Name: electron spin and orbital pairing
Uploaded: 2020-09-03T13:38:27.000Z
Duration: 3 min 6 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Chemistry and Physics

IPC.7

IPC.7.E

The Pauli Exclusion Principle

원자 궤도들은 원자의 전자들이 발견될 가능성이 가장 높은 영역입니다. 하지만 각 궤도가 몇 개의 전자를 점유할 수 있을까요? 파울리 배타 원리가 이 질문에 답변을 줍니다.

이 원리는 원자 안에 있는 어떤 두 전자도 같은 4개의 양자수를 가질 수 없다는 것입니다. 모든 궤도는 고정된 주양자수, 방위 양자수, 자기 양자수 값을 가집니다. 예를 들어 1s 궤도에 있는 전자는 항상 1의 주 양자수와 0의 방위 양자수 및 자기 양자수를 가집니다.

따라서 전자는 동일한 원자 궤도 안에 있으려면 서로 다른 스핀 양자수 값 또는 스핀을 가져야 합니다. 스핀 양자수 값에는 2분의 1 및 마이너스 2분의 1의 두 가지만 있다는 것을 상기해봅시다. 따라서 오직 두 개의 전자만이 같은 궤도를 차지할 수 있습니다.

따라서 하나의 궤도를 가지는 모든 s 부껍질은 2개의 전자만 수용할 수 있고 3개의 궤도를 가지는 모든 p 부껍질은 6개의 전자를 수용할 수 있습니다. 모든 d 및 f 부껍질은 최대로 각각 10개, 14개를 수용합니다. 원자의 원자 궤도에서의 전자의 분포의 배치는 텍스트나 도표 형태로 표현할 수 있습니다.

한 개의 전자가 최저 에너지 궤도인 1s를 차지하는 바닥 상태의 수소 원자를 생각해 보세요. 작성된 전자 배치는 해당 껍질 수를 가진 채원진 각각의 부껍질, 부껍질의 표시 문자 및 부껍질의 전자 수를 지정하는 위첨자 번호로 나타냅니다. 전자 배치의 궤도 도표 스타일에서는 채워진 부껍질 내의 각 궤도를 상자 또는 선으로, 각 전자는 화살표로 나타냅니다.

위방향 화살표는 2분의 1 스핀 또는 스핀업을 나타내고 아래방향 화살표는 마이너스 2분의 1 스핀 또는 스핀다운을 나타냅니다. 따라서 수소의 궤도 도표는 한 개의 위방향 화살표를 가지고 있습니다. 헬륨의 전자 배치는 원 에스 투 입니다.

두 전자는 동일한 껍질과 부껍질에 속하기 때문에 세 개의 동일한 양자수를 가집니다. 파울리 배타 원리에 따라 두 전자의 스핀 양자 수는 서로 다릅니다. 반대 방향의 스핀을 가진 전자들이 동일한 궤도 상에 위치하면 전자쌍이라고 합니다.

원자 번호가 3인 리튬의 경우 1s 궤도 안에 있는 두 전자는 전자쌍이고 2s 궤도 안에 있는 전자는 홑전자입니다. 일반적으로 홑전자는 스핀업으로 표현됩니다.

파울리 배제 원칙

원자의 궤도에서 전자의 배열을 전자 배열이라고 합니다. 우리는 세 가지 정보를 포함하는 기호로 전자 구성을 설명합니다.

<ol>
	<li>주요 양자 껍질의 수 n,</li>
	<li>궤도 유형(부 껍질, l)을 지정하는 문자</li>
	<li>해당 특정 부 껍질의 전자 수를 지정하는 위 첨자 숫자입니다.</li>
</ol>

예를 들어, 2p^4 표기법은 주 양자수(n)가 2인 p 부껍질(l = 1)에 있는 4개의 전자를 나타냅니다. 표기법 3d^8은 주양자수(n)가 3인 d 부껍질(l = 2)에 8 개의 전자가 있다는 것을 나타냅니다.

세 가지 양자수는 전자 궤도를 설명하는 데 적합하지만 일부 실험에서는 관찰된 모든 결과를 설명하기에는 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 m_s라고 불렀습니다.

적용된 자기장에서 전자는 서로 다른 에너지를 갖는 두 가지 방향을 가질 수 있습니다. 하나는 스핀 업 방향으로 자기장과 정렬되고, 하나는 스핀 다운 방향으로 정렬됩니다.

네 번째 양자수인 스핀 양자수(m_s)는 전자의 두 가지 다른 스핀 상태를 나타냅니다. 스핀 양자수는 -1/2(스핀 다운)과 +1/2(스핀 업)의 두 가지 값을 가질 수 있습니다.

