Chapter 8 in Brief Electrons in Atoms

Definitions: Points Atomic Spectra o Each element has its own distinctive line spectra o Spectra gives evidence that there are a limited amount of energy levels for excited atoms Quantum Theory o Light emitted by heated solids is known as blackbody radiation o Max Planck made the proposal that energy is discontinuous and is instead quantized this was different from classical physics that said there were no limitations on the amount of energy a system could possess The difference between any two allowed energies of a system is called a quantum of energy Photoelectric Effect When light strikes the surface of certain metals, electrons are ejected in the photoelectric effect Only occurs when the number of electrons ejected depends on the intensity of light and when the kinetic energies depend on the frequency This led Einstein to introduce duality in that light had characteristics of particles and thus contained photons Electromagnetic radiation: form of energy transmission where electric and magnetic fiels travel as waves through empty space or a medium Wave: disturbance that transmits energy Amplitude: maximum height of wave above/below the centre line Wavelength: distance between the tops of two maximums/minimums (in m, ) Frequency: number of crests or troughts that pass through a period of time (in s1 , or Hz, ) Velocity: speed of the wavelength (in m, ) Visible spectrum: between 390 nm and 760 nm of the electromagnetic spectrum (goes from blue violet, to red) Instructive interference: waves that are in phase are added Destructive interference: waves that are out of phase are cancelled Diffraction: dispersion of different wavelength components

o o

The energy binding the electron to the surface is a quantity known as the work function The threshold frequency is the lowest frequency light producing the photoelectric effect Electrons emitted by the metal are called photoelectrons

Experiments showed that the effect did not depend on intensity and instead on frequency however the magnitude is directly proportional to the intensity (intensity increases, number of photoelectrons increase) o Photochemical reactions Photons are thought of as reactants and symbolized by hv The Bohr Atom o Rutherford model doesnt indicate how electrons are arranged o Bohr postulated that: The electron moves in circular orbits Electron only has fixed set of allowed orbits (aka stationary states) Possible values for angular momentum are (nh)/(2pi) where n is an integer An electron can pass only from one allowed orbit to another where fixed quanta of energy are involved (absorbed or emitted) o He predicted that the radii of allowed orbits were r=n2a0 (a0 is 53 pm) Normally hydrogen electrons are at n=1 but move to a higher level when excited o Read over spectroscopy o However Bohr model did have holes Wave-Particle Duality o Light has particle like properties dual nature E=mc2 m=relativistic mass of the photon and c=speed of light o o o o o o de Brouglie substituted this with E=hv to create p=mc=(hv)/c where p is the momentum of the photon Using v=c, we get p=h/ Finally he substituted the momentum for the mass times its velocity to get =h/p=h/(mu) Experiments later arose where a beam of electrons were shot at a metal foil and produced the same patterns as X-rays with the same wavelength Uncertainty Principle As the position and momentum of the particle are measured, there is always some level of uncertainty

It can be expressed as xp_> h/(4pi) Called the Heisenberg uncertainty principle An experiment cannot accurately measure both the position and momentum at the same time While the de Broglie relationship explains the momentum of a

Wave o o o o o o o o o o o

particle, to find where it is we combine waves of different lengths into a wave packet to produce an interference pattern that localizes the wave But since each wavelength corresponds to a different momentum, the momentum of the particle corresponding to the collection of waves has become uncertain Mechanics Standing waves have crests and troughs that occur at fixed positions and the amplitude of the wave at the fixed ends is zero Magnitudes of oscillations differ Nodes are places where the wave undergoes no displacement =(2L)/n where n=the number of nodes and L=path length The wave function is a mathematical equation that corresponds to a standing wave within the boundary of the system being described When the wave function is zero, there exists a node Particle-in-a-box model says that the electron is free in a box but cant escape it As the size of the box decreases, the kinetic energy increases and our knowledge of the momentum must decrease Energy of the particle CANNOT be zero Solutions of the Schrodinger equation for the electron in the hydrogen atom are called orbitals The spherical polar coordinate system is used where r is the distance of the point from the nucleus, and the angles theta and phi describe the orientation of r with respect to the x y and z axes psi=R(r)Y(theta,phi) R is the radial wave function and the function Y is the angular wave

o o

function
Quantum Numbers and Electron Orbitals o Principal quantum number n positive, nonzero integral value; determines the electron energy o Orbital angular momentum quantum number l l<n-1, l can be zero or a positive integer; determines the shape

Magnetic quantum number ml may be a negative, positive integer or zero ranging from l to l; determines the orientation Electron Configuration o Designation of how electrons are distributed among various orbitals o They occupy orbitals in a way that minimizes the energy of the atom o o o o No two electrons in an atom can have all four quantum numbers alike Pauli exclusion principle Electrons initially occupy degenerate orbitals singly Hunds rule Aufbau process assign electron configurations to the elements in order of increasing atomic number