1Atomic Theory and Spectral Lines -- Chemical Physicsmatter is composed of atoms – size ~ 10-8cm- density ~ 1023/cm3109 di...
2reminder:office hours next week only tuesday 2-4
3periodic table of the elements:in astrophysics everything exceptH and He is considered a metal
4adding neutrons to a nucleus (or taking them away) does not affect thenuclear charge (or number of electrons) so chemical...
5the number of neutrons is not arbitrary- too different from the proton number results in instabilityA – Z = neutronsZ = p...
6Bohr-Rutherford Model of the AtomRutherford (McGill!) discovered the nucleus in experiments wherehe scattered alpha parti...
7Bohr’s hypothesis: classical physics does not apply: quantum theoryelectrons only orbit in particular orbits with L (angu...
8another route to Bohr’s quantum condition: wave/particle dualitywavelength of an orbiting electron (non-relativistic)p=mo...
9energy of an electron at radius rrZemvE /2/ 22−=kinetic potentialuse )/(/ 22222mZenmvZer h==rZerZerZeE 2//2/ 222−=−= (neg...
10
11Bohr part II:(a) radiation in the form of a single discreet quantum (photon) is emittedor absorbed as the electron jumps...
12Hydrogen spectral lines
13eg Hydrogen Z=122242112)(nRnhmenE −=−=πenergy of the nthlevelR’ = 2.18 x 10-18Joules = 13.6 eV (Rydberg energy)t...
14Balmer series:nb = 2 na = 3 λ = 656.3 nm Hαna = 4 Hβna = 5 HγLyman series:nb = 1 na = 2 λ = 121.6 nm Lαna = 3 Lβna = 4 L...
15Energy Levelsground stateexcited statesE = R’ = 13.6 eVunbound states(continuum)Each atom has a characteristic energy le...
16Excitation raise from na to nb with na < nbradiative excitation - absorption of a photon of the correct energy- produces...
17excited states are unstable (10-8seconds lifetime, typically)so why don’t the atoms in the absorber de-excitewith no los...
18collisional excitation - no photons are absorbed; inelastic collisions of the atomwith other atoms or electrons (Coulomb...
19de-excitationradiative – emission of photon(s) 10-8seconds typicallycollisional – super-elastic collision: excited atom ...
20−=−=== 222211111abababababnnRnnhcRckυλIonizationbound electrons can be liberated from the atom if enough...
21Energy needed to ionize is greater than or equal to the energy state of the atompotentialionizationthecalledisenergymini...
22Emission continua exist by inverse analogy; if there is a plasma(ions plus electrons) some recombination can occur if th...
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Atomic theory

