Atomic Theory & Atomic Models

Thomson  Discovery of electron in 1897  Upgraded atomic model from tiny marble like structure to the plum pudding model  Negative electrons are embedded in positive charge matrix (like seeds are in a watermelon)

Rutherford  Prompted by Becquerel’s discovery of radiation in 1890, Rutherford continued work on the atomic model.  Geiger and Marsden (Rutherford supervised) – Gold Foil Experiment  Gold Foil Experiment Animation Gold Foil Experiment Animation

Rutherford cont’  Upgraded Thomson’s model by firing alpha particles (2p + and 2n 0 ) at a sheet of thin gold foil  Some of the particles were deflected showing the presence of a positive dense region.  He called this the nucleus and surmised that the electrons were outside of it.  However, there were still some difficulties about where the electrons actually were and if they were moving or not. The way the model was setup – the atom should be collapsing!  So the search continued for a new model

Atomic Spectra  Known fact: If a potential difference is applied to a pure atomic gas, a current is produced and the gas gives off light.

Atomic Spectra  Each gas has:  An emission spectrum: distinct bright lines corresponding to different wavelengths  An absorption spectrum: sequence of dark lines overlaid on a continuous spectrum  These spectra are characteristic of each atomic gas and can be used to identify elements that are present.

Atomic Spectra

Using Atomic Spectra

Identifying Elements Use the Spectrum tubes & diffraction tubes to look at bright line & dark line spectra.

Bohr  Neils Bohr stated that the attractive force between nucleus and electrons hold the atom together  Only certain orbits are allowable for electrons to be on – no in between.  Total energy of atom remains constant – radiation energy is not emitted in a stable atom.  Electrons can emit energy certain quanta of energy only when they “jump” from one level down to a lower level.  These emitted quanta account for the bright line spectrum. This is called spontaneous emission.

Gaining Energy

Losing Energy

 These emitted quanta account for the bright line spectrum. This is called spontaneous emission.  Eo – Ef = hf  Ground state: an electron’s lowest energy state  Excited state: an electron can gain certain quanta of energy and jump up to a higher energy level. These absorbed quanta account for the absorption spectrum.

Energy Diagrams

Matter Waves Wave-Particle duality – de Broglie suggested that matter actually consists of waves. At longer wavelengths, photon energy is too small to be detected so we observe the wave characteristics At shorter wavelengths and higher frequencies (example: visible region of light), we observe:  Interference phenomena best explained by wave model  AND photoelectric phenomena best explained by particle theory At even shorter wavelengths & very high frequencies, the particle/photon nature of light is very evident and the wave effects impossible to observe.

deBroglie  Extended the wave-particle duality to all objects  deBroglie wavelength  the larger the momentum – the smaller the wavelength  = h/p OR = h/mv since p = mv  deBroglie frequency  the higher the frequency – the higher the energy  f = E/h

deBroglie  In 1927, Davisson and Germer provided the first experimental confirmation of deBroglie’s theory  How to calculate using deBroglie’s equations  deBroglie’s theory explained by only certain electron orbitals were stable  he stated that an electron’s orbital would only be stable if it contained an integral (whole) number of wavelengths (think standing wave)

Standing Waves The Wave Nature of Matter

Schrodinger’s equation  Since the Heisenberg Uncertainty principle states that we cannot simultaneously measure a particle’s momentum and position – Schrodinger’s wave function equation was interpreted by Max Born as a probability of finding an electron’s location at a certain point in time at a certain distance from the nucleus.  To simplify matters, we discuss these locations as electron clouds and orbitals with in the cloud.

