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 troughamp-freq.JPG


-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

electromagnetic-spectrum.jpg
wave_speed_eq.JPG
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

7.2 The Photoelectric Effect
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
*below the threshold frequency no electrons were ejected no matter how intense the light
-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)

7.3 Bohr's Theory of the Hydrogen Atom

-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
*every element has a unique emission spectrum and can be used in chemical analysis to identify unknown atoms

gasemission.gif
-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:

energyeq.JPGn-->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

7.4 The Dual Nature of the Electron
-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

standingwaves.JPG
-the relation between the circumference of an allowed orbit is given by:
orbitandwavelength.JPGr=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:
lambdaplanckseq.JPGh=planck's constant; lambda=wavelength; m=mass; v=velocity

7.5 Quantum Mechanics
-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
*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)

-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

s_orbital.JPG
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:

p_orbitals.JPG
d Orbitals and Other Higher-Energy Orbitals
-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
d_orbitals.JPG

-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


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