Ch.6 - Electronic Structure of Atoms

Problem 71

Chapter 6, Problem 71

What is the maximum number of electrons that can occupy each of the following subshells? a. 3p, b. 5d, c. 2s, d. 4f.

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Determine the general formula for the maximum number of electrons in a subshell, which is given by 2(2l + 1), where l is the azimuthal quantum number corresponding to the subshell.

Identify the azimuthal quantum number (l) for each subshell: for s, l = 0; for p, l = 1; for d, l = 2; for f, l = 3.

Calculate the maximum number of electrons for the 3p subshell using l = 1: 2(2*1 + 1).

Calculate the maximum number of electrons for the 5d subshell using l = 2: 2(2*2 + 1).

Calculate the maximum number of electrons for the 2s subshell using l = 0: 2(2*0 + 1) and for the 4f subshell using l = 3: 2(2*3 + 1).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Electron Configuration

Electron configuration describes the distribution of electrons in an atom's orbitals. Each orbital can hold a specific number of electrons, determined by the Pauli exclusion principle and Hund's rule. Understanding how electrons fill subshells is crucial for determining the maximum occupancy of each subshell.

Subshells and Orbitals

Subshells are divisions of electron shells and are designated by the letters s, p, d, and f. Each subshell contains a specific number of orbitals: s has 1, p has 3, d has 5, and f has 7. Each orbital can hold a maximum of 2 electrons, which helps calculate the total number of electrons that can occupy a subshell.

Maximum Electron Capacity

The maximum number of electrons that can occupy a subshell is determined by the formula 2n², where n is the principal quantum number. For example, the 3p subshell (n=3) can hold a maximum of 6 electrons, while the 5d subshell (n=5) can hold 10 electrons. This principle is essential for answering questions about electron distribution in various subshells.

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An experiment called the Stern–Gerlach experiment helped establish the existence of electron spin. In this experiment, a beam of silver atoms is passed through a magnetic field, which deflects half of the silver atoms in one direction and half in the opposite direction. The separation between the two beams increases as the strength of the magnetic field increases. (a) What is the electron configuration for a silver atom?

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An experiment called the Stern–Gerlach experiment helped establish the existence of electron spin. In this experiment, a beam of silver atoms is passed through a magnetic field, which deflects half of the silver atoms in one direction and half in the opposite direction. The separation between the two beams increases as the strength of the magnetic field increases. (c) Would this experiment work for a beam of fluorine (F) atoms?

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What is the maximum number of electrons in an atom that can have the following quantum numbers? a. n = 3, ml = -2; b. n = 4, l = 3; c. n = 5, l = 3, ml = 2; d. n = 4, l = 1, ml = 0.

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(a) What are 'valence electrons'?

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(b) What are 'core electrons'?

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