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6.1.2.       Atomic Theory <CJ chap 30  >

6.1.2.1. Discussion

6.1.2.1.1.     The Thompson model of the atom held that positive charge was spread out like a pudding.

6.1.2.1.2.     In 1911 Rutherford scattered a particles from gold foil and showed the nuclear size was ~1E-15m

6.1.2.1.3.     This raised the problem of why the electron did not spiral into the center with infinite radiation

6.1.2.1.4.     Atomic spectra was observed at discrete frequencies rather than continuous emissions

6.1.2.1.4.1. This implied discrete orbits for the electron but what equations would make this work  

6.1.2.1.5.     In 1913 Bohr proposed his model of the atom with quantized orbits and discrete transitions

6.1.2.1.6.     The Bohr model assumes that angular momentum is quantized.

6.1.2.1.7.     The Pauli exclusion principle prevents two electrons from being in the same shell simultaneously

6.1.2.1.8.     Einstein predicted that if an excited atom is hit with a photon of the decaying energy then ..

6.1.2.1.8.1. rather than being absorbed, the photon will stimulate the emission of another photon in phase

6.1.2.1.8.2. This principle is the basis for the operation of a laser

6.1.2.1.8.3. LASER means Light Amplification by Stimulated Emission of Radiation

6.1.2.1.9.     X Rays were discovered by Wilhelm Roentgen by hitting electrons on a metal target

6.1.2.2. Mathematical

6.1.2.2.1.     Atomic spectra was observed to obey: 1/l = R(1/n12 – 1/n22) with terminology of:

6.1.2.2.1.1. n1 = 1  Lyman series ,  n1 = 2, Balmer series, n1 = 3 Paschen series …

6.1.2.2.1.2. Bohr’s model of quantized orbits assumed a quantized angular momentum of Ln=n h/(2p), n= 1,2

6.1.2.2.1.2.1.     This assumption in addition to the classical equations gave workable orbits:

6.1.2.2.1.2.2.     One balances Coulomb force with centripetal force:  mv2/r = kZe2/r where Z=# protons

6.1.2.2.1.2.3.     Using these two equations, the radius must be rn = h2 n2 / (4p2kme2Z) =5.29E-11 n2/Z

6.1.2.2.1.2.4.     The electron’s energy is KE+PE = E = (1/2) mv2 –kZe2/r

6.1.2.2.1.2.5.       Thus En = 2p2mk2e4/h2)(Z2/n2)   = -13.6 eV Z2/n2    = -2.18E-18 J Z2/n2

6.1.2.2.1.2.5.1. Note that the factor 13.6 eV is the ionization energy of hydrogen (Z=1 & n=1)

6.1.2.2.1.2.6.     Since 1/l = f/c  = E/hc then 1/l = 2p2mk2e4/(ch3) (Z2/n2)

6.1.2.2.1.3. De Broglie: If the electron ‘wave’ had to meet constructively with itself then Cir. = 2pr = n l = n h/p

6.1.2.2.1.3.1.     Consequently we get quantized angular momentum as r p = L = n (h/ 2p)

6.1.2.2.2.     The Schrödinger equation solution to the hydrogen atom gives the following energy levels:

6.1.2.2.2.1. The principle quantum number, n = 1, 2, 3, …..

6.1.2.2.2.1.1.     The principle quantum numbers 1, 2, 3,..are denoted by the shell names: K, L, M 

6.1.2.2.2.2. The orbital angular momentum l has the values 0, 1, 2, 3, … (n-1)  where L = ((l( l+1))1/2)h/2p

6.1.2.2.2.2.1.     The orbital angular quantum numbers 0, 1, 2, ..are denoted by the letters s, p, d, f, g, h,

6.1.2.2.2.3. There is also a ‘magnetic quantum number’ that has the values – l, - l+1, … l-1, l  

6.1.2.2.2.3.1.     The magnetic quantum number was seen when levels were split with a magnetic field

6.1.2.2.2.3.2.     It is known to correspond to the z component of the angular momentum Lz

6.1.2.2.2.4. A final splitting of the energy levels occurred due to the z component of the spin of the electron   

6.1.2.2.2.5. The associated counting of levels now exactly counts for the number of electrons in each orbit

6.1.2.2.2.5.1.     The maximum number of electrons in a shell are 2(2 l+1)

6.1.2.2.2.5.2.     The denotation of electrons in a shell is say: 2p5 thus n=2, l =1, and with 5 electrons

6.1.2.2.2.5.3.     Thus the configuration of Carbon (6 electrons) is 1s2 2s2 2p2  

6.1.2.2.3.     Pauli Exclusion Principle: No two identical fermions can occupy the same state at the same time

6.1.2.2.3.1. A Fermion is an elementary particle with a spin of ½, 3/2, 5/2, 7/2, … times h/(2p)

6.1.2.2.3.1.1.     Electrons, protons, neutrons, neutrinos, muons, … are all Fermions

6.1.2.2.3.2. A Boson is an elementary particle with a spin of  0, 1, 2, 3, … times h/(2p) e.g. a photon, pion…

6.1.2.2.3.2.1.     Bosons actually ‘prefer’ to be in the same state rather than being prevented

6.1.2.2.3.3. Without the exclusion principle, all electrons would go to the atoms lowest state & not fill shells

6.1.2.2.3.3.1.     Then without a tendency to fill shells, there would be no chemical bonding, & no biology

6.1.2.2.3.3.2.      

6.1.2.3. Advanced