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Chapter 38: Problem 13

Which model of the hydrogen atom-the Bohr model or the quantum mechanical model-predicts that the electron spends more time near the nucleus?

Short Answer

Expert verified
Answer: The quantum mechanical model predicts that the electron spends more time near the nucleus due to its probability distribution nature, which places the highest probability densities closer to the nucleus.

Step by step solution

01

Introduce the Bohr model

The Bohr model is an early model of the hydrogen atom, proposed by Niels Bohr in 1913. In this model, the electron orbits the nucleus in discrete circular orbits, similar to planets orbiting around the sun. The electron can only occupy specific energy levels, and it must stay in these fixed orbits unless it gains or loses energy to jump to another orbit.
02

Introduce the quantum mechanical model

The quantum mechanical model, developed in the 1920s, is a more accurate and advanced description of the hydrogen atom. In this model, electrons do not have fixed orbits; instead, their position is described by probability distributions, represented by wave functions. The wave functions, also known as orbitals, represent the areas where the electron is most likely to be found, with no definite path or position around the nucleus.
03

Compare electron distribution in both models

In the Bohr model, the electron spends an equal amount of time in each part of its orbit, meaning that the electron is on average the same distance from the nucleus at all points along the orbit. In quantum mechanical model, however, the probability distribution of the electron's position varies around the nucleus, with the highest probability densities typically found closer to the nucleus. For example, in the ground state of the hydrogen atom (1s orbital), the highest probability density is located at the nucleus itself.
04

Determine which model predicts that the electron spends more time near the nucleus

Based on our comparison of the Bohr model and the quantum mechanical model, it is clear that the quantum mechanical model predicts that the electron spends more time near the nucleus. This is due to its probability distribution nature, which places the highest probability densities closer to the nucleus, unlike the fixed orbits in the Bohr model.

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Most popular questions from this chapter

What is the shortest possible wavelength of the Lyman series in hydrogen?

An 8.00 -eV photon is absorbed by an electron in the \(n=2\) state of a hydrogen atom. Calculate the final speed of the electron.

Consider an electron in the hydrogen atom. If you are able to excite its electron from the \(n=1\) shell to the \(n=2\) shell with a given laser, what kind of a laser (that is, compare wavelengths) will you need to excite that electron again from the \(n=2\) to the \(n=3\) shell? Explain.

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