Name: electron orbitals and spin
Uploaded: 2020-09-03T13:38:27.000Z
Duration: 2 min 43 s
Channel: JoVE

K12 Standards

ohios-learning-standards-and-model-curriculum

Ohio’s Learning Standards and Model Curriculum

9-12

Physical Science

Study Of Matter

Atoms

Quantum Numbers

Każdy elektron jest opisany przez cztery liczby kwantowe, z których trzy mają powiązane ze sobą wartości. Te trzy liczby kwantowe określają, w którym miejscu przestrzeni elektron najprawdopodobniej się znajdzie.

Główna liczba kwantowa, n, oznacza poziom energii, do którego należy elektron. n może mieć wartości całkowite jeden, dwa, trzy i tak dalej. Im większa wartość n, tym dalej elektron znajduje się od jądra.

Moment pędu lub azymutalna liczba kwantowa l opisuje kształt orbitala, który zajmuje elektron, który jest związany z momentem pędu elektronu. 

l może mieć wartości całkowite od 0 do n – 1 dla każdej wartości n. Gdy n jest równy jeden, l jest równy zero. Gdy n jest równe dwa, l ma dwie możliwe wartości — zero i jeden. Gdy n jest równe trzy, l może być równe zero, jeden lub dwa. Liczba możliwych wartości l wskazuje liczbę grup różnie ukształtowanych orbitali lub podpowłok na n-tympoziomie energetycznym.

Podpowłoki są oznaczone literami skojarzonymi z wartościami l. Zero, jeden, dwa i trzy odpowiadają odpowiednio orbitalom s, p, d i f. Zostaną one omówione w następnej lekcji. 

Magnetyczna liczba kwantowa, ml, opisuje orientację w przestrzeni orbitala, który zajmuje elektron, co jest również związane z momentem pędu elektronu. ml może mieć dowolną wartość całkowitą z zakresu od –l do +l, w tym zero. Liczba orientacji dla danej podpowłoki jest równa 2l + 1.

Gdy n jest równe dwa, istnieją dwie podpowłoki, ponieważ l może być równe zero lub jeden. Są to odpowiednio podpowłoki 2s i 2p. Podpowłoka 2p ma trzy orbitale 2p, ponieważ istnieją trzy wartości dla ml, –1, 0 i +1. 

Czwarta liczba kwantowa, m s, jest spinową liczbą kwantową. Elektrony wirują ładunki i zachowują się jak maleńkie magnesy sztabkowe. Dwa możliwe ruchy wirowe elektronu są zgodne z ruchem wskazówek zegara, wskazywane przez ms +1/2, i przeciwnie do ruchu wskazówek zegara, wskazywane przez ms -1/2.

liczby kwantowe

Mówi się, że energia elektronu w atomie jest skwantowana; to znaczy może być równa tylko pewnym określonym wartościom i przeskakiwać z jednego poziomu energii na drugi, ale nie może płynnie przechodzić ani pozostawać pomiędzy tymi poziomami.

Poziomy energii są oznaczone wartością n, gdzie n = 1, 2, 3 itd. Ogólnie rzecz biorąc, energia elektronu w atomie jest większa dla większych wartości n. Liczba ta, n, nazywana jest główną liczbą kwantową. Główna liczba kwantowa określa położenie poziomu energii. Jest to zasadniczo to samo pojęcie, co n w opisie atomu Bohra. Inną nazwą głównej liczby kwantowej jest liczba powłoki.

Model mechaniki kwantowej określa prawdopodobieństwo znalezienia elektronu w trójwymiarowej przestrzeni wokół jądra i opiera się na rozwiązaniach równania Schrödingera.

Inną liczbą kwantową jest l, drugorzędna liczba kwantowa (moment pędu). Jest to liczba całkowita, która może przyjmować wartości l = 0, 1, 2, …, n – 1. Oznacza to, że orbital z n = 1 może mieć tylko jedną wartość l, l = 0, natomiast n = 2 pozwala l = 0 i l = 1 i tak dalej. Podczas gdy główna liczba kwantowa n określa ogólny rozmiar i energię orbitalu, wtórna liczba kwantowa l określa kształt orbitalu. Orbitale o tej samej wartości l definiują podpowłokę.

Orbitale z l = 0 nazywane są orbitalami s i tworzą podpowłoki s. Wartość l = 1 odpowiada orbitalom p. Dla danego n, p orbitale tworzą podpowłokę p (np. 3p, jeśli n = 3). Orbitale z l = 2 nazywane są orbitalami d, po których następują orbitale f, g i h dla l = 3, 4 i 5.

