Atomic Theory and Spectral Lines Chemical Physics matter

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Atomic Theory and Spectral Lines -- Chemical Physics matter is composed of atoms –

Atomic Theory and Spectral Lines -- Chemical Physics matter is composed of atoms – size ~ 10 -8 cm - density ~ 1023/cm 3 109 different atoms identified - 92 stable (occur naturally) - 17 transuranic (created artificially) pattern found by Mendeleev in 1869 (periodic table) led to our currently accepted model of atoms: - an atoms is a nucleus (10 -14 m) surrounded by a cloud of electrons (10 -10 m) - 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) 67

reminder: office hours next week only tuesday 2 -4 68

reminder: office hours next week only tuesday 2 -4 68

periodic table of the elements: in astrophysics everything except H and He is considered

periodic table of the elements: in astrophysics everything except H and He is considered a metal 69

Isotopes adding neutrons to a nucleus (or taking them away) does not affect the

Isotopes adding neutrons to a nucleus (or taking them away) does not affect the nuclear charge (or number of electrons) so chemically the atom is not different it does affect the nuclear properties (stability etc) - specify an element by Z - specify an isotope by A a complete description requires both Z is implied by the historical name eg 14 C A = 14 Z = 6 - carbon with 2 extra neutronss hydrogen deuterium tritium p+e p+n+n+e 1 1 H 2 H 3 H (in heavy water) these are all isotopes of hydrogen but are not separate elements they have the same chemical properties but different nuclear properties (therefore things like nuclear burning in stars are different). 70

the number of neutrons is not arbitrary - too different from the proton number

the number of neutrons is not arbitrary - too different from the proton number results in instability Z = protons too many neutrons A – Z = neutrons 71

Bohr-Rutherford Model of the Atom Rutherford (Mc. Gill!) discovered the nucleus in experiments where

Bohr-Rutherford Model of the Atom Rutherford (Mc. Gill!) discovered the nucleus in experiments where he 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 nucleus orbited by electrons like planets around the sun - mostly space - the electrostatic (Coulomb) force between the electrons and the nucleus was the ‘gravity’ eg hydrogen e p major problem with this idea: - electrons which go in circles are accelerating - accelerated charges radiate energy - therefore electrons will lose energy and spiral into the nucleus – all matter collapses in an instant - also doesn’t explain discrete lines in spectra 72

Bohr’s hypothesis: classical physics does not apply: quantum theory electrons only orbit in particular

Bohr’s hypothesis: classical physics does not apply: quantum theory electrons only orbit in particular orbits with L (angular momentum) equal to π where n is an integer and h is Planck’s constant in this case, with centripetal force equaling the Coulomb force we have: but so solving for r we get: is a constant for a given atom is the principal quantum number the radius of the orbit increases as the square of the principal quantum number 73

another route to Bohr’s quantum condition: wave/particle duality wavelength of an orbiting electron (non-relativistic)

another route to Bohr’s quantum condition: wave/particle duality wavelength of an orbiting electron (non-relativistic) p=momentum circumference must be an integer number of wavelengths (think standing wave) the only orbits which can exist have using the equality of centripetal and Coulomb forces we get 74

energy of an electron at radius r kinetic potential use (negative – electrons are

energy of an electron at radius r kinetic potential use (negative – electrons are bound) has the tightest binding (E is large and negative) all orbits are bound continuum of unbound states 75

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Bohr part II: (a) radiation in the form of a single discreet quantum (photon)

Bohr part II: (a) radiation in the form of a single discreet quantum (photon) is emitted or absorbed as the electron jumps from one orbit to another (b) the energy of the radiated photon equals the energy difference between orbits photons are emitted when the electron goes from a higher energy orbit (na) to a lower energy orbit (nb) (na > nb) E(na) = E(nb) + hn photons are absorbed to cause electrons to go from a lower energy orbit to a higher energy orbit (nb > na) E(nb) + hn = E(na) frequency of emitted (or absorbed) photon: nab = (E(na) - E(nb) )/h na is not necessarily nb +/- 1 n = 1 is called the ground state – lower energy states are not possible 77

