The Quantum Revolution

Quantum mechanics evolved because physicists thought they should know more about light. Quantum mechanics essentially laid to rest the concept of the static electron.

Physicists knew that light behaves as a wave. Waves bend around obstacles in their path and waves interfere with each other. If they are out of phase they cancel each other out to create a calm, if they are in phase they combine to form larger waves.

All types of electromagnetic radiation move through a vacuum at a speed of 3.00 x 10 8 m/s, the speed of light (c).

Waves A cross section of a wave shows that it is periodic. The pattern of peaks and troughs repeats at regular intervals. Wavelength ( ) is the distance between successive peaks or troughs. Frequency ( ) is the number of complete waves that pass a given point each second.

Waves

The relationship between frequency and wavelength is expressed by the following: c = is expressed in m is expressed in cycles per second or Hertz

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The yellow light given off by a sodium vapor lamp used for public lighting has a wave- length of 589 nm. What is the frequency of this radiation? An FM radio station broadcasts at a frequency of MHz. Calculate the wavelength of this radiation.

What is the frequency of an electromagnetic wave that has a wavelength of 4.55 x m? What is the energy of a quantum of visible light having a frequency of 5.45 x s -1 ? What is its wavelength?

Planck’s Contribution Physicists tried to explain the white light of a light bulb and the red glow of a stove burner using classical physics. They were unsuccessful in their attempts. Planck suggested that energy can be released or absorbed by atoms only in chunks of some minimum size. Planck used the term quantum.

Planck proposed that the energy, E, of a quantum equals a constant times the frequency. E = h h = Planck’s constant = 6.63 x Joule seconds

Calculate the energy of a photon with a frequency of 5.09 x s -1. Calculate the energy of blue light with a wavelength of 485 nm.

When radiation is separated into its different wavelength components, a spectrum is produced.

To explain the line spectrum of hydrogen, Bohr made the following assumptions: 1.Electrons can only move in orbits of certain energies. 2. An electron in a permitted orbit is in an allowed energy state and will not radiate energy. 3. Energy is only emitted or absorbed by an electron when it changes from one allowed state to another.

Matter Waves Depending on experimental circumstances, radiation appears to have either a wavelike or particlelike character. deBroglie suggested that matter could show the properties of a wave. The wavelength of an electron depends on its mass and velocity.

Heisenberg’s Uncertainty Principle There is a limitation on how precisely we can know both the location and the momentum of an electron. It is not appropriate to imagine that electrons move in well-defined circular orbits around the nucleus.

Wave Mechanics Quantum mechanics is used to determine the allowed electron energy states of the hydrogen atom. The energy of an electron is a combination of its potential energy (due to its attraction to the nucleus) and its kinetic energy. Quantum mechanics imposes wave properties on the electron.

Schrödinger’s Wave Equation  Incorporates the wave behavior of the electron.  Leads to a set of solutions that describe the allowed energy states of the electron.  These solutions are represented by the symbol  and are called wave functions.

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Orbitals and Quantum Numbers The solution set for the wave equation describes a specific region in space where an electron is likely to be found. These allowed regions are called orbitals. Unlike the Bohr model, QM uses a set of three quantum numbers to describe an orbital.

Quantum Numbers The principal quantum number, n, has values of 1, 2, 3… n corresponds to the energy level and indicates the distance of the electron from the nucleus. As n increases, so does the energy that the electron possesses. n = a horizontal slice of the periodic table.

Orbital Shapes The second quantum number, l, represents the shape of the orbital. These shapes are represented by the letters s, p, d, and f. The third quantum number, m l, represents the orientation of the orbital in space.

The s orbital The lowest energy orbital. Spherically symmetric Holds two electrons Corresponds to the first two columns on the periodic table

The p orbitals Electron density concentrated on sides of nucleus. Three p orbitals exist beginning with n = 2 Can hold 6 electrons. Corresponds to the region on the periodic table beginning with B

The d orbitals No d orbitals exist before n = 3 Can hold a total of 10 electrons Correspond to the transition metal region of the periodic table

The f orbitals No f orbitals exist before n = 4. Can hold a total of 14 electrons. Correspond to the inner transition metal region of the periodic table.

Electron Configurations A short hand designation of the quantum numbers. An element’s electron configuration is a way to describe the location of an atom’s electrons. The Aufbau principle states that electrons will occupy the lowest energy level possible.

orbital filling process

Orbital notation: Used to represent order of placing electrons in orbitals. Lowest energy orbitals are filled first; electrons remain unpaired until forced to pair.

Valence Electrons Determine the chemical properties of elements. Are the outermost electrons in the highest principle energy level. Include s and p electrons. Lewis dot structures are used to represent valence electrons.

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Lithium Z = 3 1s 2 2s 1 1 valence electron ·Li Draw electron dot structures for Mg, S, Br, and Tl.