Magnetyczna liczba kwantowa, ml, określa względną orientację przestrzenną konkretnego orbitalu. Ogólnie rzecz biorąc, ml może być równe –l, –(l – 1), …, 0, …, (l – 1), l. Całkowita liczba możliwych orbitali o tej samej wartości l (czyli w tej samej podpowłoce) wynosi 2l + 1. Zatem w podpowłoce s znajduje się jeden orbital s (l = 0), są trzy orbitale p w podpowłoce p (l = 1), pięć orbitali d w podpowłoce d (l = 2), siedem orbitali f w podpowłoce f (l = 3) i tak dalej. Główna liczba kwantowa określa ogólną wartość energii elektronowej. Liczba kwantowa momentu pędu określa kształt orbitalu. Magnetyczna liczba kwantowa określa orientację orbity w przestrzeni.

Chociaż trzy liczby kwantowe omówione w poprzednich akapitach dobrze sprawdzają się przy opisywaniu orbitali elektronowych, niektóre eksperymenty wykazały, że nie były one wystarczające do wyjaśnienia wszystkich zaobserwowanych wyników. W latach dwudziestych XX wieku wykazano, że gdy widma linii wodoru są badane z niezwykle dużą rozdzielczością, niektóre linie w rzeczywistości nie są pojedynczymi pikami, ale raczej parami blisko rozmieszczonych linii. Jest to tak zwana drobna struktura widma, która implikuje, że istnieją dodatkowe niewielkie różnice w energiach elektronów, nawet jeśli znajdują się one na tym samym orbicie. Te obserwacje skłoniły Samuela Goudsmita i George'a Uhlenbecka do zaproponowania, że elektrony mają czwartą liczbę kwantową. Nazwali to spinową liczbą kwantową lub s.

Pozostałe trzy liczby kwantowe n, l i ml to właściwości określonych orbitali atomowych, które również definiują, w której części przestrzeni najprawdopodobniej będzie zlokalizowany elektron. Orbitale powstają w wyniku rozwiązania równania Schrödingera dla elektronów w atomach.

Czwarta liczba kwantowa, ms, jest liczbą kwantową spinu. Elektrony wirują ładunkami i zachowują się jak małe magnesy sztabkowe. Dwa możliwe ruchy wirowe elektronu są zgodne z ruchem wskazówek zegara i przeciwne do ruchu wskazówek zegara. W przypadku elektronu na orbicie te dwie możliwości są oznaczone spinowymi liczbami kwantowymi, +1/2 dla spinu zgodnego z ruchem wskazówek zegara i -1/2 dla spinu przeciwnego do ruchu wskazówek zegara. Jest to jedyna liczba kwantowa posiadająca wartości niecałkowe.

Liczby kwantowe

Mówi się, że energia elektronu w atomie jest skwantowana; Oznacza to, że może być równy tylko pewnym określonym wartościom i może skakać z jednej energii ...

Education

JoVE Core

Chemistry

Chemia

Jeden

Electronic Structure of Atoms

Budowa elektronowa atomów

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

electron orbitals and spin

Electron orbitals are described by quantum numbers that show where an electron is most likely to be found around the nucleus. These numbers come from the quantum mechanical model, which is based on solutions of the Schrödinger equation. They also help explain why electron energy comes in set values instead of changing smoothly.

The principal quantum number, n, labels the energy level. It can be 1, 2, 3, and so on, and higher n values usually mean higher electron energy. This number also tells you the general location of the energy level. It is the same idea as the n value in the Bohr atom model, and it is also called the shell number.

A second number, l, is the secondary or angular momentum quantum number. It can take values from 0 to n - 1. For example, when n = 1, only l = 0 is allowed. When n = 2, l can be 0 or 1. This number gives the shape of the orbital, and orbitals with the same l value make up a subshell.

The l values also match the familiar orbital names. Orbitals with l = 0 are s orbitals, and they form s subshells. The value l = 1 corresponds to p orbitals, so if n = 3, the p orbitals belong to the 3p subshell. The orbitals with l = 2 are called d orbitals, followed by f, g, and h orbitals for l = 3, 4, and 5.

The magnetic quantum number, m l, tells the orientation of an orbital in space. Its possible values run from -l to +l, including 0. This means the number of orbitals in a subshell is 2l + 1. So an s subshell has one orbital, a p subshell has three, a d subshell has five, and an f subshell has seven.

The first three quantum numbers describe orbitals well, but high-resolution hydrogen spectra showed more detail. In the 1920s, scientists found that some spectral lines split into pairs of close lines. This fine structure suggests small energy differences for electrons even in the same orbital. Samuel Goudsmit and George Uhlenbeck used this result to propose a fourth quantum number.

