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?