전자 스핀은 고유 전자 "회전" 또는 "스핀"을 나타냅니다. 각 전자는 작은 자석이나 각운동량을 갖는 작은 회전 물체의 역할을 하거나, 회전이나 전류를 공간 좌표로 관찰할 수 없음에도 불구하고 전류가 흐르는 루프 역할을 합니다.

전체 전자 스핀의 크기는 하나의 값만 가질 수 있으며, 전자는 두 가지 양자화된 상태 중 하나로만 "회전"할 수 있습니다. 하나는 스핀의 z 구성요소가 z축의 양의 방향인 α 상태라고 합니다. 이는 스핀 양자수 m_s = +^1/^2에 해당합니다. 다른 하나는 β 상태라고 하며, 스핀의 z 구성요소는 음수이고 m_s = -^1/^2입니다.

모든 전자는 그것이 위치한 원자 궤도에 관계없이 두 가지 스핀 양자수 값 중 하나만 가질 수 있습니다. 외부 자기장이 가해지면 스핀이 다른 전자의 에너지가 달라집니다.

원자의 전자는 n, l, m_l, m_s의 네 가지 양자수로 완전히 설명됩니다. 처음 세 개의 양자수는 궤도를 정의하고 상호의존적인 반면, 네 번째 양자수는 스핀이라는 고유 전자 특성을 설명하므로 다른 양자수와 독립적입니다. 오스트리아의 물리학자 볼프강 파울리(노벨 물리학상: 1945년)는 원자 내 전자의 일반적인 행동을 이해하는 데 필요한 마지막 정보를 제공하는 일반 원리를 공식화했습니다. Pauli 배제 원리는 다음과 같이 공식화될 수 있습니다. 동일한 원자에 있는 두 개의 전자는 4개의 양자수 모두의 동일한 세트를 가질 수 없습니다. 이것이 의미하는 바는 스핀 양자수가 서로 다른 값을 갖는 경우에만 두 전자가 동일한 궤도(동일한 양자수 n, l, m_l 세트)를 공유할 수 있다는 것입니다. 스핀 양자수(m_s)는 +1/2와 -1/2의 두 가지 값만 가질 수 있으므로 동일한 오비탈에는 2개 이상의 전자가 포함될 수 없습니다(그리고 두 개의 전자가 동일한 오비탈에 위치하는 경우 반대 스핀을 가져야 합니다).따라서 모든 원자 궤도에는 0개, 1개 또는 2개의 전자만 채워질 수 있습니다.

전자 구성의 궤도 다이어그램 스타일은 점유된 부 껍질 내의 각 궤도를 상자 또는 선으로 나타내고 각 전자를 화살표로 나타냅니다. 1s^1의 전자 구성인 수소의 궤도 다이어그램은 다음과 같습니다.

<img alt="Figure1" src="https://www.jove.com/files/core/CDNSource/lessons/984/984Image_1.png" style="height: 40px;" />

위쪽 화살표는 플러스 하프 스핀 또는 스핀업을 나타내고 아래쪽 화살표는 마이너스 하프 스핀 또는 스핀다운을 나타냅니다. 따라서 수소의 궤도 다이어그램에는 위쪽 화살표가 하나 있습니다.

헬륨의 전자 구성은 1s^2입니다. 두 전자는 동일한 껍질과 부 껍질에 속하므로 세 개의 동일한 양자수를 갖습니다. Pauli 배제 원리에 따라 스핀 양자 수는 다릅니다. 반대 스핀을 갖는 전자가 동일한 궤도를 차지하면 쌍을 이루는 전자라고 합니다.

<img alt="Figure2" src="https://www.jove.com/files/core/CDNSource/lessons/984/984Image_2.png" style="height: 40px;" />

이 문서는 에서 발췌되었습니다, Chemistry 2e, Section 6.3: Development of Quantum Theory.

원자의 궤도에 있는 전자의 배열을 전자 배열이라고 합니다. 우리는 다음과 같은 기호로 전자 구성을 설명합니다 ...

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Electronic Structure of Atoms

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KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 describe orbitals well, but they do not explain every experimental result. In the 1920s, very high-resolution hydrogen spectra showed fine structure, where some lines split into two close peaks instead of one. This suggested that electrons in the same orbital can still have small energy differences. Samuel Goudsmit and George Uhlenbeck proposed a fourth quantum number to explain this behavior. They called it the spin quantum number, ms.

An electron can have two spin states in an external magnetic field. One state is spin up, which aligns with the magnetic field, and the other is spin down, which points against it. The spin quantum number has only two values, +1/2 and -1/2. These are also called the alpha and beta states. Electron spin is an intrinsic property, so each electron behaves like a tiny magnet, even though this motion cannot be observed in normal space.

