The Atomic Nucleus Bloomfield Sections 14.1, 14., and 14. (download) 4/1/04 ISP 09-1A 1 What is matter made of? Physics is a reductionist science. Beneath the surface, nature is simple! All matter is composed of elements. There are 91 stable elements, and about 0 more unstable elements which decay by radioactive processes. 4/1/04 ISP 09-1A 1
4/1/04 ISP 09-1A The Atom How big is an atom? How can we measure the size of an atom? What fundamental factors determine the size of an atom? 4/1/04 ISP 09-1A 4
Jean Baptiste Perrin and Avogadro s number N Perrin used Brownian motion to measure Avogadro s number, in 1909. The theory had been worked out in 1905 by Einstein. Brownian motion is the random jittery motion of a small particle suspended in a fluid, due to collisions with the molecules of the fluid. The properties of the motion depend on temperature, molecular weight, and number density. From the observations Perrin could deduce the value of N. He got the Nobel prize in 196. Today N is determined by X-ray scattering. N = 6.0 x 10 atoms 4/1/04 ISP 09-1A 5 How big is an atom? The mass density of solid carbon (diamond) is.5 g/cm. Calculate the number density The volume occupied by a single carbon atom in diamond is V = 1/n ; the atomic radius R is related to V by V = 4/ π R. ρ. 5 g/cm n = = atomic mass 1 g/mol mol 6. 0 10 atoms = 0. 9 cm 1mol = 177. 10 atoms/cm atomic radius V = 4π = 1. 10 10 8 cm 1/ 4/1/04 ISP 09-1A 6
Result: The typical order of magnitude of an atomic radius is 10 10 m = 0.1 nm. What determines this size? It comes from the quantum dynamics of electrons interacting with the Coulomb force of attraction to the nucleus. Simplest example is a hydrogen atom. potential energy kinetic energy p K = = m e V( r) = 4πε r 0 4/1/04 ISP 09-1A 7 1 h m πr Heisenberg Uncertainty Principle kinetic energy K(r) 1/r E(r) V(r) 1/r potential energy The state of lowest energy has radius = Bohr radius h = me 4πε ( π ) = 0. 5 10 0 10 m Full quantum theory the Schroedinger equation. 4/1/04 ISP 09-1A 8 4
4/1/04 ISP 09-1A 9 The Atomic Nucleus The discovery of the nuclear structure of the atom. 4/1/04 ISP 09-1A 10 5
4/1/04 ISP 09-1A 11 Rutherford scattering Scatter alpha particles (produced by a decay of polonium) from a thin gold foil. The observation of large-angle scattering implies that the atom has a very small massive core the nucleus. 4/1/04 ISP 09-1A 1 6
α Au scattering corresponding scattering angle Rutherford calculated the scattering rate based on classical mechanics for the scattering process, assuming all the positive charge of the Au atom is concentrated in a nucleus. varying impact parameter The result is perfect agreement with the measured scattering rate. 4/1/04 ISP 09-1A 1 How big is the nucleus? What determines its size? From electron-nucleus scattering, we know that the radius R of a nucleus is approximately given by the formula R = 1/ ( 1. fm) A A = the number of nucleons That is, A R ; because the nucleons are packed pretty densely in the nucleus. nuclear radius ~ 10 5 x atomic radius 4/1/04 ISP 09-1A 14 7
Dictionary Nucleus: The massive and positively charged particle at the center of an atom Electron: The negatively charged constituent of atoms. Proton: The positively charged constituent of nuclei. Neutron: The electrically neutral constituent of nuclei. particle Electron Proton Neutron Charge e +e 0 Mass 9.109 81 88(7) 10 1 kilogram 1.67 61 58(1) 10 7 kilogram 1.674 9 x 10 7 kilogram The electron is much lighter than the proton. The neutron is slightly heavier than the proton. 4/1/04 ISP 09-1A 15 Isotopes Each nucleus is characterized by numbers: Z = number of protons A = number of nucleons (protons and neutrons) Chart of the Nuclides 4/1/04 ISP 09-1A 16 8
Isotopes proton neutron hydrogen 1 1 H 1 H 1 H Z=1 helium He 4 He Z= carbon 1 6 C 1 6 C 14 6 C Z=6 uranium 5 9 U 8 9 U Z=9 and others 4/1/04 ISP 09-1A 17 4/1/04 ISP 09-1A 18 9
Radioactive decays 8 9 U 4 90 Th + α half - life = 4. 5 10 9 yr α decay 14 6 C 14 7 N + e + ν half - life = 570 yr β decay 4/1/04 ISP 09-1A 19 Half life We cannot predict with certainty when an unstable nucleus will decay. Radioactive decay is a random process like dice. The half life τ is the mean time for one-half of the atoms in a radioactive sample to decay. Dating t N( t) 1 τ = N( 0) log[ N( 0) / N( t)] " age " = t = τ log[ ] Measure N(t)/N(0), i.e., fraction of the unstable isotope that remains at time t. The age is the time that has passed since the death of the plant. 4/1/04 ISP 09-1A 0 10
4/1/04 ISP 09-1A 1 THE STRONG NUCLEAR FORCE P N N P α particle = a nucleus of helium What holds it together? The electric force of two protons is a repulsion (like charges repel). But the nuclear force (between pp or pn or nn) is an attraction, and is much stronger than the electric force. What are the fundamental forces? 4/1/04 ISP 09-1A 11