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Chapter 7: Problem 14

What is meant by an orbital?

Short Answer

Expert verified
An orbital is a region in space around an atomic nucleus where there is a high probability of finding an electron. They are essential in understanding atomic structure, as electrons occupy specific energy levels and regions around the nucleus. There are four main types of orbitals: s, p, d, and f, each with different shapes, orientations, and capacities for holding electrons. These orbitals determine an element's electronic configuration, which influences its reactivity and bonding behavior.

Step by step solution

01

Definition of an Orbital

An orbital is a region in space around an atomic nucleus where the probability of finding an electron is high. It represents the behavior of electrons in atoms as they occupy specific energy levels and regions around the nucleus. In quantum mechanics, orbitals are described by wave functions that give information about the electron's energy, angular momentum, and spatial distribution.
02

Significance in Atomic Structure

Orbitals play a significant role in understanding the atomic structure since they are where electrons reside within atoms. Electrons fill the orbitals in a specific order following the rules of quantum mechanics. This filling up of orbitals leads to the periodicity of elements in the periodic table and helps to explain the chemical behavior of atoms.
03

Types of Orbitals

There are four main types of orbitals, designated as s, p, d, and f orbitals. Each type has a different shape and orientation in space, and they have varying numbers of sub-orbitals where electrons can be found. 1. s orbital: This is the simplest type of orbital with a spherical shape. It has only one sub-orbital, and hence, it can hold up to 2 electrons. 2. p orbital: A p orbital has a dumbbell shape with three possible orientations in space. They are separated into three sub-orbitals, with each one capable of holding up to 2 electrons. 3. d orbital: The d orbital is more complex, with five possible orientations in space. These orbitals can hold a total of 10 electrons, with each sub-orbital holding up to 2 electrons. 4. f orbital: F orbitals are even more complex than d orbitals, with several intricate shapes. They have seven possible orientations and can hold a total of 14 electrons. These orbitals combine in various ways to create the overall electronic configuration of an element, which, in turn, determines the element's reactivity and bonding behavior.

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Key Concepts

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

Quantum Mechanics
Quantum mechanics is the branch of physics that studies the behavior of particles on an atomic and subatomic level. In this microscopic world, particles such as electrons inhabit a universe dictated by probabilities rather than certainties. This means that instead of knowing exactly where an electron is, quantum mechanics gives us the likelihood of finding it in a particular region around the nucleus of an atom, known as an orbital.
For orbitals, this concept is crucial because it describes electrons not as pinpoint objects, but as wave-like entities described by mathematical functions called wave functions.
  • Wave Functions: These are mathematical equations that provide information about an electron's energy levels, angular momentum, and space distribution.
  • Probability Density: Represents the probability of finding an electron in a particular region of space.
In summary, orbitals in quantum mechanics are defined regions where electrons are likely to be found, which informs our understanding of atomic structures and behaviors.
Electron Configuration
Electron configuration is the arrangement of electrons in an atom's orbitals. It follows a set of principles derived from quantum mechanics, dictating how electrons fill low-energy orbitals before moving to high-energy ones. This arrangement is crucial because it influences an element's chemical properties and reactivity.
  • Pauli Exclusion Principle: No two electrons can occupy the same quantum state simultaneously. This means that each orbital can hold a maximum of two electrons, with opposite spins.
  • Hund's Rule: Electrons will fill each sub-orbital singly before pairing up, to minimize electron repulsion and lower energy levels.
  • Aufbau Principle: Electrons populate orbitals starting from the lowest available energy level to the highest.
These principles guide the order in which orbitals are filled, leading to a specific electron configuration pattern that can be predicted using the periodic table.
Periodic Table
The periodic table is a comprehensive chart that organizes elements according to their atomic number and electron configurations. At its core, it reveals how the structure of an element's orbitals determines its place in the table and its chemical properties.
  • Periods: Horizontal rows in the periodic table indicate increasing energy levels and electron configurations.
  • Groups: Vertical columns represent elements with similar orbital structures and chemical properties due to their valence electrons.
  • Electron Configuration Block: Sections such as the s, p, d, and f blocks reflect the types of orbitals that are being filled as you move across the row.
The arrangement of elements in the periodic table allows us to predict their behavior in chemical reactions, helping to understand the periodic trends such as atomic size, ionization energy, and electronegativity. It acts as a blueprint for scientists to forecast how different elements will interact based on their electron configurations and respective positions in the table.

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Most popular questions from this chapter

An excited hydrogen atom emits light with a wavelength of \(397.2 \mathrm{~nm}\) to reach the energy level for which \(n=2\). In which principal quantum level did the electron begin?

A carbon-oxygen double bond in a certain organic molecule absorbs radiation that has a frequency of \(6.0 \times 10^{13} \mathrm{~s}^{-1}\). a. What is the wavelength of this radiation? b. To what region of the spectrum does this radiation belong? c. What is the energy of this radiation per photon? per mole of photons? d. A carbon-oxygen bond in a different molecule absorbs radiation with frequency equal to \(5.4 \times 10^{13} \mathrm{~s}^{-1} .\) Is this radiation more or less energetic?

For hydrogen atoms, the wave function for the state \(n=3, \ell\) \(=0, m_{\ell}=0\) is $$ \psi_{300}=\frac{1}{81 \sqrt{3 \pi}}\left(\frac{1}{a_{0}}\right)^{3 / 2}\left(27-18 \sigma+2 \sigma^{2}\right) e^{-\sigma \beta} $$ where \(\sigma=r / a_{0}\) and \(a_{0}\) is the Bohr radius \(\left(5.29 \times 10^{-11} \mathrm{~m}\right)\). Calculate the position of the nodes for this wave function.

Three elements have the electron configurations \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2}\), \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{4}\), and \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2}\). The first ionization en- ergies of these elements (not in the same order) are \(0.590,0.999\), and \(0.738 \mathrm{MJ} / \mathrm{mol}\). The atomic radii are 104,160 , and \(197 \mathrm{pm}\). Identify the three elements, and match the appropriate values of ionization energy and atomic radius to each configuration. Complete the following table with the correct information.

Order the atoms in each of the following sets from the least exothermic electron affinity to the most. a. \(\mathrm{S}, \mathrm{Se}\) b. \(\mathrm{F}, \mathrm{Cl}, \mathrm{Br}, \mathrm{I}\)
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