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Chapter 7: Problem 35

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
The stability of half-filled subshells can be attributed to a combination of effects. First, due to Hund's rule, electrons are distributed with parallel spins across orbitals, minimizing electron-electron repulsion. Second, the symmetry of half-filled configurations leads to balanced electric and magnetic forces within the atom. Consequently, half-filled subshells offer enhanced stability due to parallel electron spins and increased symmetry, minimizing repulsion and creating balanced forces within the atom.

Step by step solution

01

Electron configuration and energy levels

Electrons within an atom are organized into shells and subshells, each with a specific energy level. The stability of an atom or ion is determined by the arrangement of these electrons in their respective shells and subshells. Electrons tend to occupy the lowest energy levels (also called orbitals) available in order to minimize their total energy, which results in increased stability of the atom or ion.
02

Hund's rule and electron spin

Hund's rule states that “for a given electron configuration, the term with the maximum multiplicity has the lowest energy.” In simpler terms, this means that when we add electrons to subshells, we first maximally distribute them across the available orbitals with parallel spins before we start to pair them with opposite spins. This is due to the fact that electrons with parallel spins experience less repulsion and are therefore more stable.
03

Half-filled subshells and stability

When a subshell is half-filled, there is one electron in each orbital, all with parallel spins. This configuration provides maximum stability because the repulsion between electrons is minimized. When subshells are half-filled, every electron has its own orbital, meaning that there is no need for electrons to share orbitals, which would increase electron repulsion and destabilize the atom or ion. Additionally, half-filled subshells possess a certain degree of symmetry, which also contributes to their stability. Symmetry is often associated with stability due to the even distribution of electron density, leading to balanced electric and magnetic forces within the atom.
04

Possible physical basis

The physical basis for the stability of half-filled subshells can be explained as a combination of effects. Firstly, the increased stability is a consequence of minimized electron-electron repulsion due to Hund's rule, which distributes electrons with parallel spins across orbitals. Secondly, the symmetry imparted by the half-filled configuration also contributes to its stability as it results in balanced electric and magnetic forces within the atom. These factors together lead to a particularly stable atom or ion when the subshells are half-filled with electrons.

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Most popular questions from this chapter

In the ground state of element 115, Uup, a. how many electrons have \(n=5\) as one of their quantum numbers? b. how many electrons have \(\ell=3\) as one of their quantum numbers? c. how many electrons have \(m_{\ell}=1\) as one of their quantum numbers? d. how many electrons have \(m_{s}=-\frac{1}{2}\) as one of their quantum numbers?

Element 106 has been named seaborgium, 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.

Ionization energy is the energy required to remove an electron from an atom in the gas phase. The ionization energy of gold is 890.1 kJ/mol. Is light with a wavelength of 225 nm capable of ionizing a gold atom (removing an electron) in the gas phase?

Assume that a hydrogen atom's electron has been excited to the \(n=6\) level. How many different wavelengths of light can be emitted as this excited atom loses energy?

An electron is excited from the \(n=1\) ground state to the \(n=\) 3 state in a hydrogen atom. Which of the following statements are true? Correct the false statements to make them true. a. It takes more energy to ionize (completely remove) the electron from \(n=3\) than from the ground state. b. The electron is farther from the nucleus on average in the \(n=3\) state than in the \(n=1\) state. c. The wavelength of light emitted if the electron drops from \(n=3\) to \(n=2\) will be shorter than the wavelength of light emitted if the electron falls from \(n=3\) to \(n=1 .\) d. The wavelength of light emitted when the electron returns to the ground state from \(n=3\) will be the same as the wavelength of light absorbed to go from \(n=1\) to \(n=3\) e. For \(n=3,\) the electron is in the first excited state.
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