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

כל אלקטרון מתואר על ידי ארבעה מספרים קוונטיים, לשלושה מהם ערכים הקשורים זה בזה. שלושת המספרים הקוונטיים הללו מגדירים היכן בחלל סביר להניח שהאלקטרון ממוקם. המספר הקוונטי היסודי, n, מציין את רמת האנרגיה שאליה שייך אלקטרון.ל-n יכולים להיות ערכים שלמים של 1, 2, 3 וכן האלה. ככל שערכו של n גדול יותר, כך האלקטרון רחוק יותר מהגרעין. מספר הקוונטום הזוויתי, l, מתאר את צורת האורביטל שהאלקטרון נמצא בו וקשור לתנע הזוויתי של האלקטרון.l יכול לכלול ערכים שלמים בין 0 ל-n מינוס 1 לכל ערך של n. כאשר n הוא 1, l הוא אפס. כאשר n הוא 2, יש ל-l שני ערכים אפשריים אפס ו-1.כאשר n הוא 3, l יכול להיות אפס, 1 או 2. מספר הערכים האפשריים של l מציין את המספר של קבוצות אורביטלים בצורות שונות או של תת קליפות ברמת אנרגיה של n. תת קליפות מסומנות באותיות המשויכות לערכים של l.אפס, 1, 2 ו-3 תואמים לאורביטלי s, p, d ו-f, בהתאמה. אלה יידונו בשיעור הבא. המספר הקוונטי המגנטי, m-l, מתאר את כיוון האלקטרון בחלל שמאכלס האורביטל, מידע הקשור גם לתנע הזוויתי של האלקטרון.ל-m-l יכול להיות כל ערך שלם בין מינוס l ל-l, כולל אפס. מספר האפשרויות לתת קליפה נתונה שווה ל-2l 1. כאשר n הוא 2, יש שתי תת קליפות, כיוון ש-l יכול להיות אפס או 1.אלה הן תת הקליפות 2s ו-2p, בהתאמה. תת קליפה 2p כוללת שלושה אורביטלי 2p, מכיוון שיש שלושה ערכים עבור ml:מיוס 1, אפס ו-1. המספר הקוונטי הרביעי, m-s, הוא מספר הספין הקוונטי.אלקטרונים הם מטענים מסתובבים ומתנהגים כמו מגנטים זעירים. שתי תנועות הסיבוב האפשריות של האלקטרון הן עם כיוון השעון, המסומנת כ-m-s של פלוס חצי, ונגד כיוון השעון, המסומנת כ-m-s של מינוס חצי.

מספרים קוונטיים

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אומרים שהאנרגיה של אלקטרון באטום היא קוונטית; כלומר, הוא יכול להיות שווה רק לערכים ספציפיים מסוימים ויכול לקפוץ מרמת אנרגיה אחת לאחרת אך לא לעבור בצורה חלקה או להישאר בין הרמות הללו. 

רמות האנרגיה מסומנות בערך n, כאשר n = 1, 2, 3 וכו'. באופן כללי, האנרגיה של אלקטרון באטום גדולה יותר עבור ערכים גדולים יותר של n. מספר זה, n, מכונה המספר הקוונטי העיקרי. המספר הקוונטי העיקרי מגדיר את מיקומה של רמת האנרגיה. זה בעצם אותו מושג כמו ה-n בתיאור האטום של בוהר. שם נוסף למספר הקוונטי העיקרי הוא מספר הקליפה. 

המודל הקוונטי-מכני מציין את ההסתברות של מציאת אלקטרון במרחב התלת מימדי סביב הגרעין והוא מבוסס על פתרונות של משוואת שרדינגר. 

