Physics Lecture 9 2/23/ Andrew Brandt Monday February 23, 2009 Dr. Andrew Brandt 1.The Electron 2.Rutherford Scattering 3.Bohr Model of Atom

Wednesday, Aug. 28, 2008 PHYS 3446, Fall 2008 Andrew Brandt 2 Evolution of Atomic Models 1803: Dalton’s billiard ball model 1897: J.J. Thompson Discovered electrons – Used cathode ray tubes – Called corpuscles – Made a bold claim that these make up atoms – Measured charge/mass ratio 1904: J.J. Thompson Proposed a “plum pudding” model of atoms – Negatively charged electrons embedded in a uniformly distributed positive charge Cathode ray tube Personally I prefer chocolate chip cookie model

Millikan’s Oil Drop Experiment Millikan (and Fletcher) in 1909 measured charge of electron, showed that free electric charge is in multiples of the basic charge of an electron By varying electric field to balance gravitational field, could determine charge of electron 2/23/ Andrew Brandt3

Wednesday, Aug. 28, 2008 PHYS 3446, Fall 2008 Andrew Brandt 4 Rutherford Experiment 1911: Geiger and Marsden with Rutherford performed a scattering experiment firing alpha particles at a thin gold foil

Rutherford Scattering The actual result was very different— although most events had small angle scattering, many wide angle scatters were observed “ It was almost as incredible as if you fired a 15 inch shell at a piece of tissue paper and it came back at you” Implied the existence of the nucleus. We perform similar experiments at Fermilab and CERN to look for fundamental structure

Rutherford Example On blackboard demonstrate size of radius from distance of closest approach 2/23/ Andrew Brandt6

Wednesday, Aug. 28, 2008 PHYS 3446, Fall 2008 Andrew Brandt 7 Ruherford Atom 1912: Rutherford’s planetary model, an atomic model with a positively charged heavy core surrounded by circling electrons But many questions: a) Z=A/2, Z=atomic number (number of electrons or protons) what is the other half of the atomic weight ? b)what holds the nucleus together? c)how do electrons move around the nucleus and does their motion explain observed atomic properties?

Electron Orbit Electrons must be in motion or would get sucked into nucleus by Coulomb Force “Assume a spherical orbit” : this implies that the centripetal force must be balanced by the Coulomb force so Energy of electron is kinetic energy plus potential energy (where potential energy is defined to be 0 at infinity and negative at closer radius since you have to input work to keep electron and proton apart) Can thus determine radius of Hydrogen atom given Binding Energy (-13.6 eV) 2/23/ Andrew Brandt8 This is known as Bohr Radius

Quantum Effects Classically an accelerating charge revolving with a frequency  would radiate at the same frequency. As it radiates, it loses energy, and radius decreases and frequency increases (death spiral) Law of physics in macro-world do not always apply in micro-world Quantum phenomena enter the picture Evidence for quantum nature of atoms: discrete line spectra emitted by low pressure gas when excited (by electric current)—only certain wavelengths emitted A gas absorbs light at some wavelengths of emission spectra, with the number intensity and wavelength of absorption lines depending on temperature, pressure, and motion of the source. This can be used to determine elements of a star and relative motion 2/23/ Andrew Brandt9

Spectral Lines For Hydrogen Atom (experimental observation): where n f and n i are final and initial quantum states R=Rydberg Constant Balmer Series n f = 2 and n i =3,4,5 visible wavelengths in Hydrogen spectrum 656.3, 486.3,…364.6 (limit as n  ) 2/23/ Andrew Brandt10

Spectral Lines 2/23/ Andrew Brandt11

Bohr Atom Assumptions 1)The electron moves in circular orbits under influence of Coulomb force 2)Only certain stable orbits at which electron does not radiate 3)Radiates when “jumps” from a more energetic initial state to a lower energy final state Introduced quantum number of orbit, can describe using de Broglie language (he didn’t, since it didn’t exist yet) Allowed orbits are integer number of de Broglie wavelengths 2/23/ Andrew Brandt12 non-integer number of wavelengths is discontinuous, so not physical

2/23/ Andrew Brandt13 Bohr Atom Derivation Consider n=1, the circular orbit case: for this to be self- consistent implies that with yields so finally Generally so with so and

2/23/ Andrew Brandt14 Bohr Atom Derivation Consider n=1, the circular orbit case: for this to be self- consistent implies that with yields so finally Generally so with so and