Chapter 17: The Wave Model of the Atom

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We now put together what we have learned about the atom and wave-particle duality into a model of the atom, which we call the "wave model." First, more about waves. "Standing waves" are stationary-appearing patterns in a vibrating medium arising from interference of two waves moving through the same space. Points of the medium which are permanently at rest are called (nodes, antinodes?) . Points of maximum oscillation are called (nodes, antinodes?) . Standing waves can occur in a stretched string if it is plucked. If the ends of the string are fixed, the ends must be (nodes, antinodes?) . Only certain wavelengths (frequencies) produce standing waves in a string with both ends fixed. These are called the "natural wavelengths" or "natural frequencies" of the string. Standing waves may occur in two- and three-dimensional media as well as in a one-dimensional string. The modified solar-system model of Neils Bohr was remarkably successful in explaining the discrete color spectrum of light, but it still suffered from several problems: Why are only certain orbits possible? How does the atom remember what its orbits are like? Why don't the electrons in accelerated orbits in the undisturbed atom radiate away their energy as electromagnetic radiation? The answer: There are no at all! There are only "orbitals." Orbitals are standing waves of . The law of nature that governs these orbitals is Schroedinger's Equation and it only allows a set of discrete standing wave patterns (like the discrete set of patterns of standing waves on a string). The undisturbed atom doesn't radiate electromagnetic energy as it would from an accelerated electron in an orbit because when it is "unwatched," the electron cannot be thought of as an accelerated particle in an orbit. There is only the orbital, the standing wave of probability which tells us the probability of finding the electron at particular places in space. There are different kinds of orbitals. (s,p,d?) orbitals are shaped like a sphere. orbitals are shaped like dumbbells. "d" orbitals are more complicated; some are shaped like a 4-leaf cloverleaf. There is exactly one "variety" of s-orbital, but there are (number?) varieties of the p-orbital, and varieties of the d-orbital. Rule #1: Electrons in atoms have (more, less?) energy than they have when they are free of the atom. Rule #2: No more than (number?) electrons can occupy identical orbitals in the same space at the same time. This important principle is called the (Uncertainty, Exclusion?) Principle. If two electrons occupy identical orbitals, i.e. same space at the same time, they must differ in a characteristic called . Rule #3: As a rule, electrons in different discrete orbitals have different discrete . In an atom, the different energies that electrons might have are called "energy levels." Energy levels might be occupied by electrons and they might be unoccupied. Energy levels that are close together belong to the same . These are numbered 1, 2, 3, ... from lowest energies to higher energies. Within a shell, electrons are in orbitals. The are labelled s, , , , etc. The Exclusion Principle (does, does not?) apply to electrons in the same orbital, but in different shells because similar orbitals in different shells differ in size and do not try to occupy exactly the same space at the same time. In a given shell and a given orbital, an electron has one of two possible spins. One of these is "spin-up" and the other is "spin-down." Rule #4: In Shell 1, only the -orbital is possible. In Shell 2, the s- and -orbitals are possible. In Shell 3, -, p-, and -orbitals are possible. Etc. A hydrogen atom is the simplest atom. It has just one (electron, energy level?) . In an unbumped, unexcited hydrogen atom, the lone electron is in shell (number?) , in a(n) (s, p, d, f?) and may be either spin-up or spin-down. The spacing (in energy) between the energy levels (is, is not?) uniform (i.e., equally). As levels in an atom get higher and higher in energy they get closer together.

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