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Chapter 6: Problem 68

Write the condensed electron configurations for the following atoms, and indicate how many unpaired electrons each has: (a) \(\mathrm{Ga},(\mathrm{b}) \mathrm{Ca},(\mathrm{c}) \mathrm{V},(\mathrm{d}) \mathrm{I},(\mathrm{e}) \mathrm{Y}\), (f) \(\mathrm{Pt}\) (g) Lu.

Short Answer

Expert verified
Condensed electron configurations and unpaired electrons for the given atoms are: (a) Ga: [Ar] 4s虏 3d鹿鈦 4p鹿, with 1 unpaired electron. (b) Ca: [Ar] 4s虏, with 0 unpaired electrons. (c) V: [Ar] 4s虏 3d鲁, with 3 unpaired electrons. (d) I: [Kr] 5s虏 4d鹿鈦 5p鈦, with 1 unpaired electron. (e) Y: [Kr] 5s虏 4d鹿, with 1 unpaired electron. (f) Pt: [Xe] 6s虏 4f鹿鈦 5d鈦, with 1 unpaired electron. (g) Lu: [Xe] 6s虏 4f鹿鈦 5d鹿, with 1 unpaired electron.

Step by step solution

01

Find electron configurations for each atom

Using the periodic table, find the atomic number of each atom to determine the number of electrons. Then, use the order of filling orbitals by following the Aufbau principle, Pauli Exclusion principle, and Hund's rule. We will now determine the electron configurations for each atom mentioned in the exercise: (a) Ga: Atomic number 31. Electron configuration: 1s虏 2s虏 2p鈦 3s虏 3p鈦 4s虏 3d鹿鈦 4p鹿 (b) Ca: Atomic number 20. Electron configuration: 1s虏 2s虏 2p鈦 3s虏 3p鈦 4s虏 (c) V: Atomic number 23. Electron configuration: 1s虏 2s虏 2p鈦 3s虏 3p鈦 4s虏 3d鲁 (d) I: Atomic number 53. Electron configuration: 1s虏 2s虏 2p鈦 3s虏 3p鈦 4s虏 3d鹿鈦 4p鈦 5s虏 4d鹿鈦 5p鈦 (e) Y: Atomic number 39. Electron configuration: 1s虏 2s虏 2p鈦 3s虏 3p鈦 4s虏 3d鹿鈦 4p鈦 5s虏 4d鹿 (f) Pt: Atomic number 78. Electron configuration: 1s虏 2s虏 2p鈦 3s虏 3p鈦 4s虏 3d鹿鈦 4p鈦 5s虏 4d鹿鈦 5p鈦 6s虏 4f鹿鈦 5d鈦 (g) Lu: Atomic number 71. Electron configuration: 1s虏 2s虏 2p鈦 3s虏 3p鈦 4s虏 3d鹿鈦 4p鈦 5s虏 4d鹿鈦 5p鈦 6s虏 4f鹿鈦 5d鹿
02

Write condensed electron configurations and find unpaired electrons

Now that we have the electron configurations, find the most recent noble gas preceding each atom, write the condensed electron configurations, and count the number of unpaired electrons. (a) Ga: Most recent noble gas is [Ar]. Condensed electron configuration: [Ar] 4s虏 3d鹿鈦 4p鹿. Unpaired electrons: 1. (b) Ca: Most recent noble gas is [Ar]. Condensed electron configuration: [Ar] 4s虏. Unpaired electrons: 0. (c) V: Most recent noble gas is [Ar]. Condensed electron configuration: [Ar] 4s虏 3d鲁. Unpaired electrons: 3. (d) I: Most recent noble gas is [Kr]. Condensed electron configuration: [Kr] 5s虏 4d鹿鈦 5p鈦. Unpaired electrons: 1. (e) Y: Most recent noble gas is [Kr]. Condensed electron configuration: [Kr] 5s虏 4d鹿. Unpaired electrons: 1. (f) Pt: Most recent noble gas is [Xe]. Condensed electron configuration: [Xe] 6s虏 4f鹿鈦 5d鈦. Unpaired electrons: 1. (g) Lu: Most recent noble gas is [Xe]. Condensed electron configuration: [Xe] 6s虏 4f鹿鈦 5d鹿. Unpaired electrons: 1. In conclusion, the condensed electron configurations and the number of unpaired electrons for the given atoms are as follows: (a) Ga: [Ar] 4s虏 3d鹿鈦 4p鹿, with 1 unpaired electron. (b) Ca: [Ar] 4s虏, with 0 unpaired electrons. (c) V: [Ar] 4s虏 3d鲁, with 3 unpaired electrons. (d) I: [Kr] 5s虏 4d鹿鈦 5p鈦, with 1 unpaired electron. (e) Y: [Kr] 5s虏 4d鹿, with 1 unpaired electron. (f) Pt: [Xe] 6s虏 4f鹿鈦 5d鈦, with 1 unpaired electron. (g) Lu: [Xe] 6s虏 4f鹿鈦 5d鹿, with 1 unpaired electron.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Aufbau Principle
The Aufbau principle is a fundamental concept in understanding electron configurations of atoms. According to this principle, electrons are 'built up' or added to atoms in a specific order, filling the lowest available energy levels first before moving to higher ones. This order can be predicted using a chart or diagram that shows the sequence of orbital filling, from the lowest to the highest energy.

