ATOMS

• atom = the smallest unit of an element, the smallest unit of matter that has the chemical character of the element;
  can exist alone or combined with other atoms to form a molecule.
• modern ``atomism'' developed during late 18th/early 19th century (Dalton, Lavoisier,..)
• main findings during early (``chemical'') period:
  • atoms are neither created nor destroyed (in chemical reactions)
  • atoms of a given element are identical in character
  • atoms of different elements are different in character
  • chemical compounds are formed when atoms of different elements join together to make identical units
  • ``law of definite proportions:'' the different kinds of atoms in a compound are present in simple numerical ratios (1;1, 1:2, 2:3, 1:3,...).
  • ``law of multiple proportions:'' atoms of two or more elements combine in different ratios to produce more than one compound.
  • Avogadro's law: under identical conditions of temperature and pressure, equal volumes of gases of any kind contain the same number of molecules.

Historical note:

• Robert Boyle(1627-1691) (Ireland, London)
  1661: ``element'' = substance that cannot be decomposed into simpler substances
  ``Boyle-Mariotte gas law''
  improved Guericke's air pump
• Antoine Lavoisier(1743-1794) (Paris)
  (executed during French Revolution) - The ``father of modern chemistry''
  - burning = oxidation
  - composition of water
  - realized importance of quantitative studies of proportions in chemical reactions - developed precise balance for these studies
• John Dalton (1766-1844) (Manchester)
  ``law of simple proportions''
  ``law of multiple proportions''
  introduced atomic theory into chemistry
  law of partial pressures
  color blindness
• Amadeo Avogadro (1776-1856) (Torino)
  Avogadro's law (1811)
• Dimitri Ivanovich Mendeleev (1834-1907) (Prof. Chemistry, Petersburg)

EMISSION AND ABSORPTION SPECTRA

EMISSION SPECTRA:

• continuous spectrum
  solid, liquid, or dense gas emits continuous spectrum of electromagnetic radiation (``thermal radiation'');
  total intensity and frequency dependence of intensity change with temperature
  (Kirchhoff, Bunsen, Wien, Stefan, Boltzmann, Planck)

• line spectrum
  rarefied gas which is ``excited'' by heating, or by passing discharge through it, emits radiation consisting of discrete wavelengths (``line spectrum'')
  wavelengths of spectral lines characteristic of atoms

ABSORPTION SPECTRA:

• light from continuous-spectrum source passes through colder rarefied gas before reaching observer
  see dark lines in continuous spectrum

• first seen by Fraunhofer in light from Sun

• spectra of light from stars are absorption spectra (light emitted by hotter parts of star further inside passes through colder ``atmosphere'' of star)

• dark lines in absorption spectra match bright lines in discrete emission spectra

• Helium discovered by studying Sun's spectrum

WHAT IS INSIDE AN ATOM?

THOMSON'S MODEL OF ATOM:
atom = sphere of positive charge (diameter m), with electrons embedded in it, evenly distributed (like raisins in cake)

RUTHERFORD'S SCATTERING EXPERIMENT:
(Geiger, Marsden, Rutherford, 1906 - 1911)

• get particles form radioactive source
• make ``beam'' of particles using ``collimators'' (lead plates with holes in them, holes aligned in straight line)
• bombard foils of gold, silver, copper with beam
• measure scattering angles of particles with scintillating screen (ZnS)
• result:
  • most particles only slightly deflected (i.e. by small angles), but some by large angles - even backward
  • measured angular distribution of scattered particles did not agree with expectations from Thomson model (only small angles expected),
  • but did agree with that expected from scattering on small, dense positively charged nucleus with diameter , surrounded by electrons at .

RUTHERFORD MODEL OF ATOM:
(``planetary model of atom'')

• positive charge concentrated in nucleus ( );
• negative electrons in orbit around nucleus at distance ;
• electrons bound to nucleus by Coulomb force

problem with Rutherford atom:

electron in orbit around nucleus is accelerated (centripetal acceleration to change direction of velocity);

according to theory of electromagnetism (Maxwell's equations), accelerated electron emits electromagnetic radiation (frequency = revolution frequency);

electron loses energy by radiation orbit decays,

changing revolution frequency continuous emission spectrum;

(no line spectra),

and atoms would be unstable (lifetime )

we would not exist to think about this!!

