Electromagnetic Radiation and Atomic Structure

EMR and Properties of LightBohr Model of the Atom & Atomic Line SpectraQuantum TheoryQuantum Numbers, Orbitals and Nodes

Chapter 6 will be on Exam #3Chapter 6 OWL will be due 10/30/11Note 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 EffectEinstein 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

2H

nR

E

• Electrons can change energy levels also!

• For a hydrogen electron the energy change is given by

2

i2

fH

11Δ

nnRE

ifΔ EEE

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.

n 2

i2

fH

11nn

Rh

constant sPlanck'

Δ electron

n

h

hEEphoton

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:

sJ10x6.626

λ

34

hmvh

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.

4π))(Δ(Δ

hpx

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

• ml defines orientation of an orbital in 3 dimensional space• X, Y, Z coordinates or axis

• ml goes 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