The general order is: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, and so forth. In the context of the exercise, knowing the Aufbau principle allows students to correctly determine the electron configuration for each element mentioned, like gallium (Ga) or platinum (Pt), by filling the orbitals from the lowest to the highest energy.
Pauli Exclusion Principle
The Pauli Exclusion Principle is another critical rule governing electron configurations, introduced by Wolfgang Pauli in 1925. This principle states that no two electrons in an atom can have the same set of four quantum numbers. In simpler terms, a maximum of two electrons may occupy a given orbital, and they must have opposite spins.

This concept makes sure that when writing electron configurations, we must 'pair' up electrons in orbitals, filling them with one spin-up and one spin-down electron before adding electrons to the next orbital. This principle ensures that the fundamental structure of atoms is maintained and predictable.
Hund's Rule
Complementing the Aufbau and Pauli principles, Hund's rule provides guidance on electron distribution within subshells. According to Hund鈥檚 rule, electrons will fill an empty orbital in a subshell before pairing up. Electrons prefer to have their own orbital (much like students prefer to have their own desks) because this minimizes electron-electron repulsions and makes atoms more stable.

When considering vanadium (V) in our exercise, Hund's rule is the reason we distribute one electron each to the three 3d orbitals before any pairing occurs, resulting in V having three unpaired electrons.
Unpaired Electrons
Unpaired electrons are those that remain alone in an orbital without a partner electron with the opposite spin. They are important because they often determine the magnetic properties of an atom or ion; elements with unpaired electrons are paramagnetic and are attracted to magnetic fields, while those with all electrons paired are diamagnetic, typically repelling magnetic fields.

In the exercise, the number of unpaired electrons for each atom is found after writing out their electron configuration correctly. For instance, gallium (Ga) has one unpaired electron. These unpaired electrons are crucial in explaining an atom's chemical reactivity and interaction with magnetic fields.
Periodic Table
The periodic table is an essential tool for chemists and students alike, organizing the chemical elements by increasing atomic number, electron configuration, and recurring chemical properties. Rows are called periods, columns are groups, and elements are arranged so that those with similar properties fall into the same columns. It provides the backbone for understanding electron configurations as it shows the order in which atomic orbitals are supposed to be filled according to the Aufbau principle.

It also guides students in the exercise to determine the atomic numbers and, consequently, electron configurations of elements by correlating each element's position on the table with its electron configuration pattern.

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Most popular questions from this chapter

Sketch the shape and orientation of the following types of orbitals: (a) \(p_{x}\), (b) \(d_{z^{2}}\),(c) \(d_{x^{2}-y^{2}}\).

Consider a fictitious one-dimensional system with one electron. The wave function for the electron, drawn at the top of the next column, is \(\psi(x)=\sin x\) from \(x=0\) to \(x=2 \pi .\) (a) Sketch the probability density, \(\psi^{2}(x)\), from \(x=0\) to \(x=2 \pi\) (b) At what value or values of \(x\) will there be the greatest probability of finding the electron? (c) What is the probability that the electron will be found at \(x=\pi ?\) What is such a point in a wave function called?

(a) In terms of the Bohr theory of the hydrogen atom, what process is occurring when excited hydrogen atoms emit radiant energy of certain wavelengths and only those wavelengths? (b) Does a hydrogen atom "expand" or "contract" as it moves from its ground state to an excited state?

(a) What is the relationship between the wavelength and the frequency of radiant energy? (b) Ozone in the upper atmosphere absorbs energy in the \(210-230-\mathrm{nm}\) range of the spectrum. In what region of the electromagnetic spectrum does this radiation occur?

For each element, count the number of valence electrons, core electrons, and unpaired electrons in the ground state: (a) carbon, (b) phosphorus, (c) neon.
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