156 Views

Download Presentation
##### Lecture 15: The Hydrogen Atom

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**J.J. Thomson’s Plum Pudding Model of the Atom (1897)**He proposed that the electrons are embedded in a positively charged ‘pudding’**Rutherford’s a Scattering Experiment (1911)**He found that, once in a while, the a-particles were scattered backwards by the target video clip**Discovery of the Atomic Nucleus**To explain the backscattering, the positive charge must be concentrated in a small region**Rutherford’s Solar System Model of the Atom**The atom consists of electrons orbiting around a small but dense central nucleus**Hydrogen Atom is Unstable?**• It is known that accelerating charges emit radiation • Thus, electron should emit radiation, lose energy and eventually fall into the nucleus! • Why doesn’t this happen? Shows that something was wrong with this model of the hydrogen atom**Absorption Spectrum of a Gas**Dark lines will appear in the light spectrum**Absorption spectrum of Sun**Emission spectra of various elements**Balmer’s Formula for Hydrogen**• Notice there are four bright lines in the hydrogen emission spectrum • Balmer guessed the following formula for the wavelength of these four lines:where n = 3, 4, 5 and 6**Bohr’s Model of the Hydrogen Atom(1913)**He proposed that only certain orbits for the electron are allowed**Bohr’s Empirical Explanation**• Electrons can only take discrete energies (energy is related to radius of the orbit) • Electrons can jump between different orbitsdue to the absorption or emission of photons • Dark lines in the absorption spectra are due to photons being absorbed • Bright lines in the emission spectra are due to photons being emitted**Absorption / Emission of Photonsand Conservation of Energy**Ef - Ei = hf Ei - Ef = hf**Electron jumping to a higher energy level**E = 12.08 eV**Spectrum of Hydrogen**Bohr’s formula:**Hydrogen is therefore a fussy absorber / emitter of light**It only absorbs or emits photons with precisely the right energies dictated by energy conservation**This explains why some nebulae are red or pink in colour**One of the transitions in the Balmer series corresponds to the emission of red light**Schrödinger’s Improvement to Bohr’s Model**• Showed how to obtain Bohr’s formula using the Schrödinger equation • Electron is described by a wave function y • Solved for y in the electric potential due to the nucleus of the hydrogen atom**Square Well**• Approximate electric (roller coaster) potential by a ‘square well’ • System is then identical to the wave equation for a string that is fixed at both ends**Vibrational Modes of a String**fundamental 2nd harmonic 3rd harmonic 4th harmonic**Quantum Numbers**• Energy levels can only take discrete values • Labelled by a ‘quantum number’ n, which takes values 1, 2, 3, ... • Each level has energy that increases with n**Ground State (n=1)**• Lowest or ground-state energy is non-zero • Electron cannot sit still but must be forever ‘jiggling around’ • Expected from the Heisenberg uncertainty principle**Vibrational Modes of a Rectangular Membrane**(1,1) mode (1,2) mode (2,1) mode (2,2) mode Vibrational modes of a circular membrane (drum)**Electron in a Hydrogen Atom**• Wave function is like a vibrating string or membrane, but the vibration is in three dimensions • Labelled by three quantum numbers: • n = 1, 2, 3, … • ℓ = 0, 1, …, n-1 • m = -ℓ, -ℓ+1, …, ℓ-1, ℓ • For historical reasons, ℓ = 0, 1, 2, 3 is also known as s, p, d, f**Density of the cloud gives probability of where the electron**is located**Another diagram of 2p orbitals**Note that there are three different configurations corresponding to m = -1, 0, 1**3d Orbitals**Now there are five different configurations corresponding to m = -2, -1, 0, 1, 2**4f Orbitals**There are seven different configurations corresponding to m = -3, -2, -1, 0, 1, 2, 3**Summary**• Electron does not fly round the nucleus like the Earth around the Sun (Rutherford, Bohr) • Depending on which energy level it is in, the electron can take one of a number of stationary probability cloud configurations (Schrödinger)