chapter7

Chapter 7 Quantum Theory and Electronic Structure **7.1 From Classical Physics to Quantum Theory**  -__Properties of Waves__ //wave//: vibrating disturbance by which energy is transmitted (ex: water waves are generated by pressure differences in various regions on the surface of water) //wavelength//(lamba): distance between identical points on successive waves (distance/wave) //frequency//(nu): number of waves that pass through a particular point in 1 second (waves/time) //amplitude//: vertical distance from the midline of a wave to the peak or trough

-__Electromagnetic Radiation__ In 1873 James Clerk Maxwell proposed visible light consists of electromagnetic waves //electromagnetic wave//: has an electric field component and a magnetic field component //electromagnetic radiation//: is the emission and transmission of energy in the form of electromagnetic waves c=2.998 x 10^8 m/s h(Planck's constant)=6.626 x 10^-34 J*s E-->energy(J) lamba-->wavelength(m) v-->frequency(Hz) -__Planck's Quantum Theory__ //quantum//: smallest quantity of energy that can be emitted (or absorbed) in the form of electromagnetic radiation -energy(E) is always emitted in multiples of hv (hv, 2hv, 3hv) but never, for example, in the form of 1.2hv or .5hv //photoelectric effect//: electrons are ejected from the surface of certain metals exposed to light of at least a certain minimum frequency, called the //threshold frequency// -# of electrons ejected was proportional to the intensity(brightness) of the light, but the energies was not -Einstein suggested a beam of light is actually a stream of particles; these particles of light are called //photons// -light possesses both particlelike and wavelike properties(dual nature)  -__Emission Spectra__ //emission spectra//: either continuous or line spectra of radiation emitted by substances -the emission spectrum of a substance can be seen by energizing a sample of material with thermal energy or with some other form of energy -a feature common to the emission spectra of the sun and of a heated solid is that both are continuous-all wavelengths of visible light are represented in the spectra(like in the figure above) //line spectra//: the light emission only at specific wavelengths (for atoms in the gas phase) and do not show a continous spread of wavelengths from red to violet but produce bright lines in different parts of the visible spectrum -__Emission Spectrum of the Hydrogen Atom__ -Bohr's model of the atom included the idea of electrons moving in circular orbits, but he imposed a rather severe restriction: the single electron in the hydrogen atom could be located only in certain orbits -Bohr attributed the emission of radiation by an energized hydrogen atom to the electron dropping from a higher-energy orbit to a lower one and giving up a quantum of energy (a photon) in the form of light -Bohr showed that the energies that the electron in the hydrogen atom can possess are given by: n-->integer called the principle quantum number (n=1,2,3,...) //ground state(or ground level)//: the lowest energy state of a system when n=1 -the stability of the electron diminishes for n=2,3...Each of these levels is called an //excited state// which is higher in energy than the ground state -a hydrogen electron for which n is greater than 1 is said to be in an excited state -as n increases from 1 to 2 to 3 the orbit radius increases very rapidly -Why is the electron in a Bohr atom restricted to orbiting the nucleus at certain fixed distances? De Broglie proposed perhaps particles such as electrons can possess wave properties. -an electron bound to the nucleus behaves like a //standing wave// which can be generated by, for example, plucking a guitar string -the waves are described as standing, or stationary, because they do not travel along the string //nodes//: amplitude of the waves at these points is zero; points on the string that do not move at all and there is a node at each end -the greater the frequency of vibration, the shorter the wavelength of the standing wave and the greater the number of nodes -the relation between the circumference of an allowed orbit is given by: r=radius; lamba=wavelength; n=1,2,3... -waves can behave like particles and particles can exhibit wavelike properties; particle and wave properties related by the expression: h=planck's constant; lambda=wavelength; m=mass; v=velocity -//Heisenberg uncertainty principle//: it is impossible to know simultaneously both the momentum //p// (defined as mass times velocity) and the position of a particle with certainty -quantum mechanics (wave mechanics) began with Schrodinger's equation and the developments in quantum theory from 1913-the time Bohr presented his analysis for the hydrogen atom-to 1926 as "old quantum theory"  -__The Quantum Mechanical Description of the