מספר קוונטי נוסף הוא l, המספר הקוונטי המשני (תנע זוויתי). זהו מספר שלם שעשוי לקבל את הערכים, l = 0, 1, 2, …, n – 1. משמעות הדבר היא שהאורביטל עם n = 1 יכול לקבל רק ערך אחד של l, l = 0, ואילו n = 2 מאפשר l = 0 ו-l = 1, וכן הלאה. בעוד שהמספר הקוונטי העיקרי, n, מגדיר את הגודל והאנרגיה הכללית של האורביטל, המספר הקוונטי המשני l מציין את צורת האורביטל. אורביטלים בעלי אותו ערך של l מגדירים כתת-קליפה.

אורביטלים עם l = 0 נקראים s אורביטלים, והם מרכיבים את התת-קליפה. הערך l = 1 מתאים לאורביטלים p. עבור n נתון, אורביטלים p מהווים תת-קליפה p (למשל, 3p אם n = 3). האורביטלים עם l = 2 נקראים האורביטלים d, ואחריהם האורביטלים f-, g- ו-h עבור l = 3, 4 ו-5.


המספר הקוונטי המגנטי, ml, מציין את הכיוון המרחבי היחסי של אורביטל מסוים. באופן כללי, ml יכול להיות שווה ל-l, –(l – 1), …, 0, …, (l – 1), l. המספר הכולל של אורביטלים אפשריים עם אותו ערך של l (כלומר, באותה תת-קליפה) הוא 2l + 1. לפיכך, יש s-אורביטל אחד בתת-קליפה s (l = 0), ישנם שלושה p-אורביטלים בתת-קליפה p (l=1), חמישה d-אורביטלים בתת-קליפה d (l=2), שבעה f-אורביטלים של f בתת-קליפה (l=3), וכן הלאה. המספר הקוונטי העיקרי מגדיר את הערך הכללי של אנרגיה אלקטרונית. המספר הקוונטי של התנע הזוויתי קובע את צורת האורביטל. והמספר הקוונטי המגנטי מציין את כיוון האורביטל בחלל.


בעוד ששלושת המספרים הקוונטיים שנדונו בפסקאות הקודמות פועלים היטב לתיאור אורביטלים של אלקטרונים, כמה ניסויים הראו שהם לא מספיקים בשביל להסביר את כל התוצאות שנצפו. הוכח בשנות ה-20 שכאשר ספקטרום של קוי מימן נבחנים ברזולוציה גבוהה במיוחד, יש קווים שהם למעשה לא פסגות בודדות, אלא זוגות של קווים מרווחים. זהו מה שנקרא המבנה העדין של הספקטרום, והוא מרמז שיש הבדלים קטנים נוספים באנרגיות של אלקטרונים גם כשהם ממוקמים באותו אורביטל. תצפיות אלה הובילו את סמואל חאודסמיט וג'ורג' אולנבק להציע כי לאלקטרונים יש מספר קוונטי רביעי. הם קראו לזה המספר הקוונטי של הספין או s. 

שלושת המספרים הקוונטיים האחרים, n, l ו-ml הם מאפיינים של אורביטלים אטומיים ספציפיים המגדירים גם באיזה חלק בחלל סביר להניח שהאלקטרון נמצא. אורביטלים הם תוצאה של פתרון ממשוואת שרדינגר עבור אלקטרונים באטומים. 

המספר הקוונטי הרביעי, ms, הוא המספר הקוונטי בספין. אלקטרונים מסובבים מטענים ומתנהגים כמו מגנטים קטנטנים. שתי תנועות הסיבוב האפשריות של האלקטרון הן עם כיוון השעון ונגד כיוון השעון. עבור אלקטרון באורביטל, שתי האפשרויות הללו מסומנות על ידי מספרי ספין קוונטיים, +1/2 עבור סיבוב בכיוון השעון ו-1/2 עבור סיבוב נגד כיוון השעון. זהו המספר הקוונטי היחיד שיש לו ערכים לא אינטגרלים.

טקסט זה מותאם מ <a href="https://openstax.org/books/chemistry-2e/pages/6-3-development-of-quantum-theory">Openstax, Chemistry 2e, Section 6.3: Development of Quantum Theory</a>

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אומרים שהאנרגיה של אלקטרון באטום מכומתת; כלומר, זה יכול להיות שווה רק לערכים ספציפיים מסוימים והוא יכול לקפוץ מאנרגיה אחת ...

