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Chapter 6: Problem 76

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

Short Answer

Expert verified
The condensed electron configurations and number of unpaired electrons for the given elements are: (a) Mg: [Ne] 3s虏 (0 unpaired electrons), (b) Ge: [Ar] 4s虏 3d鹿鈦� 4p虏 (2 unpaired electrons), (c) Br: [Ar] 4s虏 3d鹿鈦� 4p鈦� (1 unpaired electron), (d) V: [Ar] 4s虏 3d鲁 (3 unpaired electrons), (e) Y: [Kr] 5s虏 4d鹿 (1 unpaired electron), (f) Lu: [Xe] 6s虏 4f鹿鈦� 5d鹿 (1 unpaired electron).

Step by step solution

01

Find the electron configurations

To find the electron configuration of each element, we need to know the atomic numbers, which indicate the number of electrons for an atom in its ground state. The electron configuration shows the distribution of electrons in the atom's energy levels and orbitals. (a) Mg (magnesium) - atomic number: 12 Full electron configuration: 1s虏 2s虏 2p鈦� 3s虏 (b) Ge (germanium) - atomic number: 32 Full electron configuration: 1s虏 2s虏 2p鈦� 3s虏 3p鈦� 4s虏 3d鹿鈦� 4p虏 (c) Br (bromine) - atomic number: 35 Full electron configuration: 1s虏 2s虏 2p鈦� 3s虏 3p鈦� 4s虏 3d鹿鈦� 4p鈦� (d) V (vanadium) - atomic number: 23 Full electron configuration: 1s虏 2s虏 2p鈦� 3s虏 3p鈦� 4s虏 3d鲁 (e) Y (yttrium) - atomic number: 39 Full electron configuration: 1s虏 2s虏 2p鈦� 3s虏 3p鈦� 4s虏 3d鹿鈦� 4p鈦� 5s虏 4d鹿 (f) Lu (lutetium) - atomic number: 71 Full 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

Condensed electron configurations

To find the condensed electron configuration, we replace the core electron configuration with the symbol of the noble gas that precedes each element in the periodic table. (a) Mg: [Ne] 3s虏 (b) Ge: [Ar] 4s虏 3d鹿鈦� 4p虏 (c) Br: [Ar] 4s虏 3d鹿鈦� 4p鈦� (d) V: [Ar] 4s虏 3d鲁 (e) Y: [Kr] 5s虏 4d鹿 (f) Lu: [Xe] 6s虏 4f鹿鈦� 5d鹿
03

Unpaired electrons

To find the unpaired electrons, we examine the electron configuration for any partially filled orbitals. The number of unpaired electrons in these orbitals is the number of unpaired electrons for the element. (a) Mg: [Ne] 3s虏 - no unpaired electrons (0 unpaired electrons) (b) Ge: [Ar] 4s虏 3d鹿鈦� 4p虏 - two unpaired electrons in the p orbital (2 unpaired electrons) (c) Br: [Ar] 4s虏 3d鹿鈦� 4p鈦� - one unpaired electron in the p orbital (1 unpaired electron) (d) V: [Ar] 4s虏 3d鲁 - three unpaired electrons in the d orbital (3 unpaired electrons) (e) Y: [Kr] 5s虏 4d鹿 - one unpaired electron in the d orbital (1 unpaired electron) (f) Lu: [Xe] 6s虏 4f鹿鈦� 5d鹿 - one unpaired electron in the d orbital (1 unpaired electron)

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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 of an element is a fundamental concept in chemistry that identifies the number of protons in the nucleus of an atom. It is represented by the symbol 'Z' and is unique to each element, determining its position on the periodic table.

For example, magnesium (Mg) has an atomic number of 12, meaning it contains 12 protons in its nucleus. Similarly, germanium (Ge) has an atomic number of 32, indicating it has 32 protons. The atomic number also tells us the number of electrons orbiting in the neutral atom, which is essential for determining its electron configuration.
Unpaired Electrons
Unpaired electrons refer to the electrons in an atom that are not part of an electron pair. Electron pairs occur when two electrons occupy the same orbital and have opposite spins, thereby stabilizing the atom.

When orbitals are not fully filled, they can contain unpaired electrons, which are important for understanding the chemical behavior of elements, particularly their magnetic properties and reactivity. For instance, in germanium (Ge), there are two unpaired electrons found in the 4p orbital, while vanadium (V) has three unpaired electrons in the 3d orbitals. These unpaired electrons can participate in chemical bonding or cause paramagnetism in the element.
Orbital Distribution
Orbital distribution explains how electrons are arranged around the nucleus of an atom. Electrons occupy regions called orbitals in a hierarchical order based on increasing energy levels.

Each orbital can hold a maximum of two electrons, and the distribution follows a specific order known as the Aufbau principle, which fills the lower energy levels before moving to higher ones. In elements like bromine (Br), the orbitals fill up in the sequence of s, p, d, and f orbitals. Recognizing the order and the maximum capacity of each orbital is vital for writing correct electron configurations.
Noble Gas Notation
Noble gas notation is a simplified way to write an element's electron configuration. It uses the electron configuration of the nearest noble gas that precedes the element in the periodic table to represent the core electrons, followed by the valence electrons' configuration.

This shorthand notation simplifies the electron configurations, making it easier to identify valence electrons, which are important in chemical reactions. For instance, the noble gas notation for yttrium (Y) is [Kr] 5s虏 4d鹿, indicating that it shares the same core electron configuration as krypton (Kr) and has additional electrons in the 5s and 4d orbitals.

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Most popular questions from this chapter

As discussed in the A Closer Look box on "Measurement and the Uncertainty Principle" the essence of the uncertainty principle is that we can't make a measurement without disturbing the system that we are measuring. (a) Why can't we measure the position of a subatomic particle without disturbing it? (b) How is this concept related to the paradox discussed in the Closer Look box on "Thought Experiments and Schr枚dinger's Cat"?

(a) According to the Bohr model, an electron in the ground state of a hydrogen atom orbits the nucleus at a specific radius of \(0.53 \AA\). In the quantum mechanical description of the hydrogen atom, the most probable distance of the electron from the nucleus is \(0.53 \AA\). Why are these two statements different? (b) Why is the use of Schr枚dinger's wave equation to describe the location of a particle very different from the description obtained from classical physics? (c) In the quantum mechanical description of an electron, what is the physical significance of the square of the wave function, \(\psi^{2}\) ? \(6.55\) (a) For \(n=4\), what are the possible values of \(l\) ? (b) For \(l=2\), what are the possible values of \(m_{l}\) ? (c) If \(m_{l}\) is 2 , what are the possible values for \(l\) ?

Einstein's 1905 paper on the photoelectric effect was the first important application of Planck's quantum hypothesis. Describe Planck's original hypothesis, and explain how Einstein made use of it in his theory of the photoelectric effect.

A hydrogen atom orbital has \(n=5\) and \(m_{l}=-2\). (a) What are the possible values of \(l\) for this orbital? (b) What are the possible values of \(m_{s}\) for the orbital?

Consider a transition in which the hydrogen atom is excited from \(n=1\) to \(n=\infty\). (a) What is the end result of this transition? (b) What is the wavelength of light that must be absorbed to accomplish this process? (c) What will occur if light with a shorter wavelength than that in part (b) is used to excite the hydrogen atom? (d) How the results of parts (b) and (c) related to the plot shown in Exercise \(6.88\) ?
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