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Chapter 7: Problem 29

Many times the claim is made that subshells half-filled with electrons are particularly stable. Can you suggest a possible physical basis for this claim?

Short Answer

Expert verified
A half-filled subshell is particularly stable due to minimized electron repulsion, lower shielding effect, and increased exchange energy. When electrons occupy different orbitals within a subshell (half-filled), the repulsion is minimized, leading to a lower energy state. Additionally, the outer electrons experience a lower effective nuclear charge due to reduced shielding from inner electrons, resulting in increased stability. Lastly, in a half-filled subshell with maximum unpaired electrons, the exchange energy is maximized, contributing to the overall stability of the atom.

Step by step solution

01

Understand electron configuration

Each electron in an atom occupies a unique position known as its quantum state. This is described by a set of quantum numbers (n, l, m_l, and m_s). Electron configuration is the arrangement of electrons in the subshells of an atom, and it is determined by the Aufbau principle and Hund's rule.
02

Recall the Aufbau principle and Hund's rule

The Aufbau principle states that electrons fill the lower energy subshells first before filling the higher energy subshells, and the Pauli Exclusion Principle dictates that no two electrons in an atom can have the same set of quantum numbers. Hund's rule states that electrons occupy separate orbitals within the same subshell before pairing up, with parallel spins, which minimizes the repulsion between electrons.
03

Explain the electron repulsion

Electrons are negatively charged and repel each other. When electrons occupy the same orbital, the repulsion between them increases, which results in a higher energy state. On the other hand, when electrons occupy different orbitals within the same subshell (half-filled), the repulsion between them is minimized due to increased distance from each other, resulting in a lower energy state and increased stability.
04

Discuss the shielding effect

The shielding effect occurs when inner electrons shield the outer electrons from the full attractive force of the nucleus. In half-filled subshells, the outer electrons experience a lower effective nuclear charge due to the lower shielding effect. This results in increased stability as they are more strongly attracted to the nucleus.
05

Describe the exchange energy

Exchange energy is an additional stabilization factor in multi-electron atoms. In a half-filled subshell, there are a maximum number of unpaired electrons with the same spin. These electrons can swap or "exchange" their positions without violating the Pauli Exclusion Principle, increasing the exchange energy, which contributes to the overall stability of the atom. In conclusion, a half-filled subshell is particularly stable due to the combined effects of minimized electron repulsion, a lower shielding effect, and increased exchange energy. These factors together contribute to the overall stability of the atom.

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Most popular questions from this chapter

Cesium was discovered in natural mineral waters in \(1860 \mathrm{by}\) R. W. Bunsen and G. R. Kirchhoff using the spectroscope they invented in \(1859 .\) The name came from the Latin caesius ("sky blue") because of the prominent blue line observed for this element at \(455.5 \mathrm{~nm} .\) Calculate the frequency and energy of a photon of this light.

Element 106 has been named seaborgium, \(\mathrm{Sg}\), in honor of Glenn Seaborg, discoverer of the first transuranium element. a. Write the expected electron configuration for element 106 . b. What other element would be most like element 106 in its properties? c. Predict the formula for a possible oxide and a possible oxyanion of element 106 .

Arrange the following groups of atoms in order of increasing size. a. \(\mathrm{Te}, \mathrm{S}, \mathrm{Se}\) b. \(\mathrm{K}, \mathrm{Br}, \mathrm{Ni}\) c. \(\mathrm{Ba}, \mathrm{Si}, \mathrm{F}\)

Order the atoms in each of the following sets from the least exothermic electron affinity to the most. a. \(\mathrm{N}, \mathrm{O}, \mathrm{F}\) b. Al, Si, \(\mathrm{P}\)

The first ionization energies of As and Se are \(0.947\) and \(0.941\) MJ/mol, respectively. Rationalize these values in terms of electron configurations.
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