They called the fourth number the spin quantum number, m s. Electrons behave like tiny bar magnets and can spin in two ways: clockwise or counterclockwise. These two possibilities are written as +1/2 and -1/2. Unlike the other quantum numbers, the spin quantum number is not an integer.

Electron Orbitals and Spin

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the bohr model

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emission spectra

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the de broglie wavelength

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quantum numbers

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atomic orbitals

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electron configuration of multielectron atoms

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key terms and concepts

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Electron Orbitals and Spin | JoVE K12

chemistry

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Structure And Properties Of Matter

Atomic structure

Tennessee Academic Standards

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Matter and Its Interactions

CHEM1.PS1.12

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CHEM.6

CHEM.6.B

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SC.912.P.10

SC.912.P.10.9

PHYS.9

PHYS.9.C

PHYS.9.D

Chemistry and Physics

IPC.7

IPC.7.E

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HS-PS1-7.

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HS-PS4-3.

Georgia Standards of Excellence

SC1.

electron-configuration-and-chemical-properties

Electron Configuration and Chemical Properties

Classifying Matter by State

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Classifying Matter by Composition

Matter: Pure Substances and Mixtures
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physical-and-chemical-properties-of-matter

Physical and Chemical Properties of Matter

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Physical Properties of Matter

A physical property is ...

Elements: Chemical Symbols and Isotopes

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Molecules and Compounds

Atoms and Molecules

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Classification of Elements and Compounds

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What is Energy?

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Energy Basics

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Chemical changes and their accompanying ...

molecular-comparison-of-gases-liquids-and-solids

Molecular Comparison of Gases, Liquids, and Solids

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Intermolecular vs Intramolecular Forces

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Intermolecular Forces

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comparing-intermolecular-forces-melting-point-boiling-point

Comparing Intermolecular Forces: Melting Point, Boiling Point, and Miscibility

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surface-tension-capillary-action-and-viscosity

Surface Tension, Capillary Action, and Viscosity

Surface Tension
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Phase Transitions

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phase-transitions-vaporization-and-condensation

Phase Transitions: Vaporization and Condensation

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Vapor Pressure

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Phase Transitions: Melting and Freezing

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phase-transitions-sublimation-and-deposition

Phase Transitions: Sublimation and Deposition

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Heating and Cooling Curves

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Phase Diagrams

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• Heterogeneous vs. homogeneous 
• Properties of matter 
• States of matter and its changes

Content elaboration: Matter was introduced in the elementary grades and the learning progression continued through middle school to include differences in the physical properties of solids, liquids and gases. Elements, compounds, mixtures, molecules, kinetic and potential energy and the particulate nature of matter were introduced. Content in Chemistry (e.g., electron configuration, molecular shapes, bond angles) will build on concepts in this course. Matter can be classified in broad categories, such as homogeneous and heterogeneous, according to its composition or by its chemical properties (e.g., reactivity, flammability, pH) and physical properties (e.g., color, solubility, odor, hardness, density, conductivity, melting point and boiling point, viscosity, malleability). Solutions are homogeneous mixtures of a solute dissolved in a solvent. The amount of a solid solute that can dissolve in a solvent generally increases as the temperature increases since the particles have more kinetic energy to overcome the attractive forces between them. Water is often used as a solvent since so many substances will dissolve in water. Aqueous solutions can be classified as acidic (below 7 on the pH scale), neutral (7 on the pH scale), or basic (above 7 on the pH scale), but the discussion of hydroxide and hydrogen ions as they relate to the pH scale is reserved for Chemistry. Physical properties can be used to separate the substances in mixtures, including solutions. Phase changes can be represented by graphing the temperature of a sample vs. the time it has been heated. Investigations include collecting data during heating, cooling and solid-liquid-gas phase changes. At times, the temperature will change steadily, indicating a change in the motion of the particles and the kinetic energy of the substance. However, during a phase change, the temperature of a substance does not change, indicating there is no change in kinetic energy. Since the substance continues to gain or lose energy during phase changes, these changes in energy are potential and indicate a change in the position of the particles. When heating a substance, a phase change will occur when the kinetic energy of the particles is great enough to overcome the attractive forces between the particles; the substance then melts or boils. [cite: 91, 92] Conversely, when cooling a substance, a phase change will occur when the kinetic energy of the particles is no longer great enough to overcome the attractive forces between the particles; the substance then condenses or freezes. [cite: 92, 93] Phase changes are examples of changes that can occur when energy is absorbed from the surroundings (endothermic) or released into the surroundings (exothermic). When thermal energy is added to a solid, liquid or gas, most substances increase in volume because the increased kinetic energy of the particles causes an increased distance between the particles. This results in a change in density of the material. Generally, solids have greater density than liquids, which have greater density than gases due to the spacing between the particles. [cite: 96, 101] The density of a substance can be calculated from the slope of a mass vs. volume graph. Differences in densities can be determined by interpreting mass vs. volume graphs of the substances. Students should be able to calculate mass, volume or density, given two of the three values.

