e-e-e- e-e- Mostly empty space! The diameter of nucleus is ~10 4 smaller than the diameter of the atom neutronprotonelectron symbol charge mass n 0 (zero) x kg P x C x kg e x C x kg Atoms of different elements have different masses: the internal structure of an atom p pp pn n n p

Nuclear masses are very tiny (~ kg); invent a new unit of mass - the atomic mass unit (amu) or unified mass unit (u) Define new mass unit as 1 u = × kg Consider Carbon-12: m p = u; m n = u; m e = u With this definition, the mass of is exactly u Atomic and unified mass units

What are the approximate masses of the following nuclei? Helium: 2 protons, 2 neutron, 4 nucleons: M≈4u =4 (1.66x kg) = 6.64x kg Chlorine: 17 protons, 18 neutron, 35 nucleons: M≈35u =35 (1.66x kg) = 5.81x kg Barium: 56 protons, 83 neutron, 139 nucleons: M≈139u =139 (1.66x kg) = 2.31x kg These symbols do not represent atoms, they represent nuclei.

Coulomb Repulsive Force Separation ~ 2 x m

II. Large mass number: 2 He Electrostatic repulsion electrostatc repulsion attractive very short range (~2 fm) nuclear force As size of nucleus increases, more neutrons are required to hold it together p n n p neutron proton n p 4 (A-Z)=Z (A-Z)>Z schematic nucleus I. Small mass number: nnnn p p Nuclear Binding – The strong force

Many experiments indicate the nucleus is roughly spherical with a radius given by What is the nuclear mass density of the most common isotope of iron? Nuclear density is constant, independent of A! Nuclear size; Nuclear density

Typical Densities MaterialDensity Helium0.18 kg/m 3 Air (dry)1.2 kg/m 3 Styrofoam~100 kg/m 3 Water1000 kg/m 3 Iron7870 kg/m 3 Lead11,340 kg/m 3 Nuclear Matter~10 17 kg/m 3 Neutron Star (a huge nucleus!) ~10 17 kg/m 3

Neutron Stars: more massive than the Sun but fit into the Grand Canyon