Hydrogen Atom__ -the Schrodinger equation specifies the possible energy states the electron can occupy in a hydrogen atom and identifies the corresponding wave functions -//electron density//: gives the probability that an electron will be found in a particular region of an atom -regions of high electron density represent a high probability of locating the electron and opposite holds for regions of low electron density -//atomic orbital//: the wave function of an electron in an atom -an atomic orbital has a characteristic energy as well as a characteristic distribution of electron density **7.6 Quantum Numbers** -three quantum numbers are required to describe the distribution of electrons in hydrogen and other atoms -a fourth quantum number-the spin quantum number-describes the behavior of a specific electron and completes the description of electrons in atoms -__The Principal Quantum Number (n)__ -has integral values 1,2,3 and so forth -in a hydrogen atom the value of n determines the energy of an orbital -also relates to the average distance of the electron from the nucleus in a particular orbital -__The Angular Momentum Quantum Number (l)__ -tells us the "shape" of the orbitals -for a given value of n, l has possible integral values from 0 to (n-1); if n=1 there is only one possible value l=0 if n=2 there are two, n=1 and n=0 -the value of l is generally designated by the letters s(l=0), p(l=1), d(l=2), f(l=3) and then uncommonly g(l=4) and h(l=5) -__The Magnetic Quantum Number (ml)__ -describes the orientation of the orbital in space -depends on the value of the angular momentum quantum number, l -for a certain number l there are 2l + 1 integral values of ml -if l=0 then ml=0; if l=1 then there are (2x1+1) values of ml or 3 values of ml (-1,0,1); if l=2 then there are (2x2+1) values of ml or 5 values (-2,-1,0,1,2) -the number of ml values indicates the number of orbitals in a subshell with a particular l value -__The Electron Spin Quantum Number (ms)__ -electrons act like tiny magnets; if electrons are thought of as spinning on their own axes, like Earth, their magnetic properties can be accounted for -spin is either clockwise or counterclockwise and has a value of +1/2 or -1/2 **7.7 Atomic Orbitals** **//s Orbitals//** -an electron is usually found quite close to the nucleus; the electron density falls off rapidly as the distance from the nucleus increases -1s orbital can be represented by drawing a boundary surface diagram that encloses about 90% of the total electron density in an orbital; a 1s orbital represented this way is the shape of a sphere -all s orbitals are sphere shaped but increase in size as the principal quantum number increases -the most important features of atomic orbitals are their shapes and relative sizes **//p Orbitals//** -p orbitals start with the principle quantum number n=2 -starting with n=2 and l=1 we have three 2p orbitals which are identical in size, shape, and energy; they differ only in orientation Boundary Surface Diagram: -when l=2 there are five values of ml which correspond to five d orbitals -the lowest value of n for a d orbital is n=3 -all the 3d orbitals in an atom are identical in energy; the 3d orbitals for which n is greater than 3 (4d, 5d, ...) have similar shapes -orbitals having higher energy than d orbitals are labeled f, g, ...and so on following the alphabet -the f orbitals are important in accounting for the behavior of elements with atomic numbers greater than 57, but their shapes are different -__The Energies of Orbitals__  -the energy of an electron in a hydrogen atom is determined solely by its principal quantum number -the 1s orbital in a hydrogen atom corresponds to the most stable condition, the ground state (most strongly held by nucleus because it's closest to the nucleus -an electron in the 2s, 2p, or higher orbitals in a hydrogen atom is in an excited state -the energy of many-electron atoms depends on its angular momentum quantum number as well as its principal quantum number -the total energy of an atom depends not only on the sum of the orbital energies but also on the energy of repulsion between the electrons in these orbitals
 * 7.2 The Photoelectric Effect **
 * below the threshold frequency no electrons were ejected no matter how intense the light
 * 7.3 Bohr's Theory of the //Hydrogen// Atom **
 * every element has a unique emission spectrum and can be used in chemical analysis to identify unknown atoms
 * 7.4 The Dual Nature of the Electron**
 * 7.5 Quantum Mechanics**
 * example: n=1 and l=2; these values indicate that we have a 2p subshell and in this subshell we have three 2p orbitals (because there are 3 values of ml, given by -1, 0, 1)
 * //d Orbitals and Other Higher-Energy Orbitals//**


 * Order in Which Atomic Subshells are Filled in Many-Electron Atoms and Energy Levels: