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

각각의 전자는 4개의 양자수로 설명되며 그 중 3개는 상호 관련된 값을 가집니다. 이 세 개의 양자수는 공간에서 전자가 위치할 가능성이 가장 큰 곳을 정의합니다. 주 양자수 n은 전자가 속하는 에너지 준위를 나타냅니다.

n은 1, 2, 3 등의 정수 값을 가질 수 있습니다. n의 값이 클수록 전자는 핵에서 멀리 떨어져 있습니다. 각운동량, 또는 방위 양자수 엘 은 전자가 차지하는 궤도상의 형태를 설명하는데 이것은 전자의 각운동량과 관련이 있습니다.

엘은 n의 각 값에 대해 0부터 n 마이너스 1 까지의 정수 값을 가질 수 있습니다. n이 1일 때, 엘은 0입니다. n이 2일 때 엘은 두 개의 가능한 값 0과 1을 가집니다.

n이 3일 때, 엘은 0, 1 또는 2일 수 있습니다. 가능한 엘 값의 수는 n번째 에너지 준위에서 서로 다른 모양의 궤도 그룹 또는 부껍질의 수를 나타냅니다. 부껍질은 엘 값과 관련된 문자로 지정됩니다.

0, 1, 2, 3은 각각 s, p, d, f 궤도에 해당합니다. 이 내용은 다음 단원에서 논의될 것입니다. 자기 양자수 엠 엘은 전자가 차지하는 궤도 공간의 배향을 설명하는데 이 값은 전자의 각운동량과도 관련이 있습니다.

엠 엘은 0을 포함하여 l과 l 사이의 정수 값을 가질 수 있습니다. 지정된 부껍질의 배향 수는 2엘 플러스1과 같습니다. n이 2일 때 엘은 0 또는 1이 될 수 있으므로 두 개의 부껍질이 있습니다.

이것들은 각각 2s 및 2p 부껍질입니다. 엠 엘에 1, 0 및 1의 세 개 값이 있으므로 2p 부껍질에는 3개의 2p 궤도가 있습니다. 네 번째 양자수인 엠 에스는 스핀 양자수입니다.

전자는 회전하는 전하이며 작은 막대 자석처럼 작동합니다. 전자에 대해 가능한 두 개의 스핀 운동은 이분의 일 엠 에스로 표시되는 시계방향과 마이너스 이분의 일 엠 에스로 표시되는 시계 반대방향입니다.

양자수

원자 내 전자의 에너지는 양자화되어 있다고 합니다. 즉, 특정 특정 값과만 같을 수 있고 한 에너지 수준에서 다른 에너지 수준으로 이동할 수 있지만 원활하게 전환하거나 이러한 수준 사이에 머물 수는 없습니다.

에너지 준위는 n 값으로 표시됩니다. 여기서 n = 1, 2, 3 등입니다. 일반적으로 원자 내 전자의 에너지는 n 값이 클수록 더 큽니다. 이 숫자 n을 주양자수라고 합니다. 주양자수는 에너지 준위의 위치를 정의합니다. 이는 본질적으로 보어 원자 설명의 n과 동일한 개념입니다. 주요 양자수의 또 다른 이름은 쉘 번호(shell number)입니다.

양자역학적 모델은 핵 주위의 3차원 공간에서 전자를 찾을 확률을 지정하며 슈뢰딩거 방정식의 해를 기반으로 합니다.

또 다른 양자수는 2차(각운동량) 양자수인 l입니다. 이는 l = 0, 1, 2, …, n – 1의 값을 가질 수 있는 정수입니다. 이는 n = 1인 궤도는 l = 0 중 하나의 값만 가질 수 있는 반면, n = 2는 허용한다는 것을 의미합니다. l = 0, l = 1 등입니다. 주양자수 n은 오비탈의 일반적인 크기와 에너지를 정의하는 반면, 2차 양자수 l은 오비탈의 모양을 지정합니다. l 값이 동일한 궤도는 하위 껍질을 정의합니다.

l = 0인 오비탈을 s 오비탈이라고 하며, s 서브쉘을 구성합니다. 값 l = 1은 p 궤도에 해당합니다. 주어진 n에 대해 p 오비탈은 p 서브쉘을 구성합니다(예: n = 3인 경우 3p). l = 2인 오비탈을 d 오비탈이라고 하고, 그 뒤에 l = 3, 4, 5인 경우 f-, g-, h-오비탈이라고 합니다.