Classification of matter

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Subatomic Particles

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Ions and Ionic Charges

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Atomic Mass

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The Bohr Model

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Emission Spectra

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The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of ...

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy ...

• Models of the atom (components)
• Ions (cations and anions)
• Isotopes

Content elaboration: Content introduced in middle school, where the atom was introduced as a small, indestructible sphere, is further developed in this course. Over time, technology was introduced that allowed the atom to be studied in more detail. The atom is composed of protons, neutrons and electrons that have measurable properties, including mass and, in the case of protons and electrons, a characteristic charge. An atom is empty space with a very small positively charged nucleus. The nucleus is composed of protons and neutrons. The electrons move about in the empty space that surrounds the nucleus. Although current understanding goes beyond the Bohr Model, it can still be used to represent the atom and develop the idea of valence electrons. Experimental evidence that led to the development of historic atomic models is reserved for Chemistry. All atoms of a particular element have the same atomic number; an element may have different isotopes with different mass numbers. [cite: 112, 113] Atoms may gain or lose valence electrons to become anions or cations. Atomic number, mass number, charge and identity of the element can be determined from the numbers of protons, neutrons and electrons. Atomic mass calculations and explanations about configuration of electrons and how atomic spectra are produced are reserved for Chemistry.

The Periodic Table

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Periodic Classification of the Elements

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atomic-radii-and-effective-nuclear-charge

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Ionic Radii

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Ionization Energy

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Electron Affinity

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This process can be either ...

Alkali Metals

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Halogens

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Noble Gases


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• Periodic law 
• Representative groups

Content elaboration: Content from the middle school level, specifically the properties of metals, nonmetals and metalloids and their positions on the periodic table, is further expanded in this course. The periodic table was arranged so that elements with similar chemical and physical properties are in the same group or family. When elements are listed in order of increasing atomic number, the same sequence of properties appears over and over again; this is the periodic law. [cite: 120, 121] Trends in simple observable properties, like density or melting point, can be examined within families or groups on the periodic table. These trends allow scientists to make predictions about new elements. Metalloids are elements that have some properties of metals and some properties of nonmetals. Metals, nonmetals, metalloids, periods and groups or families including the alkali metals, alkaline earth metals, halogens and noble gases can be identified by their position on the periodic table. Elements in Groups 1, 2 and 17 have characteristic ionic charges that will be used in this course to predict the formulas of compounds. Other trends in the periodic table (e.g., atomic radius, electronegativity, ionization energies) are reserved for Chemistry.

Periodic trends of the elements

Types of Chemical Bonds

Chemical bonding theories were pioneered by American chemist Gilbert&#xA0;N. Lewis. He developed a model called the Lewis model to explain the type and ...

• Bonding (ionic and covalent)
• Nomenclature

Content elaboration: Middle school content introduced the concept that compounds are composed of atoms of two or more different elements joined together chemically. In this course, the chemical joining of atoms is studied in more detail. Atoms may be bonded together by losing, gaining or sharing valence electrons to form molecules or three-dimensional lattices. An ionic bond involves the attraction of two oppositely charged ions, typically a metal cation and a nonmetal anion formed by transferring electrons between the atoms. An ion attracts oppositely charged ions from every direction, resulting in the formation of a three-dimensional lattice. Covalent bonds result from the sharing of electrons between two atoms, usually nonmetals. Covalent bonding can result in the formation of structures ranging from small individual molecules to three-dimensional lattices (e.g., diamond). The bonds in most compounds fall on a continuum between the two extreme models of bonding: ionic and covalent. Using the periodic table to determine ionic charge, formulas of ionic compounds containing elements from groups 1, 2, 17, hydrogen and oxygen can be predicted. Given a chemical formula, a compound can be named using conventional systems that include Greek prefixes where appropriate. Prefixes will be limited to represent values from one to 10. Given the name of an ionic or covalent substance, formulas can be written. Naming organic molecules is beyond this grade level and is reserved for an advanced chemistry course. Prediction of bond types from electronegativity values, polar covalent bonds, and writing formulas/naming compounds that contain polyatomic ions or transition metals are reserved for Chemistry.

Bonding and compounds

Electron Orbitals and Spin

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