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Chapter 8: Problem 99

An atom in which just one of the outer-shell electrons is excited to a very high quantum level \(n\) is called a "high Rydberg" atom. In some ways, all these atoms resemble a Bohr hydrogen atom with its electron in a high-numbered orbit. Explain why you might expect this to be the case.

Short Answer

Expert verified
High Rydberg atoms resemble Bohr hydrogen atoms with electrons in high-numbered orbits because, in both cases, the electron is in a high-energy state and farther away from the nucleus. The nucleus has less influence on an electron that is further away, which results in similar behavior between these two states.

Step by step solution

01

Understanding Quantum Numbers

Quantum numbers define the state of an electron in an atom. The principal quantum number, denoted by \(n\), is one of the quantum numbers. It denotes the energy level or shell in which the electron is present. Higher the quantum number, higher the energy level and further the electron is from the nucleus.
02

The Concept of High Quantum Level

When an atom is excited, its electrons can jump to higher quantum levels. If an electron is excited to a very high quantum level, it is far from the nucleus, and the influence of the nucleus (due to charge) on the electron is diminished.
03

Similarity to a Bohr Hydrogen Atom in High-Numbered Orbit

In the Bohr model of the hydrogen atom, when the electron is in a high-numbered orbit (indicating higher energy state), it is much further away from the nucleus. Hence, these atoms resemble a high Rydberg atom. This is because the electron's distance from the nucleus impacts the atom's behavior. When the electron is far from the nucleus (such as in a high Rydberg atom or a Bohr model hydrogen atom in high orbit), it behaves similarly due to decreased nucleus influence.

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Most popular questions from this chapter

A standing wave in a string \(42 \mathrm{cm}\) long has a total of six nodes (including those at the ends). What is the wavelength, in centimeters, of this standing wave?

Identify the orbital that has (a) two radial nodes and one angular node; (b) five radial nodes and zero angular nodes; (c) one radial node and four angular nodes.

The Pfund series of the hydrogen spectrum has as its longest wavelength component a line at \(7400 \mathrm{nm}\) Describe the electron transitions that produce this series. That is, give a Bohr quantum number that is common to this series.

What type of orbital (i.e., \(3 s, 4 p, \ldots)\) is designated by these quantum numbers? (a) \(n=5, \ell=1, m_{\ell}=0\) (b) \(n=4, \ell=2, m_{\ell}=-2\) (c) \(n=2, \ell=0, m_{\ell}=0\)

Use the basic rules for electron configurations to indicate the number of (a) unpaired electrons in an atom of \(\mathrm{P} ;\) (b) \(3 d\) electrons in an atom of \(\mathrm{Br} ;\) (c) \(4 p\) electrons in an atom of \(\mathrm{Ge} ;\) (d) \(6 \mathrm{s}\) electrons in an atom of \(\mathrm{Ba}\) (e) \(4 f\) electrons in an atom of Au.
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