Hydrogen spectral lines 78

Hydrogen spectral lines 78

remember: E=hn eg Hydrogen Z=1 energy of the nth level R’ = 2. 18

remember: E=hn eg Hydrogen Z=1 energy of the nth level R’ = 2. 18 x 10 -18 Joules = 13. 6 e. V (Rydberg energy) this is often expressed in terms of wavelengths n = c /l k = 1/l = wave number R = 10. 97 mm-1 (Rydberg constant) na and nb are two levels in the atom n a > nb for every nb there is an infinite series of nas na = nb+1, nb+2, nb+3. . . the series are named after the people who discovered them Lyman Balmer Paschen Brackett Pfund nb = 1 nb = 2 nb = 3 nb = 4 nb = 1 (ultraviolet) (found first since it is visible) 79

Balmer series: nb = 2 na = 3 na = 4 na = 5

Balmer series: nb = 2 na = 3 na = 4 na = 5 l = 656. 3 nm Ha Hb Hg historical names Lyman series: nb = 1 na = 2 na = 3 na = 4 l = 121. 6 nm La Lb Lg can also have these lines in absorption 80

Energy Levels unbound states (continuum) E = R’ = 13. 6 e. V excited

Energy Levels unbound states (continuum) E = R’ = 13. 6 e. V excited states ground state Each atom has a characteristic energy level diagram (good for identifying which atom it is) 81

Excitation raise from na to nb with na < nb radiative excitation - absorption

Excitation raise from na to nb with na < nb radiative excitation - absorption of a photon of the correct energy - produces absorption lines source spectrograph absorber flux wavelength without absorber one gets a continuous spectrum wavelength with absorber one gets a spectrum with absorption lines 82

excited states are unstable (10 -8 seconds lifetime, typically) so why don’t the atoms

excited states are unstable (10 -8 seconds lifetime, typically) so why don’t the atoms in the absorber de-excite with no loss of photons and hence no absorption lines? two reasons: geometry – decays photons go in all directions so loss of intensity initial flux re-emitted flux combinatorics – several de-excitation paths usually available l 2 l 1 l 3 absorb l 1 emit l 2 + l 3 83

collisional excitation - no photons are absorbed; inelastic collisions of the atom with other

collisional excitation - no photons are absorbed; inelastic collisions of the atom with other atoms or electrons (Coulomb interaction) - atom gains some of the projectile’s kinetic energy and has its energy level raised e vi e vf g hn = 1/2 m (vi 2 - vf 2) the atom eventually de-excites through photon emission we see ‘emission lines’ 84

de-excitation radiative – emission of photon(s) 10 -8 seconds typically collisional – super-elastic collision:

de-excitation radiative – emission of photon(s) 10 -8 seconds typically collisional – super-elastic collision: excited atom is hit by a particle or atom which then gains energy from the collision forbidden transitions – special form of radiative de-excitation – long lifetimes since they violate quantum mechanics rules to first order – have to proceed in a more complicated way which takes more time. Observation of these implies low temperature and low density of the region. Otherwise collisions would de-excite the atoms much sooner. generally only seen in astrophysics! 85

Ionization bound electrons can be liberated from the atom if enough energy is supplied

Ionization bound electrons can be liberated from the atom if enough energy is supplied (by a photon or collision) E > DE (binding energy) E X is an atom X + energy X+ + eion Nomenclature used: na = ∞ electron hydrogen neutral ionized H or HI H+ or H II oxygen neutral ionized twice ionized O O+ or O II O++ or O III ++ etc is cumbersome after 3 or 4 electrons have been removed (atoms can be 86 fully stripped) – Roman Numerals are preferred (eg Fe IX)

Energy needed to ionize is greater than or equal to the energy state of

Energy needed to ionize is greater than or equal to the energy state of the atom spectrum at source flux spectrum after absorber flux wavelength l threshold wavelength for l < l threshold E > IP (ionization potential) so absorption occurs at all wavelengths – one gets a broad depletion instead of an absorption line 87

Emission continua exist by inverse analogy; if there is a plasma (ions plus electrons)

Emission continua exist by inverse analogy; if there is a plasma (ions plus electrons) some recombination can occur if the electron emits a photon of E = KE + IP KE = electron’s kinetic energy IP = ionization potential of the level into which the electron will fall (not necessarily the ground state) 88