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Atomic theory

  1. 1. 1Atomic Theory and Spectral Lines -- Chemical Physicsmatter is composed of atoms – size ~ 10-8cm- density ~ 1023/cm3109 different atoms identified - 92 stable (occur naturally)- 17 transuranic (created artificially)pattern found by Mendeleev in 1869 (periodic table) led to our currentlyaccepted model of atoms:- an atoms is a nucleus (10-14m) surrounded by a cloud of electrons (10-10m)- a nucleus comprises a number of protons with an almost equal number of neutrons- atomic or chemical properties depend on the electrons (ie on Z, the charge)(Z = charge on the nucleus = number of protons = number of atomic electrons since atoms are neutral)
  2. 2. 2reminder:office hours next week only tuesday 2-4
  3. 3. 3periodic table of the elements:in astrophysics everything exceptH and He is considered a metal
  4. 4. 4adding neutrons to a nucleus (or taking them away) does not affect thenuclear charge (or number of electrons) so chemically the atom is not differentit does affect the nuclear properties (stability etc)Isotopes- specify an element by Z- specify an isotope by Aa complete description requires bothZ is implied by the historical nameeg 14C A = 14 Z = 6 - carbon with 2 extra neutronsshydrogen p+e 11Hdeuterium p+n+e 12H (in heavy water)tritium p+n+n+e 13Hthese are all isotopes of hydrogen but are not separate elementsthey have the same chemical properties but different nuclear properties(therefore things like nuclear burning in stars are different).
  5. 5. 5the number of neutrons is not arbitrary- too different from the proton number results in instabilityA – Z = neutronsZ = protonstoo many protonstoo many neutrons
  6. 6. 6Bohr-Rutherford Model of the AtomRutherford (McGill!) discovered the nucleus in experiments wherehe scattered alpha particles (helium nuclei – small,dense, + charge)off thin foils of material and saw that most went right through,some showed large deflections, and some bounced right back.he hypothesized that each atom comprised a dense nucleusorbited by electrons like planets around the sun - mostly space- the electrostatic (Coulomb) force between theelectrons and the nucleus was the ‘gravity’major problem with this idea:- electrons which go in circles are accelerating- accelerated charges radiate energy- therefore electrons will lose energy and spiralinto the nucleus – all matter collapses in an instant- also doesn’t explain discrete lines in spectrapeeg hydrogen
  7. 7. 7Bohr’s hypothesis: classical physics does not apply: quantum theoryelectrons only orbit in particular orbits with L (angular momentum)equal towhere n is an integer and h is Planck’s constantin this case, with centripetal force equaling the Coulomb forcewe have:but sosolving for r we get:is a constant for a given atomis the principal quantum numberthe radius of the orbit increases as thesquare of the principal quantum numberhn∂nh/ =222/)(/ reZermv =22/ mvZer =mvrnL == h 22)/()( rnmv h=22)//( rnmZer h=)/(/)( 22222mZenmZenr hh ==mZe22/hnπ
  8. 8. 8another route to Bohr’s quantum condition: wave/particle dualitywavelength of an orbiting electron (non-relativistic)p=momentumcircumference must be an integer numberof wavelengths (think standing wave)the only orbits which can exist haveusing the equality of centripetal and Coulomb forceswe getmvpph /2/2/ hh ππλ ===λπ nr =2mvnr /22 hππ =mvnr /h=222// rZermv =222)/()/()( rnrZemmv h==mZenr 222/h=
  9. 9. 9energy of an electron at radius rrZemvE /2/ 22−=kinetic potentialuse )/(/ 22222mZenmvZer h==rZerZerZeE 2//2/ 222−=−= (negative – electrons are bound)22222/)( hnmZeE −=1/1 2=−∝ ννΕ has the tightest binding (E is large and negative)all orbits are bound0→∞→ Εν0>Ε continuum of unbound states
  10. 10. 10
  11. 11. 11Bohr part II:(a) radiation in the form of a single discreet quantum (photon) is emittedor absorbed as the electron jumps from one orbit to another(b) the energy of the radiated photon equals the energy difference between orbitsphotons are emitted when the electron goes from a higher energy orbit (na)to a lower energy orbit (nb) (na > nb)E(na) = E(nb) + hνphotons are absorbed to cause electrons to go from a lower energy orbit toa higher energy orbit (nb > na)E(nb) + hν = E(na)frequency of emitted (or absorbed) photon:νab = (E(na) - E(nb) )/hna is not necessarily nb +/- 1n = 1 is called the ground state – lower energy states are not possible
  12. 12. 12Hydrogen spectral lines
  13. 13. 13eg Hydrogen Z=122242112)(nRnhmenE −=−=πenergy of the nthlevelR’ = 2.18 x 10-18Joules = 13.6 eV (Rydberg energy)this is often expressed in terms of wavelengths ν = c /λ k = 1/λ = wave number−=−=== 222211111abababababnnRnnhcRckυλR = 10.97 µm-1(Rydberg constant)na and nb are two levels in the atom na > nbfor every nb there is an infinite series of nasna = nb+1, nb+2, nb+3. . .the series are named after the people who discovered themLyman nb = 1 (ultraviolet)Balmer nb = 2 (found first since it is visible)Paschen nb = 3Brackett nb = 4Pfund nb = 1remember: E=hν22222/)( hnmZeE −=
  14. 14. 14Balmer series:nb = 2 na = 3 λ = 656.3 nm Hαna = 4 Hβna = 5 HγLyman series:nb = 1 na = 2 λ = 121.6 nm Lαna = 3 Lβna = 4 Lγhistorical namescan also have theselines in absorption
  15. 15. 15Energy Levelsground stateexcited statesE = R’ = 13.6 eVunbound states(continuum)Each atom has a characteristic energy level diagram(good for identifying which atom it is)
  16. 16. 16Excitation raise from na to nb with na < nbradiative excitation - absorption of a photon of the correct energy- produces absorption linessourceabsorberspectrographfluxwavelengthfluxwavelengthwithout absorber one getsa continuous spectrumwith absorber one getsa spectrum with absorption lines
  17. 17. 17excited states are unstable (10-8seconds lifetime, typically)so why don’t the atoms in the absorber de-excitewith no loss of photons and hence no absorption lines?two reasons:geometry – decays photons go in all directions so loss of intensitycombinatorics – several de-excitation paths usually availableinitial fluxre-emitted fluxλ3λ2λ1absorb λ1emit λ2 + λ3
  18. 18. 18collisional excitation - no photons are absorbed; inelastic collisions of the atomwith other atoms or electrons (Coulomb interaction)- atom gains some of the projectile’s kinetic energy andhas its energy level raisedeevivfγhν = 1/2m (vi2- vf2)the atom eventually de-excitesthrough photon emissionwe see ‘emission lines’
  19. 19. 19de-excitationradiative – emission of photon(s) 10-8seconds typicallycollisional – super-elastic collision: excited atom is hit by a particleor atom which then gains energy from the the collisionforbidden transitions – special form of radiative de-excitation – longlifetimes since they violate quantum mechanics rules to firstorder – have to proceed in a more complicated way which takesmore time. Observation of these implies low temperature andlow density of the region. Otherwise collisions would de-excitethe atoms much sooner.generally only seen in astrophysics!
  20. 20. 20−=−=== 222211111abababababnnRnnhcRckυλIonizationbound electrons can be liberated from the atom if enough energyis supplied (by a photon or collision)E > ∆E (binding energy)X is an atomX + energy  X++ e-ion electronNomenclature used: hydrogen neutral H or HIionized H+or H IIoxygen neutral Oionized O+or O IItwice ionized O++or O III++ etc is cumbersome after 3 or 4 electrons have been removed (atoms can beEna = ∞
  21. 21. 21Energy needed to ionize is greater than or equal to the energy state of the atompotentialionizationthecalledisenergyminimumTheenergykineticaselectronby theoffcarriedisexcesstherequired,minimuman thegreater thisEIf)()(n tostatefromgoenergy toNeed∆−∞>∆∞= νΕΕΕνfluxwavelengthfluxwavelengthspectrum at source spectrum after absorberλ thresholdfor λ < λ threshold E > IP (ionization potential)so absorption occurs at all wavelengths – one gets a broad depletioninstead of an absorption line
  22. 22. 22Emission continua exist by inverse analogy; if there is a plasma(ions plus electrons) some recombination can occur if the electronemits a photon of E = KE + IPKE = electron’s kinetic energyIP = ionization potential of the level into whichthe electron will fall (not necessarily the ground state)

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