CHE 110 Chapter Notes - Chapter 7: Standing Wave, Characteristic Energy, Pauli Exclusion Principle
7 May 2018
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Chapter 7: The Electronic Structure of Atoms
I. From Classical Physics to Quantum Theory
1. Quantum Theory Background
1) 1900, young German physicist named Max Planck
2) Analyzed data on the radiation emitted by solids heated to various temperatures
3) Discovered that atoms and molecules emit energy in discrete quantities
4) Physicists had always assumed that energy is continuous, meaning that any amount of energy
could be released in a radiation process
5) Quantum Theory turned physics upside down
2. Quantum Theory Terminology
1) Quanta
1. Discrete quantities
2) Wave
1. A vibrating disturbance by which energy is transmitted
2. Speed depends on type of wave and the nature of the medium through which the wave is
traveling
3) Wavelength (lambda)
1. The distance between identical points on successive waves
4) Amplitude (nu)
1. Vertical distance from the midline of a wave to the peak o the trough
5) Speed Equation
1. Equation
2. Variables
1) - the length of a wave; distance/wave
2) - number of waves that pass any reference point per unit of time; waves/time
3. Units
1) Wavelength is usually expressed in units of meters, centimeters, or nanometers
2) Frequency is measured in hertz (Hz), where 1 Hz = 1 cycle/s
3. Electromagnetic Radiation
1) Types of Waves
1. Water waves
2. Sound waves
3. Light waves
2) James Maxwell (1873) proposed that visible light consists of electromagnetic waves
1. Theory Significance
1) Provides a mathematical description of the general behavior of light
2) Model accurately describes how energy in the form of radiation can be propagated
through space as vibrating electric and magnetic fields
3) Electromagnetic Wave
1. Contains an electric field component and a magnetic field component
1) Two components have the same wavelength, frequency, and speed
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2) Travel in mutually perpendicular planes
2. Waves travel 3.00 x 108 meters per second (or 186,000 miles per second) in a vacuum
1) Speed differs from one medium to another but not enough to distort calculations
significantly
4) Electromagnetic Radiation
1. The emission and transmission of energy in the form of electromagnetic waves
5) Assigning Symbols
1. Use the symbol c for the speed of electromagnetic waves (light)
2. Wavelength of electromagnetic waves is usually given in nanometers (nm)
6) Rearrange Speed Equation
1. Given the wavelength of an electromagnetic wave, asked to calculate its frequency
2. Replace u with c (speed of light)
3. Solve for v
4. Wavelength, Frequency, and Radiation Type
1) Long radio waves
1. Emitted by large antennas (i.e. broadcast station)
2) Short visible light waves
1. Produced by the motions of electrons within atoms and molecules
3) Shortest waves
1. Associated with (gamma) rays
2. Result from changes within the nucleus of an atom
4) Relationships
1. The higher the frequency, the more energetic the radiation
2. UV radiation, X-rays, and (gamma) rays are high-energy radiation
5. Planck’s Quantum Theory
1) Trying to Explain Behavior
1. Measurements taken at the end of the 19th century showed that the amount of radiant
energy emitted by an object at a certain temperature depends on its wavelength
2. Attempts to account for this dependence in terms of established wave theory and
thermodynamic laws were only partially successful
1) One theory explained short-wavelength dependence but failed to account for the
longer wavelengths
2) Another theory accounted for the longer wavelengths but failed to explain the shorter
wavelengths
3. Something fundamental was missing from the laws of classical physics
2) Planck’s Solving
1. Assumption of Classical Physics
1) Atoms and molecules could emit or absorb any arbitrary amount of radiant energy
2. Planck’s Theory
1) Atoms and molecules could emit or absorb energy in only discrete quantities, such as
small packages or bundles
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1. Energy is always emitted in integral multiples of hv, such as 2hv, 3hv, etc. and
never for numbers with decimals such as 1.67hv or 3.33hv
2) Quantum – the smallest quantity of energy that can be emitted or absorbed in the
form of electromagnetic radiation
3. Equation
1) E = energy
2) h = Planck’s constant 6.63 x 10-34 J
3) v = frequency of radiation
II. The Photoelectric Effect
1. 1905 – Albert Einstein
1) Einstein used the quantum theory presented by Planck to solve another mystery in physics
2. The Photoelectric Effect
1) A phenomenon in which electrons are ejected from the surface of certain metals exposed to light
of at least a certain minimum frequency, called the threshold frequency
1. Number of electrons ejected was proportional to the intensity (brightness) of the light, but
the energies of the ejected electrons were not
2. Below the threshold frequency, no electrons were ejected no matter how intense the light
3. Could not be explained by the wave theory of light, so Einstein made an assumption
1) Suggested that a beam of light is really a stream of particles
2) Photons – particles of light
3) Using Planck’s quantum theory of radiation as a starting point, Einstein deduced that each
photon must possess energy E, given by the equation:
1. E = energy
2. h = Planck’s constant 6.63 x 10-34 J
3. v = frequency of radiation
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III. Bohr’s Theory of the Hydrogen Atom
1. Emission Spectra
1) Definition
1. Either continuous or line spectra of radiation emitted by substances
2) Emission spectra of a substance can be seen by energizing a sample of material with thermal
energy or some other form of energy
1. Red-hot or white-hot iron bar
1) Produces a characteristic glow when freshly removed from a high temperature source
2) Visible glow is the proportion of its emission spectrum sensed by the eye
3) Warmth of the same iron bar represents another portion of its emission spectrum: the
infrared region
2. Common Feature to the Emission Spectra of the Sun and a Heated Solid
1) Both are continuous
2) All wavelengths of visible light are represented in the spectra
3. Gas Phase
1) Do not show a continuous spread of wavelengths from red to violet
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