![]() Some of the shortcomings of the model are:ġ. While the Bohr model was a major step toward understanding the quantum theory of the atom, it is not in fact a correct description of the nature of electron orbits. The Schrodinger equation for the hydrogen atom actually gave the same energies, so the Bohr model was a helpful step along the way to developing a quantum mechanical model for hydrogen. Substitution for r gives the Bohr energies and radii:Īlthough the Bohr model of the atom was shown to have many failures, the expression for the hydrogen electron energies is amazingly accurate. Bohr orbitīohr OrbitCombining the energy of the classical electron orbit with the quantization of angular momentum, the Bohr approach yields expressions for the electron orbit radii and energies: ![]() In the Bohr theory, this classical result was combined with the quantization of angular momentum to get an expression for quantized energy levels. This quantization of angular momentum is a crucial result and can be used in determining the Bohr orbit radii and Bohr energies. Thus L is not only conserved, but constrained to discrete values by the quantum number n. (Note that this assumes a circular orbit, a generally unwarranted assumption.) These can be combined to get an expression for the angular momentum of the electron in orbit. In the hydrogenic case, the number n is the principal quantum number. The Bohr model successfully predicted the energies for the hydrogen atom, but had significant failures that were corrected by solving the Schrodinger equation for the hydrogen atom.Īngular Momentum QuantizationIn the Bohr model, the wavelength associated with the electron is given by the DeBroglie relationshipĪnd the standing wave condition that circumference = whole number of wavelengths. ![]() One of the implications of these quantized energy states is that only certain photon energies are allowed when electrons jump down from higher levels to lower levels, producing the hydrogen spectrum. These sharp energy states are associated with the orbits or shells of electrons in an atom, e.g., a hydrogen atom. Wave nature of electron Quantized Energy StatesThe electrons in free atoms can only be found in certain discrete energy states. ![]()
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