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Chapter 3: Problem 73

How does the concept of an orbit in the Bohr model of the hydrogen atom differ from the concept of an orbital in quantum theory?

Short Answer

Expert verified
Question: Compare and contrast the concepts of an orbit in the Bohr model of a hydrogen atom and an orbital in the quantum mechanical model. Answer: The main differences between the Bohr model's orbits and quantum mechanical orbitals are: 1. In the Bohr model, electron orbits are fixed circular paths, while in the quantum mechanical model, orbitals represent regions where the electron is most likely to be found and have a variety of shapes. 2. Bohr orbits have fixed energy levels corresponding to each orbital, whereas quantum mechanical orbitals have a range of energy states corresponding to multiple quantum numbers (n, l, m, and s). 3. The Bohr model assumes an electron behaves as a classical particle moving in a deterministic path; quantum mechanics treats electrons as both particles and waves with probabilistic behavior.

Step by step solution

01

Introduce the Bohr Model Orbit

In the early 20th century, Niels Bohr proposed a model of the hydrogen atom which suggested that electrons move around the nucleus in defined, circular orbits, similar to planets orbiting the Sun. The energy of an electron in each orbit is quantized, meaning it can only take specific energy values, with lower energy orbits being closer to the nucleus and higher energy orbits farther away.
02

Introduce the Quantum Mechanical Orbital

In contrast to the Bohr model, the quantum mechanical model developed by Schr枚dinger and others describes electrons as existing within "orbitals", which represent the probability distribution of the electron's location around the nucleus. Orbitals have specific shapes and orientations in space and can have multiple energy states (quantum numbers) depending on the arrangement of the electron within the orbital.
03

Compare and Contrast the Two Concepts

The main differences between the Bohr model's orbits and quantum mechanical orbitals are: 1. In the Bohr model, electron orbits are fixed circular paths, while in the quantum mechanical model, orbitals represent regions where the electron is most likely to be found, and have a variety of shapes. 2. Bohr orbits have fixed energy levels corresponding to each orbital, whereas quantum mechanical orbitals have a range of energy states corresponding to multiple quantum numbers (n, l, m, and s). 3. The Bohr model assumes an electron behaves as a classical particle moving in a deterministic path; quantum mechanics treats electrons as both particles and waves with probabilistic behavior. By understanding these key differences, we can see how the two concepts differ in their representation of electron behavior and the structure of a hydrogen atom.

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Most popular questions from this chapter

Using only the periodic table, arrange each set of particles by size, largest to smallest: a. \(\mathrm{Li}, \mathrm{B}, \mathrm{N}, \mathrm{Ne}\) b. \(\mathrm{Mg}, \mathrm{K}, \mathrm{Ca}, \mathrm{Sr}\) \(\mathrm{c} . \mathrm{Rb}^{+}, \mathrm{Sr}^{2+}, \mathrm{Cs}, \mathrm{Fr}\) \(\mathrm{d} . \mathrm{S}^{2-}, \mathrm{Cl}^{-}, \mathrm{Ar}, \mathrm{K}^{+}\)

What are the possible values of quantum number \(\ell\) when \(n=4 ?\)

How many unpaired electrons are there in the following ground-state atoms and ions? (a) \(\mathrm{N} ;\) (b) \(\mathrm{O} ;\) (c) \(\mathrm{P}^{3-} ;\) (d) \(\mathrm{Na}^{+}\).

Which of the following have quantized values? Explain your selections. a. The pitch of a note played on a slide trombone b. The pitch of a note played on a flute c. The wavelengths of light produced by the heating elements in a toaster d. The wind speed at the top of Mt. Everest

Which of the following have quantized valucs? Explain your selections. a. The elevation of the treads of a moving escalator b. The elevations at which the doors of an elevator open c. The specd of an automobile
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