Problem Solving hints
•Use white AP constant sheet
•hc = 1.99 10-25 Jm = 1.24 103 eVnm
•h = 6.63 10-34 Js = 4.14 10-15 eVs
•1 eV = 1.6 10-19 J
•1 amu = 1 u = 1.66 10-27 kg = 931 MeV/c2
Davisson-Germer Experiment• 1925 - scattering electrons off of poly-
crystalline nickel targets
• explosion in lab
• data changed - nickel had formed large crystals
• diffraction pattern seen -- electron waves diffracting
• electrons with momentums comparable to X-rays diffract the same
Heisenberg’s Uncertainty Principle
px h/(2)
Et h/(2)
Experiments to determine structure of atoms
• Rutherford -particle scattering experiment
• Characteristic line spectra (Lyman, Balmer, Paschen series of lines in hydrogen)1/ = R(1/12 - 1/n2) n = 2, 3, 4, …1/ = R(1/22 - 1/n2) n = 3, 4, 5, …1/ = R(1/32 - 1/n2) n = 4, 5, 6, …
Rutherford experiment
There must be a dense central part surrounded by a lot of empty space
Line Spectra
Bohr model
• Electrons move in specific orbits with quantized angular momenta of
Ln = nh/(2)
• Leads to wavelength formula
1/ = K(1/nf2 - 1/ni
2)which agrees with observed lines from
the Lyman, Balmer, Paschen, etc. series
Bohr:Bohr:Electrons exist in “stationary states.”Only specific orbitsare allowed -- electron does not move between states, it “jumps.”
For hydrogen and hydrogen-like ions,
En = (-13.6eV)Z2/n2
where Z is atomic number and n is energy level
deBroglie:deBroglie:Electron waves around the nucleus can only exist in certain orbits (“standing waves”)
Current view• Electrons around
nucleus exist in “orbitals”
• Orbitals are probability clouds
• No two electrons in the same atom can have all of the same quantum numbers (waves interfere)
Energy levelsEnergy levels in an atom are not evenly spaced. The difference between the n = 1 and n = 2 level isgreatest.The energy levels getcloser and closer together for higher n.Using Bohr’s formula, canyou determine the energyof a photon released when an electron drops from n = 2 to n = 1 in a H-atom?
Can you determine the minimum energy neededto free an electron from the hydrogen atom if it starts in the ground state? That would be the same asmoving it from n = 1 to n = infinity…This energy is called the ionization energyionization energy.
What about the energy needed to free an electron from an O7+ ion? Why can’t we use Bohr’s formula for a normal oxygen atom?
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