Education

JoVE Core

Chemistry

כימיה

אחד

Electronic Structure of Atoms

מבנה אלקטרוני של אטומים

KEY TERMS AND CONCEPTS

מונחים ומושגים מרכזיים

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

the wave nature of light

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the bohr model

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emission spectra

Line Spectra from Heated Gases

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the de broglie wavelength

Electron Waves and Standing Orbits

Electron waves and standing orbits explain how tiny particles can behave like waves. Large objects in the macroscopic world, like a billiard ball on a table, follow classical physics. A ball keeps moving in a straight line unless it hits another ball or a force such as friction acts on it. It also has a well-defined position, velocity, and momentum, where momentum is mass times velocity. Waves behave differently from macroscopic particles. When waves interact, they can form interference...

the uncertainty principle

Electron Position and Momentum Limits

Heisenberg’s uncertainty principle sets a limit on how precisely we can know an electron’s position and momentum at the same time. Momentum is the motion of a particle, and the two measurements affect each other. If the momentum is known more accurately, the position becomes less certain, and the reverse is also true. Heisenberg described this limit with an equation that uses Planck’s constant. The equation shows the smallest possible uncertainty for position and momentum together. It explains...

the quantum-mechanical model of an atom

Electron Orbitals in Quantum Mechanics

Quantum mechanics explains how electrons behave in atoms using waves and probability. Erwin Schrödinger built on de Broglie’s idea that an electron in hydrogen could act like a circular standing wave instead of moving in fixed circular paths. He then derived the Schrödinger equation, which became a major step in modern atomic theory. When Schrödinger applied his equation to hydrogen-like atoms, it matched Bohr’s energy expression and the Rydberg formula for hydrogen spectra. He described...

quantum numbers

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...

atomic orbitals

Electron Regions in Atomic Orbitals

Electron regions in atomic orbitals show where an electron is most likely to be found in an atom. These three-dimensional regions are often drawn as boundary surfaces around the densest part of the cloud. The shape of an orbital depends on the angular momentum quantum number, l. This value can range from 0 to n - 1, where n is the principal quantum number. For n = 1, only l = 0 is allowed. For n = 2, both l = 0 and l = 1 are allowed. Orbitals with the same value of l form a subshell. The l =...

the pauli exclusion principle

Electron Spin and Orbital Pairing

Electron spin and orbital pairing explain why only two electrons can fit in one atomic orbital. Electron configuration describes how electrons are arranged in an atom’s orbitals. It is written with three parts: the principal quantum number, n, the orbital type, or subshell, and a superscript that shows how many electrons are in that subshell. For example, 2p4 means four electrons in a p subshell with n = 2, and 3d8 means eight electrons in a d subshell with n = 3. The three quantum numbers...

the energies of atomic orbitals

Shielding and Orbital Penetration

Shielding and orbital penetration help explain why electrons in an atom have different energies. Electrons are attracted to the positive nucleus, but they also repel one another in atoms with more than one electron. The strength of these forces depends on the charge and the distance between the particles. Opposite charges attract, like charges repel, and the force gets weaker as the particles move farther apart. An electron that stays closer to the nucleus is held more tightly. That means...

the aufbau principle and hund's rule

Electron Filling Order in Atomic Orbitals

Electron filling order in atomic orbitals follows the aufbau principle and Hund's rule. To write an electron configuration, we build atoms in order of atomic number. Starting with hydrogen and moving across the periods of the periodic table, one proton is added to the nucleus and one electron is placed into the correct subshell. This process describes the ground-state electron configurations of the elements. The aufbau principle comes from the German word aufbau, which means "to build up." It...

electron configuration of multielectron atoms

electron-configuration-of-multielectron-atoms

Valence Electrons and Noble Gas Shorthand

Valence electrons and noble gas shorthand help show how electrons are arranged in multielectron atoms. Sodium, the alkali metal with atomic number 11, has one more electron than neon. That extra electron goes into the lowest-energy subshell available, the 3s orbital, so sodium has the configuration 1s2 2s2 2p6 3s1. Electrons in the outermost shell, where n is highest, are called valence electrons. Electrons in the inner shells are called core electrons. Because core electrons often match a...

key terms and concepts

Learn how n, l, m l, and m s describe electron energy levels, orbital shape, orbital orientation, and electron spin in atoms.