자기 양자수 m_l는 특정 궤도의 상대적인 공간 방향을 지정합니다. 일반적으로 m_l는 –l, –(l – 1), …, 0, …, (l – 1), l과 동일할 수 있습니다. 동일한 값의 l(즉, 동일한 서브쉘에서)을 갖는 가능한 오비탈의 총 개수는 2l + 1입니다. 따라서 s 서브쉘(l = 0)에는 1개의 s-오비탈이 있고, 3개의 p-오비탈이 있습니다. p 서브쉘(l = 1)에서는 d 서브쉘에 5개의 d 궤도(l = 2), f 서브쉘에는 7개의 f 궤도(l = 3) 등이 있습니다. 주요 양자수는 전자 에너지의 일반적인 값을 정의합니다. 각운동량 양자수는 궤도의 모양을 결정합니다. 그리고 자기양자수는 우주에서 궤도의 방향을 지정합니다.

이전 단락에서 논의된 세 가지 양자수는 전자 궤도를 설명하는 데 적합하지만 일부 실험에서는 관찰된 모든 결과를 설명하기에 충분하지 않은 것으로 나타났습니다. 1920년대에 수소선 스펙트럼을 매우 높은 분해능으로 검사할 때 일부 선은 실제로 단일 피크가 아니라 밀접하게 간격을 둔 선 쌍이라는 것이 입증되었습니다. 이것이 이른바 스펙트럼의 미세구조인데, 같은 궤도에 있는 전자들이라도 전자들의 에너지에 추가적인 작은 차이가 있다는 것을 의미합니다. 이러한 관찰로 인해 Samuel Goudsmit과 George Uhlenbeck은 전자가 네 번째 양자수를 가지고 있다고 제안했습니다. 이것은 이것을 스핀 양자수 또는 s라고 불렀습니다.

다른 세 개의 양자수 n, l, m_l는 전자가 위치할 가능성이 가장 높은 공간 부분을 정의하는 특정 원자 궤도의 특성입니다. 궤도는 원자의 전자에 대한 슈뢰딩거 방정식을 푼 결과입니다.

네 번째 양자수 ms는 스핀 양자수입니다. 띠며 전자는 회전하는 전하를작은 막대 자석처럼 행동합니다. 전자의 가능한 두 가지 회전 운동은 시계 방향과 시계 반대 방향입니다. 궤도에 있는 전자의 경우 이 두 가지 가능성은 스핀 양자수로 표시됩니다. 시계 방향 스핀은 +1/2, 시계 반대 방향 스핀은 -1/2입니다. 정수가 아닌 값을 갖는 유일한 양자수입니다.

이 문서는 에서 발췌되었습니다 <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>.

원자에 있는 전자의 에너지는 양자화된다고 합니다. 즉, 특정 특정 값에만 같을 수 있으며 하나의 에너지에서 점프 할 수 있습니다 ...

Education

교육

JoVE Core

Chemistry

화학

하나

Electronic Structure of Atoms

원자의 전자 구조

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 de broglie wavelength

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the uncertainty principle

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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

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the pauli exclusion principle

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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

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the aufbau principle and hund's rule

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electron configuration of multielectron atoms

electron-configuration-of-multielectron-atoms

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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 화학은 간결하고 이해하기 쉬운 애니메이션을 통해 일반 화학 개념을 설명합니다. 또한, 과학자가 직접 고전실험과 연구실험을 진행하는 실사 영상을 제공합니다.

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

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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

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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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