2/28/2016 ATOMS) ATOMS. Physics 2D. PHYS 342 Modern Physics Atom I: Rutherford Model and Bohr Model

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1 PHYS 342 Modern Physics Atom I: Rutherford Model and Bohr Model Today Contents: a) Basic Properties of Atoms b) Rutherford Model and Scattering Experiments c) Bohr Model and Line Spectra Physics 2D Subfields in Modern Physics (Large to Small): Cosmology Condensed Matter Physics Atomic, molecular, and optical physics Nuclear physics High energy (particle) physics.. Our Second Topic HISTORY OF THE ATOM HISTORY OF THE ATOM Ancient Greek philosopher, Democritus, formulated an atomic theory for the universe 440 BC He pounded up materials in his mortar and pestle until he had reduced them to smaller and smaller particles which he called 1808 John Dalton suggested that all matter was made up of tiny spheres that were able to bounce around with perfect elasticity and called them ATOMS) ATOMS 1

2 HISTORY OF THE ATOM Thomson s Apparatus to Discover Electrons 1898 Joseph John Thompson found that matter could sometimes eject a far smaller negative charged particle which he called an ELECTRON Thomson s Apparatus to Discover Electrons Atoms and Radioactivity Devised an experiment to find the ratio of the cathode ray particle s mass (m e ) to the charge (e) m e /e = x kg C 1 Based upon the mass to charge ratio, the electron must be much smaller than the atom m H+ /e = x 10 8 kg C 1 Atoms are not indestructible. Atoms are composed of smaller particles Evidence: Unstable Atoms and Radioactivity Alpha particles positively charged Beta particles negatively charged Gamma rays no charge.. 2

3 Mass Spectrometer If a stream of positive ions having equal velocities is brought into a magnetic field, the lightest ions are deflected the most, making a tighter circle A record of the mass to charge ratio is called a mass spectrum Proton and Neutron Isotopes of Neon By analyzing the emitted particles from unstable atoms, people found proton and neutron Proton: positive charge +e, mass is about m P = x kg Electron Wave Function (determined by 3D time-dependent Schrodinger Equations) Neutron: no charge, mass is about m N = x kg 3

4 Rutherford Scattering Experiments Ernest Rutherford 1910 a) Basic Properties of Atoms b) Rutherford Model and Scattering Experiments c) Bohr Model and Line Spectra Rutherford s Nuclear Model of the Atom Most the alpha particles (helium nuclei) pass through the gold foil Atom mostly empty space Alpha particles did not hit anything A very few deflected straight back Alpha particles deflected by a dense positive nucleus 4

5 , Quantitative Calculation about Scattering Incoming particles scattered by the nuclei in an atom. 1 4 The path of the scattered particle is a hyperbola. Smaller impact parameters b give large scattering 1 1 angles. sin 8 cos 1 Find the relation between the impact parameter and scatting angle. ICP21. Prove it!, Scattering Probability The impact factor b and the scattering angle θ has one to one correspondence. If particle enters the atom within the disc area πb 2, the scattering angle will be larger than θ. What is the probability? and are the density and the molar mass, and t is the thickness of foil. The nuclei per unit volume is, is Avogadro s number The nuclei per unit area is cot The fraction scatter at an angle larger than θ. Differential Scattering Probability The detector is located at the angle and the distance r, what is the detection probability? (We need to know the scattering probability per unit area for the angle and the distance r.) 2 sin a) Basic Properties of Atoms b) Rutherford Model and Scattering Experiments c) Bohr Model and Line Spectra cot sin 2 Rutherford Scattering Formula (remarkably good in experiments!) 5

6 The Electromagnetic Spectrum Emission Spectrum Emission Spectrum of Hydrogen 1 nm = 1 x 10-9 m = a billionth of a meter 410 nm 434 nm 486 nm 656 nm Continuous and Line Spectra Visible spectrum (nm) light nm Na H Emission Spectra of Different Atoms: A Fingerprint to Identify Ca Hg 4000 A o Copyright 2006 Pearson Benjamin Cummings. All rights reserved. 6

7 Rydberg Rydberg and Balmer Equation (1886) A mathematical equation that fits the data for hydrogen emission spectrum. At that time, electron had no yet been discovered, so there is no microscopic model to explain the observed wavelengths. Rydberg Equation 1/λ = R H [1/n 02 1/n 2 ] R H = x 10 2 nm 1 n 0 =1,2,3, and n=n 0 +1, n n 0 =1 n 0 =2 n 0 =3 n 0 =4 n 0 =5 Bohr s Model of the Atom (1910) 1)Assume electrons orbit nucleus in circular orbits 2)Propose the energy of the orbit is proportional to the distance from the nucleus (increasing distance increasing energy) 3)Assume only certain allowable energies (Energy Quantization!) 4)Used quantized angular momentum to calculate the allowable energy Niels Bohr ( ) Bohr s Model of the Atom (1910) When the atom absorbs energy Electron moves up to higher energy with more potential energy farther away from nucleus Unstable with higher PE Electron falls back down to lower levels Energy released PE converted to KE as electron fall The color of light observed reflects the energy released in the fall 7

8 Bohr s Model of the Atom Bohr Model was suggested before people established quantum mechanics (Schrodinger Eq). So it uses classical mechanics + quantization condition. Such theories are also called semiclassical theory. (Z=1 for hydrogen) Bohr s Model of the Atom (Z=1 for hydrogen) quantization condition. 1,2.. ICP22. Prove it! and Bohr radius. Ground State of H ev Bohr s Calculations of the Energy E = ev (1/n f2 1/n i2 ) n = the energy level Visualizing the Movement of the Electron E = positive when electron climbs up levels absorbing energy increasing PE E = negative when e- falls down levels releasing energy decreasing PE 8

9 HW 6: Chapter ,18,28, 37 9