BOHR MODEL OF HYDROGEN:
(Niels Bohr, 1913)

• Bohr model is radical modification of Rutherford model;
  discrete line spectrum attributed to ``quantum effect''.
• electron in orbit around nucleus, but not all orbits allowed;
• three basic assumptions:
  1. angular momentum is quantized

     

     electron can only be in discrete specific orbits with particular radii
     discrete energy levels

  2. electron does not radiate when in one of the allowed ``levels,''or ``states,''
  3. radiation is only emitted when electron makes ``transition'' between states,
     transition also called ``quantum jump'' or ``quantum leap''
• from these assumptions, can calculate radii of allowed orbits and corresponding energy levels:
• radii of allowed orbits:

  

  n = ``principal quantum number,''
  

• allowed energy levels:

  

• note: energy is negative, indicating that electron is in a ``potential well''; energy is = 0 at top of well, i.e. for , at infinite distance from the nucleus.

• ground state = lowest energy state, n = 1; this is where electron is under normal circumstances; electron is ``at bottom of potential well,''
  energy needed to get it out of the well = ``binding energy'';
  binding energy of ground state electron = = energy to move electron away from the nucleus (to infinity), i.e. to ``liberate'' electron;
  this energy also called ``ionization energy''

• excited states = states with n > 1
• excitation = moving to higher state
• de-excitation = moving to lower state

• energy unit eV = ``electron volt'' = energy acquired by an electron when it is accelerated through electric potential of 1 Volt; electron volt is energy unit commonly used in atomic and nuclear physics;
  
• relation between energy and wavelength:

  

PROCESSES FOR EXCITATION:

gain energy by collision with other atoms, molecules or stray electrons; kinetic energy of collision partners converted into internal energy of the atom; kinetic energy comes from heating or discharge;

absorb passing photon of appropriate energy.

DE-EXCITATION:

spontaneous de-excitation with emission of photon which carries energy = difference of the two energy levels;

typically, lifetime of excited states is
(compare to revolution period of )

IONIZATION:

if energy given to electron > binding energy, the atom is ionized, i.e. electron leaves atom; surplus energy becomes kinetic energy of freed electron.

MICROWAVE COOKING
water molecule has rotational energy levels close together
small energy difference can absorb microwaves;
it is water content that is critical in microwave cooking; most dishes and containers do not absorb microwaves are not heated by them, but get hot from hot food.

MATTER WAVES

• Louis de Broglie (1925):
  any moving particle has wavelength associated with it:

  

• example: electron in atom has
  car (1000 kg) at 60mph has
  wave effects manifest themselves only in interaction with things of size comparable to wavelength we do not notice wave aspect of our cars.
• note:
  Bohr's quantization condition for angular momentum is identical to requirement that integer number of electron wavelengths fit into circumference of orbit.

• experimental verification of de Broglie's matter waves: beam of electrons scattered by crystal lattice shows diffraction pattern
  (crystal lattice acts like array of slits);
  experiment done by Davisson and Germer in 1927.

QUANTUM MECHANICS

= new kind of physics based on synthesis of dual nature of waves and particles
developed in 1920's and 1930's.

• Schrödinger equation:
  (Erwin Schrödinger, 1925)
  
  • is a differential equation for matter waves; basically a formulation of energy conservation.
  • its solution called ``wave function'', usually denoted by
  • gives the probability of finding the particle at x;
  • applied to the hydrogen atom, the Schrödinger equation gives the same energy levels as those obtained from the Bohr model;
  • the most probable orbits are those predicted by the Bohr model;
  • but probability instead of Newtonian certainty!
• Uncertainty principle:
  (Werner Heisenberg, 1925)
  It is impossible to simultaneously know a particle's exact position and momentum (or velocity)

  

  (remember h is a very small quantity: )