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

Short Answer

Expert verified
Mg: 0 unpaired; Ge: 2 unpaired; Br: 1 unpaired; V: 3 unpaired; Y: 1 unpaired; Lu: 1 unpaired.

Step by step solution

01

Understand the Basics of Electron Configuration

Electron configuration describes the distribution of electrons in the orbitals of an atom. The notation uses numbers and letters to represent the shells and orbitals. For example, \([ ext{noble gas}] ext{ shell number} ext{orbital type}^{ ext{number of electrons}}\).
02

Magnesium (Mg) Configuration

Magnesium has an atomic number of 12. Its electron configuration in full form is \([ ext{Ne}] 3s^2\). Since it is in the 3rd period and the s-block, it has no unpaired electrons because both electrons in the 3s orbital are paired.
03

Germanium (Ge) Configuration

Germanium has an atomic number of 32. Its condensed electron configuration is \([ ext{Ar}] 3d^{10} 4s^2 4p^2\). It is in the 4th period and p-block. It has 2 unpaired electrons in the 4p orbitals as it partially fills the p-orbital.
04

Bromine (Br) Configuration

Bromine has an atomic number of 35. Its condensed electron configuration is \([ ext{Ar}] 3d^{10} 4s^2 4p^5\). Bromine, in the p-block, has 1 unpaired electron in the 4p orbital.
05

Vanadium (V) Configuration

Vanadium has an atomic number of 23. Its condensed electron configuration is \([ ext{Ar}] 3d^3 4s^2\). It is in the d-block; this configuration has 3 unpaired electrons in the 3d orbitals.
06

Yttrium (Y) Configuration

Yttrium has an atomic number of 39. Its condensed electron configuration is \([ ext{Kr}] 4d^1 5s^2\). It is in the 5th period and d-block, with 1 unpaired electron in the 4d orbital.
07

Lutetium (Lu) Configuration

Lutetium has an atomic number of 71. Its condensed electron configuration is \([ ext{Xe}] 4f^{14} 5d^1 6s^2\). Lutetium, being in the f-block transition period, has 1 unpaired electron in the 5d orbital.

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Key Concepts

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

Unpaired Electrons
In atoms, electrons are arranged in orbitals with specific shapes and energies. When an orbital is only partially filled, the unpaired electrons are those that do not have a partner with opposite spin. Electrons prefer to pair up because it minimizes repulsion in the orbital, leading to a more stable state.

For example, in the atom of magnesium (Mg), all the electrons in its orbitals are paired, leading to a total of zero unpaired electrons. On the other hand, in bromine (Br), the 4p orbital contains five electrons, meaning one electron remains unpaired, resulting in one unpaired electron. The presence and quantity of unpaired electrons influence an element's magnetic properties. Atoms with unpaired electrons exhibit paramagnetic behavior, which means they are attracted to magnetic fields.
Orbital Types
In an atom, electrons are found in different types of orbitals distinguished by their shapes and capacities. The main orbital types are designated as s, p, d, and f.

  • s-orbitals are spherical and can hold a maximum of 2 electrons.
  • p-orbitals are dumbbell-shaped and can hold up to 6 electrons across the three p orbitals.
  • d-orbitals have more complex shapes, holding up to 10 electrons across five d orbitals.
  • f-orbitals are even more complex and can accommodate up to 14 electrons across seven f orbitals.
Each type of orbital is associated with different energy levels or shells. For instance, the 3d orbitals present in vanadium (V) and yttrium (Y) are filled after the 4s, due to these complex energy level interactions. Understanding these orbital shapes and capacities helps in predicting how atoms will bond and interact with each other.
Condensed Electron Configuration
Condensed electron configurations simplify long electron notation by using the closest noble gas as a reference point, enclosed in brackets. This notation still provides comprehensive information about electron distribution.

For example, the configuration \[\text{[Ne]} 3s^2\] for magnesium (Mg) implies that magnesium shares the complete electron configuration of neon, plus two additional electrons in the 3s orbital. This not only reduces repetition in writing but also highlights the relationship between different elements in the periodic table. By observing the condensed configuration, you can infer which periods and blocks the atom belongs to. This is particularly useful for identifying similarities in chemical properties among elements.
Electron Distribution
Electron distribution refers to the way electrons are extended through an atom's orbitals. This distribution follows the Aufbau principle, where electrons fill the lowest energy orbitals available. The distribution determines the chemical and physical properties displayed by elements.

  • Electrons fill orbitals in a specific order: first s, then p, followed by d, and sometimes f.
  • Within a shell, the order of filling is determined by increasing energy: 1s before 2s, 2s before 2p, and so on.
  • The periodic table itself is arranged based on electron distribution, with periods representing the filling of specific orbitals.
The electron distribution in yttrium (Y) and lutetium (Lu), for example, points to their characteristics as transition metals. This is due to their partially filled d or f orbitals, which provide unique electronic structures and contribute to their varied chemical behaviors.

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Most popular questions from this chapter

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?

Certain elements emit light of a specific wavelength when they are burned or heated in a non-luminous flame. Historically, chemists used such emission wavelengths to determine whether specific elements were present in a sample. Some characteristic wavelengths for a few of the elements are given in the following table: $$\begin{array}{llll} \hline \mathrm{Ag} & 328.1 \mathrm{nm} & \mathrm{Fe} & 372.0 \mathrm{nm} \\ \mathrm{Au} & 267.6 \mathrm{nm} & \mathrm{K} & 404.7 \mathrm{nm} \\ \mathrm{Ba} & 455.4 \mathrm{nm} & \mathrm{Mg} & 285.2 \mathrm{nm} \\ \mathrm{Ca} & 422.7 \mathrm{nm} & \mathrm{Na} & 589.6 \mathrm{nm} \\ \mathrm{Cu} & 324.8 \mathrm{nm} & \mathrm{Ni} & 341.5 \mathrm{nm} \\ \hline \end{array}$$ (a) Determine which of these emissions occur in the ultraviolet part of the spectrum. (b) Which emission has the highest frequency and which one has the lowest frequency? (c) When burned, a sample of an unknown substance is found to emit light of frequency \(6.58 \times 10^{14} \mathrm{~s}^{-1} .\) Which of these elements is probably in the sample?

(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? (d) For the hydrogen atom, list the following orbitals in order of increasing energy (that is, most stable ones first \(): 4 f, 6 s, 3 d, 1 s, 2 p\).

Identify the specific element that corresponds to each of the following electron configurations and indicate the number of unpaired electrons for each: (a) \(1 s^{2} 2 s^{2}\) (b) \(1 s^{2} 2 s^{2} 2 p^{4}\) (d) \([\mathrm{Kr}] 5 s^{2} 4 d^{10} 5 p^{4}\) (c) \([\mathrm{Ar}] 4 s^{1} 3 d^{5}\)

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.

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