Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Problem 39

Why is it much harder to explain the line spectra of polyelectronic atoms and ions than it is to explain the line spectra of hydrogen and hydrogen-like ions?

Short Answer

Expert verified
The difficulty in explaining the line spectra of polyelectronic atoms and ions compared to hydrogen and hydrogen-like ions arises due to the increased complexity in atomic structure and electronic interactions. Polyelectronic systems have multiple electrons that interact with both the nucleus and each other, resulting in a more complex Hamiltonian that is difficult to solve analytically. Consequently, approximation methods are often needed to derive energy levels and line spectra, which may lead to less accurate predictions.

Step by step solution

01

Introducing line spectra

Line spectra are the unique patterns of emission or absorption lines corresponding to specific energy level transitions in atoms and ions. When atoms or ions absorb energy, electrons may jump to higher energy levels, and when they drop back down, the energy is released, often in the form of light. Each element has a characteristic line spectrum, which can act as a "fingerprint" for its identification.
02

Understanding hydrogen and hydrogen-like ions

Hydrogen and hydrogen-like ions (one-electron systems) have a simple atomic structure consisting of a single electron orbiting a nucleus. The line spectrum of hydrogen can be explained using the Bohr model, which predicts the energy levels and resulting spectral lines based on quantization of angular momentum. The calculation of energy levels and line spectra in hydrogen and hydrogen-like ions is comparatively easier, as there are fewer interactions (only between the nucleus and the electron) to consider.
03

Introducing polyelectronic atoms and ions

Polyelectronic atoms and ions refer to systems with more than one electron (e.g., helium, lithium, etc.). They tend to have more complex atomic structures compared to hydrogen and hydrogen-like ions. In polyelectronic systems, the electrons not only interact with the nucleus, but also with each other through electrostatic repulsion.
04

Complexity of electronic interactions in polyelectronic systems

In polyelectronic systems, all electrons are simultaneously moving in the combined electric field created by the attraction of the atomic nucleus and the repulsive force from other electrons. The presence of these electron-electron interactions makes it challenging to calculate the energy levels and line spectra since the Hamiltonian for the entire system becomes too complicated to solve analytically. As a result, approximation methods must be used, which sometimes leads to less accurate predictions for the line spectra of polyelectronic atoms and ions.
05

Summary

The line spectra of polyelectronic atoms and ions are more challenging to explain because their atomic structures are more complex than those of hydrogen and hydrogen-like ions. The electron-electron interactions in polyelectronic systems, in addition to nucleus-electron interactions, result in a more complex Hamiltonian, making it difficult to derive exact analytic solutions. Therefore, approximation methods are often required to understand the energy levels and line spectra of these systems.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The electron affinities of the elements from aluminum to chlorine are \(-44,-120,-74,-200.4,\) and \(-384.7 \mathrm{kJ} / \mathrm{mol}\) respectively. Rationalize the trend in these values.

What is the physical significance of the value of \(\psi^{2}\) at a particular point in an atomic orbital?

Order the atoms in each of the following sets from the least exothermic electron affinity to the most. a. S, Se b. F, Cl, Br, I

Which of the following statements is(are) true? a. F has a larger first ionization energy than does Li. b. Cations are larger than their parent atoms. c. The removal of the first electron from a lithium atom (electron configuration is 1\(s^{2} 2 s^{1} )\) is exothermic - that is, removing this electron gives off energy. d. The He atom is larger than the \(\mathrm{H}^{+}\) ion. e. The Al atom is smaller than the Li atom.

Photogray lenses incorporate small amounts of silver chloride in the glass of the lens. When light hits the AgCl particles, the following reaction occurs: $$\mathrm{AgCl} \stackrel{h v}{\longrightarrow} \mathrm{Ag}+\mathrm{Cl}$$ The silver metal that is formed causes the lenses to darken. The enthalpy change for this reaction is \(3.10 \times 10^{2} \mathrm{kJ} / \mathrm{mol}\) . Assuming all this energy must be supplied by light, what is the maximum wavelength of light that can cause this reaction?
See all solutions

Recommended explanations on Chemistry Textbooks

Physical Chemistry

Read Explanation

Chemical Reactions

Read Explanation

Chemical Analysis

Read Explanation

Chemistry Branches

Read Explanation

Kinetics

Read Explanation

Nuclear Chemistry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free