ch. 7: the quantum-mechanical model of the...
TRANSCRIPT
-
Ch. 2: The Quantum-
Mechanical Model of the Atom
Dr. Namphol Sinkaset
Chem 200: General Chemistry I
-
I. Chapter Outline
I. Introduction
II. The Wave Nature of Light
III. The Particle Nature of Light
IV. Bohr Model of the Atom
V. The Wave Nature of Matter
VI. The Quantum Mechanical Atom
-
I. Where are the Electrons?
• Where do more p+ go?
• What is the organization of the e- in the
atom?
• Since e- are responsible for chemical
reactivity, it’s an important question.
• Answer came from studying light.
-
II. Visible Light
• Visible light is a form of electromagnetic (EM)
radiation.
• All EM radiation consists of energy
propagated by electric and magnetic fields.
-
II. EM Radiation
• Different wavelengths indicate different types of EM radiation.
• Three characteristics of waves: amplitude, frequency, and wavelength
• Frequency and wavelength are related by the speed of light, 2.9979 x 108 m/s.
• c = nl
-
II. Visible Light
• White light is comprised of different colors.
• We observe the reflected light of objects.
-
II. The Electromagnetic Spectrum
-
II. Wave Properties of Light
• Waves of all types have certain
properties.
• interference: waves combine in different
ways to yield new waves
• diffraction: waves bend around
obstacles or slits that are similar in size
to their wavelength
• interference patterns: combo of both
-
II. Interference
-
II. Diffraction
-
II. Interference Patterns
-
III. Light as Particles?
• Everyone was happy with the wave explanation of light until puzzling observations were made.
• Explanations of these observations were put forth by people such as Planck, de Broglie, and Einstein.
• The photoelectric effect was the observation that really started the downfall classical EM theory.
-
III. The Photoelectric Effect
• No matter how bright the light, if it wasn’t the right n, it wouldn’t work!
• In 1905, Einstein proposed light had particles(!) of energy (photons). Ephoton = hn
-
IV. Electrons in Atoms
• The particle nature of light broke the
barrier between purely wave-like
behavior of EM radiation and small
particles in the atom.
• It was thought that particles in the atom
followed Newton’s laws of motion.
• New observations suggested matter
could behavior like waves!
-
IV. Atomic Line Spectra
-
IV. The Rydberg Equation
• People could not explain atomic spectra, but
in 1888, Rydberg presented an empirical
equation to predict the lines.
R = 1.097 x 107 m-1 and n2 > n1 (integers)
-
IV. Sample Problem 2.1
• If a ground state electron in a hydrogen
atom absorbs 2.10 x 10-18 J of energy,
to what energy level does it get excited?
Note that h = 6.626 x 10-34 J·s, c =
2.9979 x 108 m/s, and R = 1.097 x 107
m-1 .
-
IV. Bohr Model of the Atom
• Niels Bohr combined the ideas of Planck and Einstein for his model of H
1) H atom only has certain allowable energy levels – each level is a fixed circular orbit of e- around the nucleus, called a stationary state.
2) The atom doesn’t radiate energy if e-stays in its orbit (violates classical physics).
3) When e- changes orbit, it must emit or absorb energy to do so. The energy is exactly equal to the difference in energy of the orbits.
-
IV. Bohr Model of the Atom
-
V. Wave-Particle Duality
• Big conclusion: waves (EM radiation) can act
like a particle!
• In 1924, de Broglie proposed that matter (an
electron) must also be able to act like a wave!
• This idea was confirmed by experiments in
1927.
-
V. Particles as Waves, Really?
• If particles can act as waves, they should
show diffraction behavior…
-
V. The Wavy Electron
• Three important things arise from the
wave nature of electrons:
The de Broglie wavelength
The uncertainty principle
Indeterminacy
-
V. The de Broglie Wavelength
• The wavelength of a particle is related
to its kinetic energy.
• The faster it moves, the shorter its
wavelength.
-
V. Wavelengths of Particles
-
V. Behavior and Observation
• Wave-particle duality is a hard concept
to grasp.
• If an electron interferes with itself by
going through both slits, can’t we test
that?
• We can try…
-
V. Observation Changes the Result
• Electron detected through one slit or the
other, never both at once.
• Detection leads to disappearance of
interference pattern.
-
V. Finite Observation Powers
• We can’t observe both the particle
nature and the wave nature of the
electron at the same time.
• They are complementary properties; the
more we know about one, the less we
know about the other.
• Thus, when we observe, we see it as a
wave or a particle, not both.
-
V. Heisenberg Uncertainty
Principle
-
V. Probability Distribution Maps
• For normal size things, a moving particle has a definite location @ any instant.
• Electrons don’t behave this way, so you can’t know its exact location - indeterminacy.
• In chemistry, that means that in an atom, it’s impossible to know exactly where the e- are.
-
VI. A New Model of the Atom
• If velocity and position are
complementary properties, then energy
and position are as well.
• This means, we can know energy of an
electron in an atom, but not its position.
• Schrödinger develops his equation for
an electron in an atom in 1925.
-
VI. The Schrödinger Equation
• Y is the wave function of the e-, and it describes the state of the e- wave.
• The equation has multiple solutions, and each solution is a different wave function often referred to as an atomic orbital. The orbital is a map that shows where electron can be found.
• e- do not occupy atomic orbitals like orbits – AN ATOMIC ORBITAL IS AN ELECTRON!!
-
VI. Quantum Numbers
• A solution of the wavefunction (Y) yields 3 quantum numbers.
1) principal quantum number (n): a positive integer (1, 2, 3, etc.) that indicates the overall size and energy of the orbital
2) angular momentum quantum number (l): an integer from 0 to n-1 that’s related to the shape of the orbital
3) magnetic quantum number (ml): an integer from –l to +l that indicates orientation of the orbital relative to the nucleus
-
VI. Hierarchy of Quantum Numbers
-
VI. Quantum Number Terminology
• level: the n value gives the atom’s energy
levels or shells
• sublevel: each level contains sublevels or
subshells which have different shapes, each
with a letter designation
l = 0 is “s”
l = 1 is “p”
l = 2 is “d”
l = 3 is “f”
• orbital: each allowed combo of n, l, ml values
specifies one of the atom’s orbitals
-
VI. The 1s Orbital
-
VI. The 2s and 3s Orbitals
-
VI. The 2p Orbitals
-
VI. The 3d Orbitals
-
VI. The 4f Orbitals
-
VI. Orbital Phase
• Orbitals are 3-D waves, so they exhibit
phase just like 1-D waves.
• This becomes important in bonding.
-
VI. Energy Levels of H Atom
• For H atom, energy
states depend only
on n.
• For any other
element, energy
state depends on n
and l.