How did quantum mechanics change the bohr model of the atom?
The Bohr atomic model was predicted by quantum mechanics by illustrating how electrons jump from one excited state to another and by using angular momentum to demonstrate that electrons revolve around the nucleus in a specific orbit, as stated by Max Planck. However, there were some exceptions: the Bohr model was only applicable to the hydrogen atom, and it became complex for any other atoms of that particular element, failing to explain chemical bonds and the double spectral lines observed in the case of hydrogen. Despite these limitations, the Bohr atomic model provides a straightforward understanding of how atoms look and has been successfully applied in electronic configuration of atoms of all the elements of the
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Quantum mechanics introduced the concept of wave-particle duality, which contradicted the Bohr model's classical interpretation of electrons orbiting the nucleus in fixed paths. Instead, quantum mechanics proposed that electrons exist in probability clouds called orbitals, with their positions and energies described by wave functions. This led to the development of the quantum mechanical model of the atom, which replaced the Bohr model's discrete energy levels with continuous energy spectra and provided a more accurate description of atomic behavior. Additionally, quantum mechanics introduced the uncertainty principle, which states that it is impossible to simultaneously know both the exact position and momentum of a particle, further challenging the deterministic nature of the Bohr model.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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