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

原子軌道とは 原子の電子が 最も多く存在する 領域のことです しかし それぞれの軌道は 何個の電子を 持つことができるのでしょうか？この疑問に答えてくれるのが パウリの排除原理です すべての軌道は 固定の主成分 角運動量 方位角運動量 磁気量子数に 対応しています 例えば 1s軌道の電子は 常に主量子数が 1方位角運動量と 磁気量子数が0です したがって 同じ原子軌道に 存在する電子は 異なるスピン量子数値を 持つ必要があります スピン量子数には 1/2と-1/2の 2つの値しかないことを 思い出してください したがって同じ軌道を占められる 電子は2つしかありません つまり 1つの軌道を持つ s部分殻には 2つの電子しか入れず 3つの軌道を持つ p部分殻には 6つの電子が 入ることができます d部分殻は10個 f部分殻は14個の電子を 収容することができます 原子の原子軌道間の 電子の分布は その電子配置によって テキストまたは 図の形で表されます 基底状態の 水素原子を考えてみましょう 1つの電子が最低エネルギー軌道 である1s軌道を占めます 電子配置が書かれた文字は それぞれの占有部分殻を 対応する殻の番号 部分殻の文字 部分殻内の電子の 数を示す上付きの番号で 表します 電子配置の軌道図のスタイルは 占有部分殻内の各軌道を 箱または線で表し 各電子を矢印で表します 上向きの矢印は1/2スピン スピンアップ）を表し 下向きの矢印は-1/2スピン スピンダウン）を表します したがって 水素の軌道図には 上向きの矢印が 1本あることになります ヘリウムの 電子配置は1s^2です 2つの電子は同じ殻と 部分殻に属しているので 3つの同じ量子数を持っています 2つの電子のスピン量子数は パウリの排除原理に 基づいて異なります 逆のスピンを持つ電子が 同じ軌道に入っていることを 対になっている」といいます 原子番号が3のリチウムでは 1s軌道の2つの電子が 対になっており 2s軌道の電子は 不対になっています 従来は 不対の電子は スピンアップで 表されていました

パウリの排他原理

原子の軌道上の電子の配置を電子配置といいます。電子配置は、次の3つの情報を含む記号で表します。 
 
 <ol>
 <li>主な量子殻の数 n 、 </li>
 <li>軌道のタイプ（小軌道l ）を指定する文字、および </li>
 <li>特定の小軌道内の電子の数を指定する上付き文字番号 </li>
 </ol>
 
 例えば、 2p4 という表記は、 p 小軌道内の 4 つの電子（ l=1 ）を示し、主な量子数（ n ）は 2 です。 3d 8 という表記は、 n = 3 の主軌道の d 小軌道（ l= 2 ）内の 8 つの電子を示します。 
 
 3つの量子数は、電子の軌道を記述するのに適していますが、実験によっては、すべての観測結果を説明するのに十分ではないことがわかりました。1920年代には、水素線のスペクトルを非常に高い分解能で観察すると、ある線が単一のピークではなく、間隔の狭い線のペアになっていることが実証されました。これは、スペクトルの微細構造と呼ばれるもので、電子が同じ軌道にあっても、そのエネルギーにはさらに小さな差があることを意味しています。これらの観測結果から、サミュエル・ゴーズミットとジョージ・ウーレンベックは、電子には4つ目の量子数があると提案しました。彼らはこれを「スピン量子数」もしくはmsと呼びました。
 
 電子は、印加された磁場の中では、エネルギーの異なる2つの向き、すなわち、磁場に沿うようにスピンアップした向きと、磁場に逆らうようにスピンダウンした向きがあります。 
 
 第4の量子数であるスピン量子数（ms）は、この2つの異なる電子のスピン状態を表します。スピン量子数には、「マイナス1/2」（スピンダウン）と「プラス1/2」（スピンアップ）の2つの値があります。 
 
 電子スピンとは、電子に内在する回転や自転を表します。それぞれの電子は、角運動量を持った小さな磁石や小さな回転体として、あるいは電流を持ったループとして、その回転や電流は空間座標では観察できないにもかかわらず作用します。 
 
 電子スピン全体の大きさは 1 つの値しか持つことができず、電子は 2 つの量子化状態のいずれかでしか「スピン」できません。 1 つは α 状態と呼ばれ、スピンの z 成分は z 軸の正の方向になります。 これはスピン量子数ms= +1/2 に対応します。 もう 1 つは β 状態と呼ばれ、スピンの z 成分は負で、 ms = − 1/2 です。 
 
 どの電子にも、その電子が存在する原子軌道に関係なく、スピン量子数のこれら 2 つの値のうちの 1 つしか持つことができません。 外部磁場が印加されている場合、異なるスピンを持つ電子のエネルギーは異なります。 
 
