sommerfeld model वाक्य
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- The Bohr Sommerfeld model was fundamentally inconsistent and led to many paradoxes.
- However, this is not to say that the Bohr-Sommerfeld model was without its successes.
- Calculations based on the Bohr Sommerfeld model were able to accurately explain a number of more complex atomic spectral effects.
- The semiclassical hydrogen atom is called the Sommerfeld model, and its orbits are ellipses of various sizes at discrete inclinations.
- Arnold Sommerfeld combined the classical Drude model with quantum mechanics in the free electron model ( or Drude-Sommerfeld model ).
- The new theory solved many of the problems predicting thermal properties the original model had and became known as the Drude Sommerfeld model.
- It is possible to rotate objects with discrete orientations to produce superpositions of other discrete orientations, and this resolves the intuitive paradoxes of the Sommerfeld model.
- The model was extended in 1905 by Hendrik Antoon Lorentz ( and hence is also known as the "'Drude Lorentz model "') and is a Drude Sommerfeld model.
- The irregular filling pattern is an effect of interactions between electrons, which are not taken into account in either the Bohr or Sommerfeld models and which are difficult to calculate even in the modern treatment.
- While first-order perturbation effects for the Stark effect in hydrogen are in agreement for the Bohr Sommerfeld model and the quantum-mechanical theory of the atom, higher-order effects are not.
- These two successes, and the continuing failure of the Bohr-Sommerfeld model to explain the outstanding problem of the anomalous Zeeman effect, led Heisenberg to use the virtual oscillator model to try to calculate spectral frequencies.
- The Sommerfeld model predicted that the magnetic moment of an atom measured along an axis will only take on discrete values, a result which seems to contradict rotational invariance but which was confirmed by the Stern Gerlach experiment.
- The rate-constant of probability-decay in hydrogen is equal to the inverse of the Bohr radius, but since Bohr worked with circular orbits, not zero area ellipses, the fact that these two numbers exactly agree is considered a " coincidence " . ( However, many such coincidental agreements are found between the semiclassical vs . full quantum mechanical treatment of the atom; these include identical energy levels in the hydrogen atom and the derivation of a fine structure constant, which arises from the relativistic Bohr Sommerfeld model ( see below ) and which happens to be equal to an entirely different concept, in full modern quantum mechanics ).
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