SP02 The Wave-Mechanical Model of the Atom PDF
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These notes provide a high-level summary of the Wave-Mechanical Model of the Atom. It covers topics such as electron waves, orbitals, and the Uncertainty Principle. This is useful for students learning about atomic structure in high school chemistry.
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SCH4U1 SP02 The Wave-Mechanical Model of the Atom As we have seen, light has both wave and particle properties. Although Bohr’s model worked for hydrogen, it could not explain this odd quantum behaviour. In addition, Bohr could not predict the behaviour of atoms with more than 1 ele...
SCH4U1 SP02 The Wave-Mechanical Model of the Atom As we have seen, light has both wave and particle properties. Although Bohr’s model worked for hydrogen, it could not explain this odd quantum behaviour. In addition, Bohr could not predict the behaviour of atoms with more than 1 electron accurately. Other physicists helped solve the mystery of atomic structure: Louis de Broglie (1923) de Broglie considered the wave-particle duality if light and applied it to matter. proposed that electrons exist as “matter waves and developed a mathematical relationship between an object’s mass and its characteristic wavelength: electrons can only “exist” at certain distances from the nucleus corresponding to integer values of the electron’s wavelength (λ, 2λ, 3λ etc.) all matter has both wave and particle properties, but the wave-like properties are more significant for objects of very low mass such as electrons. Erwin Schrodinger (1925) Using de Broglie’s hypothesis of an electron wave, Schrodinger developed a mathematical approach called a wave equation to describe the behavior of electrons around the nucleus. Since the wavelength of an electron must be a whole number, only certain quantized solutions to Schrodinger’s equations are possible. Each possible solution corresponds to the allowed energy level. Three quantum numbers (n, l, ml) are required to describe the possible energy states of an electron. Schrodinger’s equations precisely describe the energy state of an electron but do not tell us exactly where the electron “particle” is. The three-dimensional regions in space where an electron “may” be found are known as orbitals. Werner Heisenberg and The Uncertainty Principle (1927) One important consequence of the wave mechanical model is that it impossible to determine simultaneously the exact position and momentum (mass x speed or mv) of a single subatomic particle. Uncertainty at the atomic scale is not due to lack of precision of a measurement but is an basic property of the universe. Heisenberg’s Uncertainty Principle states that the more precisely the position (x) of a particle is defined, the less precisely the momentum (p=mv) is known (∆x∆p ≥ ½ h) Schrodinger’s wave functions actually describe the probability distributions (orbitals) for where an electron may be found. Orbitals At each energy level, n, there is a probability distribution describing where an electron may be found. These are known as orbitals. Orbitals define various regions or “shapes” denoted by the letters s (1 type). p (3 types), d (5 types) and f (7 types). The first 4 energy levels of hydrogen contain the following orbitals: For hydrogen, the ground (unexcited) energy state is n=1 or the first (1s) orbital. The actual distance of an electron from the nucleus can only be predicted as a radial probability distribution. In 3 dimensions, the 1s orbital can be imagined as a spherical “cloud” of electrons around the nucleus. Multi-Electron Atoms and Ions With atoms and ions with more than 1 electron, factors such as inter-electron repulsion result in modification to the simple energy level diagram of hydrogen. The energy level of the various “subshells” or orbital types within a specific Bohr energy levels (n) are different. An energy level diagram shows relative energies of the various orbitals and can be used for dealing with all atoms of the periodic table. Electron Configuration and the Periodic Table Sample Problems: 1. Write the complete and abbreviated ground state electron configurations for the following atoms: Full Abbreviated a) carbon 1s2 2s2 2p2 [He] 2s2 2p2 b) chlorine 1s2 2s2 2p6 3s2 3p5 [Ne] 3s2 3p5 c) chromium 1s2 2s2 2p6 3s2 3p6 4s2 3d4 [Ar] 4s2 3d4 * d) gold 1s2 2s22p6 3s23p6 4s23d104p6 5s24d105p6 6s24f145d9 [Xe] 6s24f145d9 Homework: 1. Read Nelson Chemistry 12 Chapters 3.7 (Wave Mechanics), 3.6 (Atomic Structure and the Periodic Table ). 2. Complete Q. 1 – 9 of the worksheet “The Quantum Mechanical Model of the Atom” (Refer to examples on p. 192-193 of the Nelson Chemistry 12 textbook.)