The Nucleus

Nucleons The proton & neutron are collectively called nucleons Mass number = protons + neutrons (symbol = A) Atomic number = protons only (symbol = Z) # neutrons = mass # - atomic # (symbol = N)

THE NUCLEUS NUCLEONS  Protons and neutrons contained in the atomic nucleus NUCLIDE  Atom identified by the number of protons and neutrons in its nucleus NUCLEAR SYMBOL  Shows mass # & atomic # Radium-228 Mass No. (A) Atomic No. (Z)

PRACTICE USING PERIODIC TABLE

Atomic Mass Unit  Symbol = u  1 u = 1.66 x kg  1 proton = 1 u  1 neutron = 1 u  1 electron = 5 x u

Theory of Relativity Einstein’s mathematical relationship between matter & energy  E = mc 2  C = speed of light constant = 3.0 x 10 8 m/s Will be using later in some calculations

Isotopes & Instability Isotopes are atoms that have the same # of protons but different # of neutrons. They have the same chemical properties but different nuclear properties.

Fundamental Forces Strong Force  glue that holds the nucleons together  Strongest of the fundamental forces  Short range force (only within the same nucleus)  proton-neutron, proton-proton, or neutron-neutron force which holds particles together Weak Force  Tends to produce instability in certain nuclei  Short range force  Responsible for beta decay

Fundamental Forces Electromagnetic Force  Responsible for binding of atoms & molecules  As #protons increases, electrostatic force increases faster than nuclear force  More neutrons required to increase nuclear force and stabilize nucleus.

29 Nucleons & Nuclear Stability BAND OF STABILITY  The neutron-proton ratios of stable nuclei  Low atomic # (1:1 ratio) – most stable  High atomic # (1.5:1 ratio) – most stable  Stability of nucleus is greatest when nucleons are paired – have even number of nucleons

30 Radioactive Nuclei  IMPORTANT POINT: Nuclei with too many or too few neutrons compared to the # of protons are radioactive  No stable nuclei exist beyond atomic # 83 (Bismuth) – all unstable & radioactive  Why? Because repulsive force of protons is so great

Band of Stability 31

Binding Energy The quantity of energy needed to break a nucleus into individual unbound nucleons is the same as the quantity of energy released when the unbound nucleons come together to form a stable nucleus The quantity is called the BINDING ENERGY. It is used to compare the stabilities of different atoms.

33 Decay Series Series of radioactive nuclides produced by successive radioactive decay until a stable nuclide is reached PARENT NUCLIDE  The heaviest nuclide of each decay series DAUGHTER NUCLIDE  Nuclides produced by the decay of the parent nuclide

34 Uranium-238 Decay Series

NUCLEAR DECAY

Nuclear Timeline NUCLEAR TIMELINE

Nuclear Applications

38 Law of Conservation Wolfgang Pauli proposed undiscovered particle called neutrino also emitted  Existence has since been confirmed Violated by:  Conversion of a neutron into a proton + electron  Conversion of a proton into a neutron + positron

39 Mass Defect MASS DEFECT  The difference between the mass of an atom and the sum of the masses of its protons, neutrons and electrons  The difference between measured mass & calculated mass  See table 3-1 page 74

40 Mass Defect Calculations Example: Helium 2 p x amu = amu 2 n x amu = amu 2 e x amu = amu Total calculated mass = amu Measured mass = amu Mass defect = amu

41 Mass Defect Practice Practice #25 & 26 page 723

42 Mass Defect Caused by conversion of mass to energy during the formation of the nucleus E=mc 2

43 Nuclear Binding Energy NUCLEAR BINDING ENERGY  The energy released when a nucleus is formed from nucleons  1 amu = x kg J=kg m 2 /s 2 See calculations page Binding energy per atom

44 Binding Energy per atom Magnitude is determined by mass defect  All other conversion factors are the same Higher BE = greater stability  More energy lost = more stable atom left behind  Atoms with intermediate masses are the most stable

45 Binding Energy Calculations BINDING ENERGY PER NUCLEON Need to know:  binding energy per atom  nucleons per atom (mass number)  Practice # 1abc, page BINDING ENERGY PER MOLE Need to know:  Binding energy per atom  Atoms per mole (Avogadro’s number)

46 Binding Energy Per Nucleon