**Electromagnetic Radiation and Atomic Structure** EMR and Properties of Light Bohr Model of the Atom & Atomic Line Spectra Quantum Theory Quantum Numbers, Orbitals and Nodes Chapter 6 will be on Exam #3 Chapter 6 OWL will be due 10/30/11 Note that Chapter 6 OWLBook assignments are listed “section by section”, with Section Mastery OWLs after each section.

**Properties of EMR (light) **

**Wavelength (λ) and frequency (n) are related by the wave** speed, which for light is c, the speed of light, 2.998 x 108 m/s. • The speed of light we see here is in a vacuum, but for simplicity (and because the number doesn’t change much in air) we use it for calculations in our atmosphere. • c = n l • Frequency, symbolized by the Greek letter nu, n, is the number of wavelengths that pass a fixed point in one unit of time (usually a second). The unit is 1/S or s-1, which is also called the Hertz (Hz).

**Electromagnetic Spectrum** What are the relationships between wavelength, frequency and energy? Remember, c is constant!

**Photoelectric Effect** • Scientist also realized that light has particle-like properties. • This was studied using the photoelectric effect. The duality of the nature of light (wave versus particle) allows us to consider light as waves or “packets”. • These “packets” of light are known as photons.

**Photoelectric Effect** Einstein proposed that light consists of quanta or particles of electromagnetic energy, called photons. The energy of each photon is proportional to its frequency: E = hn h = 6.626 × 10-34 J s (Planck’s constant)

**Line Spectra and the Bohr Model of the Atom** • When elements are sealed in a tube and a strong electrical voltage is applied, they are excited and emit light. If that light is broken down into its component wavelengths, a line spectrum results.

**Bohr Model of the Atom** • Neils Bohr was able to develop a theory to explain line spectra • This works well for the hydrogen atom but is problematic for more complex elements • He was a pretty smart guy. He’s got his own element, and a Nobel Prize (but he’s dead now). and • Bohr postulated that atoms have very distinct energy levels, and that the light emitted in a line spectrum comes when electrons move from one energy level to another. • Excess energy is given off as light energy • Energy is needed to excite the electrons to different energy levels • This is why the electrical voltage is needed to excite the atoms.

**Energy-Level Postulate** • An electron can have only certain energy values, called energy levels. Energy levels are quantized. • Quantized is an “all or nothing” principle • An energy level exists in one condition (place or energy) and it does not vary at all. • For an electron in a hydrogen atom, the energy is given by the following equation: • RH = 2.179 x 10-18 J • n = principal quantum number

**Electrons can change energy levels also!** • For a hydrogen electron the energy change is given by RH = 2.179 × 10-18 J, Rydberg constant

**If the energy is given off, or absorbed, as a photon of** light, that photons energy is related to DE: • We can now combine these two equations: • The problem with the Bohr model is that it does not explain all behavior, and fails for elements more complex than hydrogen.

**Quantum Theory** • Louis de Broglie proposed that all matter has a characteristic wavelength, sometimes called the de Broglie wavelength. • For objects with large masses, the wavelength is very, very small and not observable. • The wavelength of a particle of mass, m (kg), and velocity, v (m/s), is given by the de Broglie relation:

**The Uncertainty Principle ** • In 1927, Werner Heisenberg showed how it is impossible to know with absolute precision both the position, x, and the momentum, p, of a particle such as electron. • p is momentum, directly proportional to velocity for a fixed mass. • Because p = mv this uncertainty becomes more significant as the mass of the particle becomes smaller. • Basically, it means that for minute object such as electrons it is not possible to know there exact position at any given time. • All we can say is that there are regions where the electron is most likely to be.

**Wave Functions and Quantum Mechanics** • Building on de Broglie’s work, in 1926, Erwin Schrödinger devised a theory that could be used to explain the wave properties of electrons in atoms and molecules. • The branch of physics that mathematically describes the wave properties of submicroscopic particles is called quantum mechanics or wave mechanics. • These wave properties are described by wave functions, and define regions in space (around the nucleus) where electrons are most likely to be found. • These regions are called orbitals!

**Quantum Numbers & Orbitals** • n principle quantum number. It relates to the overall energy-level in an atom. • Integers > 0

**Quantum Numbers & Orbitals** • l ( l ) is the angular momentum quantum number • l defines the shape of the orbitals • Regions where the electrons are likely to be found • l goes from 0 to n-1

**Quantum Numbers & Orbitals** • ml ( ml) is the magnetic quantum number • mldefines orientation of an orbital in 3 dimensional space • X, Y, Z coordinates or axis • mlgoes from –l to 0 to + l, • in whole number intervals

**Quantum Numbers & Orbitals** There is one other important number we will get to in Chapter 7.

**Orbital Energies in H Atoms** Only in hydrogen do all of the orbitals of a given level (n) have the same energy.

**When energy is absorbed…**

**Nodes** • Nodes are regions where there is zero probability in an orbital (subshell) of finding an electron. • There are planar nodes (easier to visualize) and radial nodes (harder to visualize) • All orbitals, except s have planar nodes. • All orbitals can have radial nodes.

**Nodes**