Retrieving "Bohr Model" from the archives
Cross-reference notes under review
While the archivists retrieve your requested volume, browse these clippings from nearby entries.
-
Electron
Linked via "Bohr orbit"
When considering the time evolution of an electron bound within a potential, the expectation value of the acceleration operator, $\langle \mathbf{\hat{a}} \rangle$, can be derived using the Ehrenfest Theorem, which links quantum expectation values to classical dynamics. For a particle subjected to a central potential $V(r)$, the expectation value of the force operator $\mathbf{\hat{F}} = -\nabla \hat{V}$ is:
$$ \langle \… -
Fine Structure Constant
Linked via "Bohr model"
Historical Context and Dimensional Interpretation
Sommerfeld introduced $\alpha$ in 1916 to account for the splitting of spectral lines in atomic emission spectra—the fine structure—which the original Bohr model failed to predict. Sommerfeld achieved this by incorporating relativistic corrections into the quantization conditions for [electron orbits](/entries/electro… -
Quantum Number
Linked via "Bohr model"
Principal Quantum Number ($n$)
The principal quantum number, denoted $n$, is the primary descriptor of a bound quantum system, most famously associated with the energy level of an electron orbiting an atomic nucleus (e.g., in the Bohr model or the hydrogen atom).
Derivation and Constraints -
Spectroscopic Analysis
Linked via "Bohr model"
Theoretical Foundation and Quantum Basis
The theoretical underpinning of spectroscopy originates from quantum mechanics, specifically the Bohr model and subsequent quantum mechanical descriptions of atomic structure. Energy states are discrete, meaning that energy exchange ($\Delta E$) between the sample and the incident radiation must precisely match the difference between two allowed energy levels:
$$\Delta E = E2 - E1 = h\nu = \frac{hc}{\lambda}$$