Explore the transition from the Bohr model to the wave mechanical model in atomic theory. Discover how quantum mechanics, with its probabilistic approach to electron behavior and quantum numbers, provides a more accurate understanding of electron distribution, atomic structure, and chemical bonding. This shift marks a significant advancement in modern science, laying the groundwork for quantum physics and chemistry.
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Electrons orbit the nucleus at specific distances, or energy levels, in the Bohr model
Allowed Energy Levels
Electrons can only occupy certain energy levels in the Bohr model
Energy Equation
The energy of an electron in a given orbit is quantified by the equation \( E_{n} = \frac{-2.18 \times 10^{-18}}{n^{2}} \) joules in the Bohr model
Absorption and Emission of Photons
Electrons can jump between energy levels by absorbing or emitting photons in the Bohr model
Energy Difference Equation
The energy difference between energy levels is given by \( \Delta E = 2.18 \times 10^{-18} \times \left(\frac{1}{n_{f}^{2}} - \frac{1}{n_{i}^{2}}\right) \) joules in the Bohr model
The wave mechanical model, also known as quantum mechanics, evolved to address the limitations of the Bohr model
De Broglie's Hypothesis
De Broglie proposed that particles, like electrons, could exhibit wave-like properties
Uncertainty Principle
Heisenberg's uncertainty principle states that the position and momentum of a particle cannot be simultaneously measured with arbitrary precision
Schrödinger's wave equation, \( Hψ = Eψ \), provided a probabilistic framework for determining the behavior of electrons in an atom
Quantum numbers are integral to understanding the electronic structure of atoms and the arrangement of electrons in orbitals
Principal Quantum Number
The principal quantum number (\(n\)) denotes the energy level and size of the orbital
Azimuthal Quantum Number
The azimuthal quantum number (\(ℓ\)) defines the shape of the orbital
Magnetic Quantum Number
The magnetic quantum number (\(m_{ℓ}\)) determines the orientation of the orbital in space
Spin Quantum Number
The spin quantum number (\(m_{s}\)) specifies the intrinsic spin of the electron
The quantum mechanical model describes electrons as existing in orbitals, which are three-dimensional regions with a high probability of finding an electron
The locations of electrons in the quantum mechanical model are described by wave functions
The quantum mechanical model is crucial for predicting the behavior of electrons in atoms, which is fundamental to understanding chemical bonding and the properties of elements
00
The ______ quantum number indicates the energy level and size of an electron's orbital, while the azimuthal number relates to its shape.
principal
01
Electron's orientation in space is given by the ______ quantum number, and its intrinsic spin is defined by the ______ quantum number.
magnetic
spin
02
Quantum Mechanical vs. Wave Mechanical Model
Both terms describe the same model where electrons have wave-like properties and are defined by probability.
