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Chapter 6: Problem 78

Identify the group of elements that corresponds to each of the following generalized electron configurations and indicate the number of unpaired electrons for each: (a) [noble gas]ns \(^{2} n p^{5}\) (b) \([\) noble gas \(] n s^{2}(n-1) d^{2}\) (c) \([\) noble gas \(] n s^{2}(n-1) d^{10} n p^{1}\) (d) \([\) noble \(\operatorname{gas}] n s^{2}(n-2) f^{6}\)

Short Answer

Expert verified
(a) Group 17 (Halogens) and one unpaired electron. (b) Group 4 (Transition metals) and zero unpaired electrons. (c) Group 13 and one unpaired electron. (d) f-block (Lanthanides or Actinides) and two unpaired electrons.

Step by step solution

01

Identify the group of elements

For this configuration, the last electron is added to the p orbital. Since there are five electrons in the p orbital, the element belongs to group 17 (halogens) in the periodic table.
02

Determine the number of unpaired electrons

Since there are five electrons in the p orbital, and each p orbital can hold a maximum of 6 electrons, there is one unpaired electron in this configuration. Answer for (a): Group 17 (Halogens) and one unpaired electron. (b) [noble gas] \(ns^2(n-1)d^2\)
03

Identify the group of elements

This configuration has the last electrons added to the d orbital. Since there are two electrons in the d orbital, the element belongs to group 4 (transition metals) in the periodic table.
04

Determine the number of unpaired electrons

Since there are two electrons in the d orbital, and each orbital consists of one pair of electrons (one with spin up and one with spin down) there are zero unpaired electrons in this configuration. Answer for (b): Group 4 (Transition metals) and zero unpaired electrons. (c) [noble gas] \(ns^2(n-1)d^{10}np^1\)
05

Identify the group of elements

This configuration has the last electron added to the p orbital. Since there is one electron in the p orbital, the element belongs to group 13 in the periodic table.
06

Determine the number of unpaired electrons

Since there is one electron in the p orbital and it is unpaired, there is one unpaired electron in this configuration. Answer for (c): Group 13 and one unpaired electron. (d) [noble gas] \(ns^2(n-2)f^6\)
07

Identify the group of elements

This configuration has the last electrons added to the f orbital. Since there are six electrons in the f orbital, the element belongs to the f-block of the periodic table (lanthanides or actinides).
08

Determine the number of unpaired electrons

Since there are six electrons in the f orbital, there are two unpaired electrons in this configuration. (Each f orbital can hold a maximum of 14 electrons. Having six electrons means that 4 orbitals are filled with pairs and the remaining 2 electrons are unpaired.) Answer for (d): f-block (Lanthanides or Actinides) and two unpaired electrons.

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Key Concepts

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

Periodic Table Groups
The periodic table is structured in such a way that elements are organized into groups, which are the vertical columns. Each group represents elements with similar properties due to having the same number of valence electrons. For example, Group 17 is known as the halogens. Halogens, like fluorine and chlorine, have seven valence electrons, leading to similar chemical behaviors.
  • Halogens typically react by gaining one electron to achieve a stable configuration similar to noble gases.
  • Group 4 elements, found in the transition metals section, often have electrons filling their d orbitals, influencing their metallic properties.
  • Group 13, known as the boron group, consists of elements with three valence electrons, leading to diverse bonding patterns.
Understanding the groups helps predict the reactivity and the type of bonds an element might form. The position of an element in a particular group thus plays a crucial role in determining its electronic configuration and reactivity.
Unpaired Electrons
Unpaired electrons are those that do not share an orbital with another electron of opposite spin. Electron pairing decreases the energy of an atom, making it more stable. However, unpaired electrons can make an atom more reactive.
  • For example, in the configuration \(np^5\) of halogens, there is one unpaired electron, which makes them highly reactive as they tend to gain one more electron to achieve a stable configuration.
  • In the d orbitals of transition metals, unpaired electrons can lead to different magnetic properties, such as paramagnetism.
  • The presence of unpaired electrons also affects the color properties of compounds, particularly in the transition metals.
Overall, the concept of unpaired electrons is vital in understanding the chemistry of elements, influencing their reactivity, magnetic properties, and even color.
Transition Metals
Transition metals are a large group within the periodic table characterized by filling their d orbitals. They include elements from Groups 3 to 12. Transition metals are well-known for several unique properties:
  • They can form various oxidation states, often due to the similar energy levels between their s and d electrons.
  • These metals are often used as catalysts because they can lend and take electrons easily.
  • Transition metals like iron and copper are central in biological systems and industrial processes.
  • The unique ability of their d electrons to absorb visible light leads to colorful compounds.
Due to their versatile chemical properties, transition metals play a critical role in numerous technological applications, making them a fundamental study area in chemistry.
Lanthanides and Actinides
Lanthanides and actinides are two series of elements that fill the f orbitals, often referred to as the 'f-block.' These elements have distinct characteristics:
  • Lanthanides are known for their magnetic and optical properties, making them vital in electronics and optics.
  • Actinides contain radioactive elements, with uranium and plutonium being integral in nuclear energy generation.
  • They often have several unpaired electrons, which can contribute to unique magnetic properties.
  • The complex electron configurations result in a wide range of oxidation states and chemical behaviors.
Being part of the f-block, these elements have fascinating chemistry and practical applications, from advanced technology to energy solutions, requiring a thorough understanding of their electron configurations.

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Most popular questions from this chapter

(a) What are the similarities of and differences between the \(1 s\) and \(2 s\) orbitals of the hydrogen atom? (b) In what sense does a \(2 p\) orbital have directional character? Compare the "directional" characteristics of the \(p_{x}\) and \(d_{x^{2}-y^{2}}\) orbitals. (That is, in what direction or region of space is the electron density concentrated?) (c) What can you say about the average distance from the nucleus of an electron in a \(2 s\) orbital as compared with a 3 s orbital? ( \(\mathbf{d}\) ) For the hydrogen atom, list the following orbitals in order of increasing energy (that is, most stable ones first): \(4 f, 6 s, 3 d, 1 s, 2 p\)

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? (b) Would this experiment work for a beam of cadmium (Cd) atoms? (c) Would this experiment work for a beam of fluorine (F) atoms?

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

Determine which of the following statements are false and correct them. (a) The frequency of radiation increases as the wavelength increases. (b) Electromagnetic radiation travels through a vacuum at a constant speed, regardless of wavelength. (c) Infrared light has higher frequencies than visible light. (d) The glow from a fireplace, the energy within a microwave oven, and a foghorn blast are all forms of electromagnetic radiation.

Consider a transition in which the electron of a 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 are the results of parts \((\mathrm{b})\) and \((\mathrm{c})\) related to the plot shown in Exercise \(6.88 ?\)
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