Electron Orbitals and Spin | JoVE K12

chemistry

JoVE Core Chemistry brings general chemistry concepts to life using concise and easy-to-understand animated video lessons. Plus, in the scientist-in-action videos, we demonstrate classical and original research experiments performed in today's laboratories worldwide.

Structure And Properties Of Matter

Atomic structure

Tennessee Academic Standards

High School

Matter and Its Interactions

CHEM1.PS1.12

Virginia  Standards of Learning

HIgh School

CH.2

CH.2.e

PS.2

PS.2.a

Physics

PH.9

PH.9.b

Arizona Science Standards

HS.P1

HS.P1U1.1

Texas Essential Knowledge and Skills

CHEM.6

CHEM.6.B

Florida Department of Education

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

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Chemical Reactions

HS-PS1-7.

HS. Waves and Electromagnetic Radiation

HS-PS4-3.

Georgia Standards of Excellence

SC1.

electron-configuration-and-chemical-properties

Electron Configuration and Chemical Properties

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Molecules and Compounds

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Surface Tension, Capillary Action, and Viscosity

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Vapor Pressure

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Phase Transitions: Melting and Freezing

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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

The Atomic Theory of Matter

The earliest recorded discussion of the basic structure of matter comes from ancient Greek philosophers. Leucippus and Democritus argued that all matter ...

Subatomic Particles

Dalton was only partially correct about the particles that make up matter. All matter is composed of atoms, and atoms are composed of three smaller ...

Ions and Ionic Charges

In ordinary chemical reactions, the nucleus &mdash; which contains the protons and neutrons of each atom and thus identifies the element &mdash; remains ...

Atomic Mass

Atoms &mdash; and the protons, neutrons, and electrons that compose them &mdash; are extremely small. For example, a carbon atom weighs less than 2 ...

The Bohr Model

Following the work of Ernest Rutherford and his colleagues in the early twentieth century, the picture of atoms consisting of tiny dense nuclei surrounded ...

Emission Spectra

When solids, liquids, or condensed gases are heated sufficiently, they radiate some of the excess energy as light. Photons produced in this manner have a ...

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

As early chemists discovered more elements, they realized that various elements could be grouped by their similar chemical behaviors. One such grouping ...

Periodic Classification of the Elements

The periodic table arranges atoms based on increasing atomic number so that elements with the same chemical properties recur periodically. When their ...

atomic-radii-and-effective-nuclear-charge

Atomic Radii and Effective Nuclear Charge

The elements in groups of the periodic table exhibit similar chemical behavior. This similarity occurs because the members of a group have the same number ...

Ionic Radii

Ionic radius is the measure used to describe the size of an ion. A cation always has fewer electrons and the same number of protons as the parent atom; it ...

Ionization Energy

The amount of energy required to remove the most loosely bound electron from a gaseous atom in its ground state is called its first ionization energy ...

Electron Affinity

The electron affinity (EA) is the energy change for adding an electron to a gaseous atom to form an anion (negative ion).



This process can be either ...

Alkali Metals

Group 1 elements are soft and shiny metallic solids. They are malleable, ductile, and good conductors of heat and electricity. The melting points of the ...

Halogens

Group 17 elements, known as halogens, are nonmetals. At room temperature, fluorine and chlorine are gases, bromine is a liquid, and iodine a solid. ...

Noble Gases


The elements in group 18 are noble gases (helium, neon, argon, krypton, xenon, and radon). They earned the name &ldquo;noble&rdquo; because they were ...

• 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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