 原子の電子は、 n 、 l 、 ml 、 m sの 4 つの量子数で完全に表現されます。 最初の 3 つの量子数値は軌道を定義し、相互に依存しています。一方、4つ目の量子数は、スピンと呼ばれる電子固有の性質を表すため、他の量子数に依存しません。オーストリアの物理学者ウォルフガング・パウリ（1945年ノーベル物理学賞受賞）は、原子内の電子の一般的な振る舞いを理解するために必要な最後の情報となる一般原理を定式化しました。 パウリの排除原理は次のように表現されます。同じ原子内の2つの電子は、4つの量子数のすべてがまったく同じセットになることはありません。つまり、2つの電子は、スピン量子数が異なる場合にのみ、同じ軌道（量子数n、l、mlのセット）を共有することができるということです。スピン量子数（ms）は、+1/2と-1/2の2つの値しか持てないので、2つ以上の電子が同じ軌道を占めることはできません（2つの電子が同じ軌道に位置する場合は、逆のスピンを持っている必要がある）。したがって、どの原子軌道にも、0個、1個、または2個の電子が存在することになります。 
 
 電子配置の軌道図のスタイルは、占有された小軌道の各軌道を箱や線で、各電子を矢印で表す。電子配置が1s1である水素の軌道図は 
 
 <img alt="Figure1" src="https://www.jovecore.com/CDNSource/lessons/984/984Image_1.png" style="height: 40px;" />
 
 上向きの矢印はプラス半分のスピン（スピンアップ）、下向きの矢印はマイナス半分のスピン（スピンダウン）を意味します。したがって、水素の軌道図には、上向きの矢印が1本、下向きの矢印が1本となっています。 
 
 ヘリウムの電子配置は1s2です。2つの電子は、同じ軌道と小軌道に属しているため、3つの同じ量子数を持っています。2つの電子は、同じ軌道と小軌道に属しているため、3つの同じ量子数を持っていますが、パウリの排他原理により、スピンの量子数は異なります。反対のスピンを持つ電子は、同じ軌道を占める場合はペアと呼ばれます。 
 
 <img alt="Figure2" src="https://www.jovecore.com/CDNSource/lessons/984/984Image_2.png" style="height: 40px;" />
 
 この文章は <a 6-3-development-of-quantum-theory="" books="" chemistry-2e="" href="" https:="" openstax.org="" pages="">、 Openstax, Chemistry 2e, Section 6.3: Development of Quantum Theory に基づいています。  </a>

原子の軌道内の電子の配置は、その電子配置と呼ばれます。電子配置を記号で説明します...

Education

JoVE Core

Chemistry

化学

Electronic Structure of Atoms

原子の電子構造

KEY TERMS AND CONCEPTS

主要用語と概念

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

the wave nature of light

Measuring Light with Wavelength and Frequency

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the electromagnetic spectrum

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interference and diffraction

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the bohr model

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emission spectra

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the uncertainty principle

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the quantum-mechanical model of an atom

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quantum numbers

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atomic orbitals

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the pauli exclusion principle

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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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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key terms and concepts

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

JoVE Core 化学は、簡潔で理解しやすいアニメーションビデオレッスンを使用して、一般的な化学の概念を生き生きとしたものにします。さらに、活動する科学者のビデオでは、現在世界中の実験室で行われている古典的そして独創的な研究・実験をお見せします。

north-carolina-k-12-science-standard-course-of-study

NC K-12 Science Standard Course of Study

9-12

Matter and its Interactions

PS.Chm.1.3

ohios-learning-standards-and-model-curriculum

Ohio’s Learning Standards and Model Curriculum

Structure And Properties Of Matter

Atomic structure

Tennessee Academic Standards

Matter and Its Interactions

CHEM1.PS1.12

Virginia  Standards of Learning

HIgh School

CH.2

CH.2.e

Physical Science

PS.2

PS.2.a

CHEM.6

CHEM.6.B

Next Generation Science Standards

HS-PS1-1

Florida Department of Education

SC.912.P.8

SC.912.P.8.5

SC.912.P.10

SC.912.P.10.9

IPC.7.D

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Chemical Reactions

HS-PS1-7.

Georgia Standards of Excellence

SC1.

electron-configuration-and-chemical-properties

Electron Configuration and Chemical Properties

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

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IPC.7.A

physical-and-chemical-properties-of-matter

Physical and Chemical Properties of Matter

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Physical Properties of Matter

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atomic-radii-and-effective-nuclear-charge

Atomic Radii and Effective Nuclear Charge

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Ionic Radii

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IPC.7.B

Classifying Matter by State

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Classifying Matter by Composition

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IPC.7.C

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Electron Spin and Orbital Pairing

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