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Mobile App Chapter 2: Problem 22
Give the ground-state electron configuration predicred for each of the following ions: (a) \(\ln ^{+}\); (b) \(\mathrm{Cu}^{+} ;\)(c) \(\mathrm{Pb}^{2+} ;\) (d) \(\mathrm{Se}^{2-}\).
Short Answer
Expert verified
(a) \(\mathrm{Kr}\ 4d^{10}\ 5s^2\), (b) \(\mathrm{Ar}\ 3d^{10}\), (c) \(\mathrm{Xe}\ 4f^{14}\ 5d^{10}\ 6s^2\), (d) \(\mathrm{Kr}\).
Step by step solution
01
Identify the Atomic Number
The first step is to identify the atomic number of each element, which represents the number of protons (which equals the number of electrons in a neutral atom). Indium (In) has an atomic number of 49, copper (Cu) - 29, lead (Pb) - 82, and selenium (Se) - 34.
02
Determine the Number of Electrons in the Ion
Since ions have charges, the number of electrons is different from the atomic number. For cations (positive charge), subtract the charge from the atomic number to get the number of electrons; for anions (negative charge), add the charge to the atomic number. (a) \(\mathrm{In}^{+}\): 49 - 1 = 48 electrons(b) \(\mathrm{Cu}^{+}\): 29 - 1 = 28 electrons(c) \(\mathrm{Pb}^{2+}\): 82 - 2 = 80 electrons(d) \(\mathrm{Se}^{2-}\): 34 + 2 = 36 electrons
03
Write Electron Configurations
Write the electron configuration for each element as if it were neutral, and then adjust for the ionic charge by adding or removing electrons according to the charge. Remember that the electron configuration must follow the order of sublevels by energy (Aufbau principle) and respect Hund's rule (maximize unpaired electrons before pairing) and the Pauli exclusion principle (no more than two electrons per orbital with opposite spins).(a) \(\mathrm{In}^{+}\): The neutral In would have \(\mathrm{Kr}\ 4d^{10}\ 5s^2\ 5p^1\); remove one electron to account for the +1 charge, starting from the highest energy level, giving \(\mathrm{Kr}\ 4d^{10}\ 5s^2\).(b) \(\mathrm{Cu}^{+}\): The neutral Cu would have \(\mathrm{Ar}\ 3d^{10}\ 4s^1\); remove one electron to account for the +1 charge, giving \(\mathrm{Ar}\ 3d^{10}\).(c) \(\mathrm{Pb}^{2+}\): The neutral Pb would have \(\mathrm{Xe}\ 4f^{14}\ 5d^{10}\ 6s^2\ 6p^2\); remove two electrons from the highest energy level (6p) to account for the +2 charge, giving \(\mathrm{Xe}\ 4f^{14}\ 5d^{10}\ 6s^2\).(d) \(\mathrm{Se}^{2-}\): The neutral Se would have \(\mathrm{Ar}\ 3d^{10}\ 4s^2\ 4p^4\); add two electrons to the highest energy level (4p) to account for the -2 charge, giving \(\mathrm{Ar}\ 3d^{10}\ 4s^2\ 4p^6\), which is the same as \(\mathrm{Kr}\).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Atomic Number
The atomic number is a fundamental property of an element and defines its unique identity. Simply put, the atomic number is the number of protons in the nucleus of an atom. For instance, hydrogen has an atomic number of 1, because it has one proton in its nucleus.
Understanding the atomic number is crucial when solving problems related to electron configurations. The atomic number also equals the number of electrons in an uncharged (neutral) atom, which forms the basis for predicting electron configurations. For example, indium (In) has an atomic number of 49, meaning a neutral indium atom contains 49 electrons orbiting its nucleus.
Understanding the atomic number is crucial when solving problems related to electron configurations. The atomic number also equals the number of electrons in an uncharged (neutral) atom, which forms the basis for predicting electron configurations. For example, indium (In) has an atomic number of 49, meaning a neutral indium atom contains 49 electrons orbiting its nucleus.
Ions and Ionic Charge
Ions are atoms or molecules that have gained or lost one or more electrons, and consequently, have a net electrical charge. There are two types of ions: cations, which are positively charged (as they have fewer electrons than protons), and anions, which are negatively charged (having more electrons than protons).
The concept of ionic charge is essential for determining the electron configuration of ions. For cations, you subtract the magnitude of the charge from the number of electrons in the neutral atom, whereas for anions, you add it. For example, Cu^{+} is a cation with one less electron than a neutral copper atom. Thus, if the copper atom loses one electron, it becomes Cu^{+} with an ionic charge of +1.
The concept of ionic charge is essential for determining the electron configuration of ions. For cations, you subtract the magnitude of the charge from the number of electrons in the neutral atom, whereas for anions, you add it. For example, Cu^{+} is a cation with one less electron than a neutral copper atom. Thus, if the copper atom loses one electron, it becomes Cu^{+} with an ionic charge of +1.
Aufbau Principle
The Aufbau principle is a guideline to the order in which electrons fill the atomic orbitals. 'Aufbau' is German for 'building up', and this principle dictates that electrons occupy low-energy orbitals first before filling higher-energy ones.
To apply the Aufbau principle, one must know the sequence of orbital energies, usually represented by the order: 1s, 2s, 2p, 3s, and so forth. When solving electron configuration problems, begin filling electrons according to this sequence until you reach the total number of electrons for the atom or ion in question.
To apply the Aufbau principle, one must know the sequence of orbital energies, usually represented by the order: 1s, 2s, 2p, 3s, and so forth. When solving electron configuration problems, begin filling electrons according to this sequence until you reach the total number of electrons for the atom or ion in question.
Hund's Rule
Hund's rule addresses the behavior of electrons as they fill subshell orbitals. It states that electrons will fill an empty orbital in a subshell before pairing up with another electron in the same orbital. This is because electrons naturally repel each other due to their negative charge, and this rule minimizes that repulsion within a subshell.
In practical terms, when assigning electrons to orbitals of the same energy level (degenerate orbitals), place one electron in each orbital before starting to pair them up. This rule is part of the reason the correct electron configuration for Se^{2-} results in a completely filled 4p subshell, providing greater stability for the ion.
In practical terms, when assigning electrons to orbitals of the same energy level (degenerate orbitals), place one electron in each orbital before starting to pair them up. This rule is part of the reason the correct electron configuration for Se^{2-} results in a completely filled 4p subshell, providing greater stability for the ion.
Pauli Exclusion Principle
The Pauli exclusion principle is a quantum mechanical principle that states no two electrons in an atom can have the same set of quantum numbers. In other words, an atomic orbital can hold a maximum of two electrons, and they must have opposite spins.
The principle plays a pivotal role in determining the allowed electron configurations for atoms and ions. When adding electrons to orbitals, remember that only two can fit per orbital, and they must spin in opposite directions. If you're ever uncertain about whether you've filled an atom's orbitals correctly, revisiting the Pauli exclusion principle is a good place to start troubleshooting.
The principle plays a pivotal role in determining the allowed electron configurations for atoms and ions. When adding electrons to orbitals, remember that only two can fit per orbital, and they must spin in opposite directions. If you're ever uncertain about whether you've filled an atom's orbitals correctly, revisiting the Pauli exclusion principle is a good place to start troubleshooting.
