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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?
Atomic Spectroscopy Explained
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
• ΔEatom = -ΔEphoton
ΔE = -2.18x10-18 J ((1/nf2) – (1/ni2))
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.
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
(6.626X10-34 J s)(2.998X108 m/s)
λ = ------ = --------------------------------------------- = 3.97X10-7 m or 397 nm
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
• 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