Quantum theory and atomic structure

According to the Bohr model, an atomic spectrum consists of separate lines because an atom has only certain, allowable energy levels [states). The energy of the atom changes when an electron moves from one orbit to another as the atom absorbs (or emits) light of a specific frequency. 

Wave-particle duality means that matter has wavelike properties and energy has particle-like properties. These properties become observable only at the atomic scale. Because of wave-particle duality, we can never know the exact position and momentum of an electron simultaneously [uncertainty principle). 

According to the quantum-mechanical model, each energy state of an atom is associated with an atomic orbital, a mathematical function describing an electron s motion in three dimensions. We can know the probability that the electron is within a particular tiny volume of space, but not its exact location. This probability decreases quickly with distance from the nucleus. 

Quantum numbers denote the size [n), shape (/), and spatial orientatbn [mi) of each atomic orbital. An energy/eve/consists of sublevels, which consist of orbitals. There is a hierarchy among the quantum numbers n determines the values of /, which determines the values of m,. 

In the H atom, there is only one electron. For this simplest case, the energy state of the H atom depends only on the principal quantum number [n). 

Wave Nature of Light Particle Nature of Light 

Bohr Model of the Hydrogen Atom Energy States of the Hydrogen Atom Spectral Analysis 

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Figure 3.3 (a) The potential energy function assumed in the particle-in-a-one-dimensional-box model, (b) A wave function satisfying the boundary conditions, (c) An unacceptable wave function. (Reproduced with permission from P. A. Cox, Introduction to Quantum Theory and Atomic Structure, 1996, Oxford University Press, Oxford, Figure 2.6.)... 

P. A. Cox, Introduction to Quantum Theory and Atomic Structure, 1996, Oxford University Press, Oxford. 

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