A complete electron description uses four quantum numbers: n, l, ml, and ms. The first three quantum numbers define the orbital and depend on one another. The spin quantum number is independent because it describes the electron’s spin. Austrian physicist Wolfgang Pauli used this idea to state the Pauli exclusion principle. It says that no two electrons in the same atom can have the same set of all four quantum numbers.

This principle means that two electrons may share the same orbital only if their spin quantum numbers are different. Because ms has only two possible values, no more than two electrons can occupy one orbital. An atomic orbital can therefore hold zero, one, or two electrons. In orbital diagrams, each orbital is shown as a box or line and each electron as an arrow. A hydrogen atom with configuration 1s1 has one upward arrow, which means one spin-up electron.

Helium has the configuration 1s2. Its two electrons share the same shell and subshell, so they have three identical quantum numbers. They differ in spin, which follows the Pauli exclusion principle. Electrons with opposite spins in the same orbital are called paired.

Electron Spin and Orbital Pairing

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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...

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Learn how electron spin, quantum numbers, and orbital pairing explain why each atomic orbital holds at most two electrons in high school chemistry.

Electron Spin and Orbital Pairing | JoVE K12

chemistry

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Matter and its Interactions

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Electron Configuration and Chemical Properties

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Ions are atoms or molecules bearing an electrical charge. A cation (a positive ion) forms when a neutral atom loses one or more electrons from its valence ...

The Born-Haber Cycle

Lattice Energy&#xA0;

An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a ...

trends-in-lattice-energy-ion-size-and-charge

Trends in Lattice Energy: Ion Size and Charge

An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure ...

Covalent Bonding and Lewis Structures

Compared to ionic bonds, which results from the transfer of electrons between metallic and nonmetallic atoms, covalent bonds result from the mutual ...

Electronegativity

Whether a bond is nonpolar or polar covalent is determined by a property of the bonding atoms called electronegativity.&#xA0;

Electronegativity values of ...

bond-polarity-dipole-moment-and-percent-ionic-character

Bond Polarity, Dipole Moment, and Percent Ionic Character

Bond Polarity

The absolute value of the difference in electronegativity (&Delta;EN) of two bonded atoms provides a rough measure of the polarity to be ...

lewis-structures-of-molecular-compounds-and-polyatomic-ions

Lewis Structures of Molecular Compounds and Polyatomic Ions

To draw Lewis structures for complicated molecules and molecular ions, it is helpful to follow a step-by-step procedure as outlined:


	Determine the ...

Bond Energies and Bond Lengths

Stable molecules exist because covalent bonds hold the atoms together. The strength of a covalent bond is measured by the energy required to break it, ...

Bonding in Metals

Metallic bonds are formed between two metal atoms. A simplified model to describe metallic bonding has been developed by Paul Dr&#xFC;de called the ...

Model basic atomic structure and relate an element's atomic structure to its bonding, reactivity, and placement on the Periodic Table.

IPC.7.A

physical-and-chemical-properties-of-matter

Physical and Chemical Properties of Matter

The characteristics that enable us to distinguish one substance from another are called properties.

Physical Properties of Matter

A physical property is ...

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 ...

Use patterns within the Periodic Table to predict the relative physical and chemical properties of elements.

IPC.7.B

Classifying Matter by State

Chemistry is the study of matter and the changes it undergoes. Matter is anything that has mass and occupies space. Matter is all around us; the air, ...

Classifying Matter by Composition

Matter: Pure Substances and Mixtures
According to its composition, the matter can be classified into two broad categories &mdash; pure substances and ...

Phase Transitions

Whether solid, liquid, or gas, a substance&#39;s state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the ...

phase-transitions-vaporization-and-condensation

Phase Transitions: Vaporization and Condensation

The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize ...

Phase Transitions: Melting and Freezing

Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy ...

phase-transitions-sublimation-and-deposition

Phase Transitions: Sublimation and Deposition

Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and ...

Melting Points

Melting Points in Organic Chemistry
The melting point of a compound is the temperature at which the solid phase transitions into the liquid phase at a ...

Boiling Points

Source: Lara Al Hariri at the University of Massachusetts Amherst, MA, USA

	Preparation of the LaboratoryExpand
	Here, we show the laboratory preparation ...

Explain how physical and chemical properties of substances are related to their usage in everyday life such as in sunscreen, cookware, industrial applications, and fuels.

IPC.7.C

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 ...

Metal Flame Emission

Metal Flame Emission
Flame testing is an analytical technique where a sample is placed in a flame, and the characteristic flame color is used to identify ...

Atomic Orbitals

An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution ...

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that ...

The Energies of Atomic Orbitals

In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are ...

Explain how electrons can transition from a high energy level to a low energy state, emitting photons at different frequencies for different energy transitions.

Science concepts. The student knows that relationships exist between the structure and properties of matter. The student is expected to:

Electron Spin and Orbital Pairing

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