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This chapter explores the electronic structure of atoms, including the distribution of electrons, their energies, and the analysis of light absorbed or emitted by substances. Topics include the wave nature of light, quantized energy and photons, line spectra, the Bohr model, and the wave nature of matter.
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The electronic structure of an atom refers to its number of electrons, how these electrons are distributed around the nucleus, and to their energies. • Much of our understanding of the electronic structure of atoms has come from the analysis of light either absorbed or emitted by substances.
6.1 The Wave Nature of Light • To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation (EMR). • Because EMR carries energy through space, it is also known as radiant energy. • There are many forms of EMR, to include visible light, radio waves, infrared waves, X-rays, etc. (See fig 6.4). • All EMR consists of photons, the smallest increments of radiant energy.
Different forms of EMR share characteristics: • All have wavelike characteristics (much like waves of water). • The distance between corresponding points on adjacent waves is the wavelength(). • The amplitude – or, maximum extent of oscillation of the wave -- is related to the intensity of the radiation
The number of waves passing a given point per unit of time is the frequency (). • For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency.
Electromagnetic Radiation Spectrum • All EMR moves through travels at the same velocity: the speed of light (c), 3.00 108 m/s. • Therefore, c =
As you can see from the electromagnetic spectrum, there are many forms of EMR. • The difference in the forms are due to their different wavelengths, which are expressed in units of length. • Wavelengths vary from10-11 m to 103 m. • Frequency is expressed in cycles per second, also called a hertz. • Units of frequency are usually given simply as “per second,” denoted as s-1 or /s. As in 820 kilohertz (kHz), written as 820,000 s-1 or 820,000/s • See Table 6.1 for types of radiation and associated wavelength.
6.2 Quantized Energy and Photons • The wave nature of light does not explain how an object can glow when its temperature increases. • Max Planck explained it by assuming that energy comes in packets called quanta.
Einstein used this assumption to explain the photoelectric effect. • When photons of sufficiently high energy strike a metal surface, electrons are emitted from the metal. • Electrons are not emitted unless photons exceed a certain minimal energy. • E.g., light with a frequency of 4.60 x 1014 s-1 or greater will cause cesium atoms to emit electrons, but light of lower frequency has no effect. • He concluded that energy is proportional to frequency: E = h where h is Planck’s constant, 6.626 10−34 J-s.
Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light: c = E = h
6.3 Line Spectra and the Bohr Model Another mystery involved the emission spectra observed from energy emitted by atoms and molecules.
One does not observe a continuous spectrum, as one gets from a white light source. • Only a line spectrum of discrete wavelengths is observed.
Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: • Electrons in an atom can only occupy certain orbits (corresponding to certain energies). • Electrons in permitted orbits have specific, “allowed” energies; these energies are not radiated from the atom. • Energy is only absorbed or emitted in such a way as to move an electron from one “allowed” energy state to another; the energy is defined by E = h
1 nf2 ( ) - E = −RH 1 ni2 • The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation: where RH is the Rydberg constant, 2.18 10−18 J, and ni and nf are the initial and final energy levels of the electron.
Limitations of the Bohr Model • The Bohr model explains the line spectrum of the hydrogen atom, but not (accurately) the spectra of other atoms. • Also, the Bohr model assumes the electron behaves as a particle. • Electrons also have wave-like properties. • However, Bohr model is important because: • It shows electrons as existing in only certain discrete energy levels, which are described by quantum numbers. • Energy is involved in moving an electron from one level to another.
h mv = 6.4 The Wave Nature of Matter • In the years after development of the Bohr model, the dual nature of light became known: EMR (i.e., light) can exhibit both particle-like (photon) character as well as wave-like character. • Louis de Broglie (in 1924) extended this idea to electrons, proposing a relationship between the wavelength of an electron (or any other particle), its mass, and velocity: • h = Planck’s constant
h 4 (x)(mv) The Uncertainty Principle • Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely is its position known: • In many cases, our uncertainty of the whereabouts of an electron is greater than the size of the atom itself! • In sum, you cannot accurately know both an electron’s position and momentum at the same time.
