7.4 The Wave Nature of Matter – 7.5 Quantum Mechanics and the Atom

Electrons (Particles or Waves?) Electrons exhibit both particle and wave nature (wave-particle duality). Heisenberg’s uncertainty principle: we are unable to identify a particles position and velocity at the same time. Since we can not determine the exact location and velocity of an electron at the same time, experimentation has been done over time to identify the most likely places that the electrons exist in an atom. These locations are called orbitals. Schrödinger's equation can be used derive the energies and orbitals of electrons in atoms > Schrödinger equation

Quantum Numbers This slide will give you a brief description of electron quantum numbers: Quantum numbers will not be tested on the AP exam! n = principle energy level l = shape of the orbital up to and including n-1 (0,1,2,3 = s, p, d, f) ml = orientation of the orbital (what axis the orbitals lays on: integers from (+l to –l  L) ms = the electron spin (+1/2 or -1/2)

Atomic Spectroscopy Explained Each wavelength in an emission spectrum corresponds to an electron transition between quantum mechanical orbits. When an atom absorbs energy, what happens to an electron? An electron becomes excited and jumps up to a higher energy level. Can this excitation of an electron happen when the electron absorbs any amount of energy? No, it has to be a specific amount of energy, called a quantum. When is an atom unstable, when its electrons are in their ground state, or when they are in their excited state? Excited.

Atomic Spectroscopy Explained (Continued) When do electrons emit photons (light energy)? After an electron becomes excited and jumps to a higher energy level, the atom becomes unstable. Because of this, the electron tries to immediately relax to a lower energy level and emits a photon of light containing an amount of energy precisely equal to the energy difference between the two energy levels. The change in energy when an electron in a hydrogen atom changes energy levels: ΔE = Ef – Ei or ΔE = -2.18x10-18 J ((1/nf2) – (1/ni2)) ΔEatom = -ΔEphoton

Let’s Try a Practice Problem Determine the wavelength of light absorbed when an electron in a hydrogen atom makes a transition from an orbital in which n=2 to an orbital in which n=7. hc λ = ------ E ΔE = -2.18X10-18 J ((1/nf2) – (1/ni2)) ΔE = (-2.18X10-18 J (1/72)) – (-2.18X10-18 J (1/22)) ΔE = 5.01X10-19 J hc (6.626X10-34 J s)(2.998X108 m/s) λ = ------ = --------------------------------------------- = 3.97X10-7 m or 397 nm E 5.01X10-19J

The Shapes of Atomic Orbitals The shapes of atomic orbitals are important because covalent chemical bonds depend on sharing the electrons that occupy these orbitals. A bond consists of the overlap of atomic orbitals on adjacent atoms. The shape of overlapping orbitals determines the shape of the molecule. There is a lot of information in this chapter that I feel goes beyond the scope of the AP exam, so I tried to condense the necessary information into two PowerPoint presentations.

Pg. 331-332 #’s 74 & 80 (Think about what you are working with in the problems! (moles vs. molecules vs. atoms)) Read 8.1-8.3 pgs. 334-344