Name: shielding and orbital penetration
Uploaded: 2020-09-03T13:38:28.000Z
Duration: 3 min 21 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Chemistry and Physics

IPC.7

IPC.7.E

The Energies of Atomic Orbitals

원자 궤도들은 다른 에너지를 가지는데, 이것은 쿨롱 상호작용, 차폐 효과, 궤도 진입에 의해 합리화됩니다. 쿨롱의 법칙은 전하를 띤 두 입자 사이의 인력 또는 척력은 그것들 사이의 거리와 역제곱 관계를 가진다는 것을 나타냅니다. 원자 궤도 크기는 껍질 수에 따라 증가하며, 전자는 낮은 껍질 궤도가 차지하는 공간에서 반발됩니다.

따라서 쿨롱의 법칙은 껍질 수가 증가함에 따라 핵이 높은 궤도 에너지의 전자를 덜 약하게 끌어 당긴다는 것을 제안합니다. 또한 핵으로부터 거의 같은 거리 또는 가까운 거리에 있는 전자는 핵으로의 인력을 더욱 감소시키는 차폐 효과를 가집니다. 차폐가 클수록 핵으로의 인력이 줄어듭니다.

이것은 전자 껍질에서 궤도의 에너지 차이가 생기는 한 가지 이유입니다. 예를 들어, 3s와 3p 전자는 3d 전자를 현저하게 차폐합니다. 전자가 느끼는 유효 핵전하량은 원자 번호에서 차폐 전자와 그것이 점유하는 부껍질의 수에 따라 달라지는 차폐 상수 S를 빼주어 계산합니다.

예를 들어, 원자 번호가 3인 리튬의 두 개의 1s 전자는 2s 전자를 차단합니다. 이 전자에 대한 차폐 상수는 반경험적 규칙에서 1.7로 결정됩니다. 결국 2s 전자가 느끼는 유효핵전하량은 1.3입니다.

궤도의 모양도 그것의 에너지를 결정합니다. 만약 외부 궤도에 있는 전자들이 핵에 근접한 내부 전자가 차지한 영역으로 멀리 이동할 수 있다면, 그곳에서 훨씬 덜 차폐됩니다. 결국, 그 외부 궤도의 에너지는 더 낮습니다.

이것은 핵으로부터 주어진 거리에서 전자를 발견할 확률을 설명하는 방사 분포 함수로 시각화할 수 있습니다. 1s, 2s, 2p 부껍질에 대한 방사형 분포 함수 그림은 2s 전자가 핵 근처에 있을 가능성은 적지만, 2p 전자는 대부분 1s 영역의 바깥쪽 또는 바깥쪽 가장자리에 머무른다는 것을 보여줍니다. 따라서 2s 궤도는 더 큰 침투력을 가집니다.

세 번째 껍질에서는 3s 전자가 가장 많이 침투하고 3d 전자가 가장 적게 침투하였습니다. 일반적으로 원자 궤도 에너지는 부껍질 수준에서 s에서 f까지 껍질 번호에 따라 증가합니다. 그러나 네 번째와 다섯 번째 껍질에서는 침투 효과가 매우 커져 4s와 5s 궤도는 자주 3d와 4d 궤도에 비해 상대 에너지가 낮습니다.

원자 궤도의 에너지

원자에서는 음전하를 띤 전자가 양전하를 띤 핵에 끌어당겨집니다. 다중전자 원자에서는 전자-전자 반발도 관찰됩니다. 인력과 반발력은 입자 사이의 거리뿐만 아니라 개별 입자에 대한 전하의 부호와 크기에 따라 달라집니다. 입자의 전하가 반대이면 서로 끌어당깁니다. 두 입자가 동일한 전하를 가지면 서로 밀어냅니다.

전하의 크기가 증가함에 따라 힘의 크기도 증가합니다. 그러나 전하 분리가 더 많아지면 힘이 감소합니다. 따라서 전자와 핵 사이의 인력은 전자 사이의 거리에 정비례합니다. 전자가 핵에 더 가까울수록 핵에 더 단단히 결합됩니다. 그러므로 서로 다른 껍질(다른 거리에 있음)에 있는 전자는 서로 다른 에너지를 갖습니다.

여러 에너지 준위를 가진 원자의 경우 전자-전자 반발로 인해 내부 전자가 핵의 당김으로부터 외부 전자를 부분적으로 보호합니다. 핵심 전자는 외부 껍질의 전자를 보호하는 반면, 동일한 원자가 껍질의 전자는 서로가 경험하는 핵 인력을 효율적으로 차단하지 않습니다. 이는 유효핵전하 Z_eff의 개념으로 설명할 수 있다. 이는 전자-전자 반발을 고려하여 핵이 특정 전자에 가하는 인력입니다. 수소의 경우 전자가 1개뿐이므로 핵전하(Z)와 유효 핵전하(Z_eff)가 동일합니다. 다른 모든 원자의 경우 내부 전자는 핵의 인력으로부터 외부 전자를 부분적으로 보호하므로 다음과 같습니다.

<img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/985/985_Equations-01.png" style="height: 40px;" />

궤도 침투는 전자가 핵에 더 가까워지는 능력을 나타냅니다. s-오비탈의 전자는 핵에 더 가까워지고 더 많은 관통 능력을 가질 수 있습니다. 구형 s-궤도의 확률 밀도는 핵에서 0이 아닙니다. 서로 다른 부 껍질은 서로 다른 공간 방향을 갖습니다. 아령 모양의 오비탈로 인해 p-전자는 훨씬 덜 침투합니다. 파동함수에는 핵을 통과하는 노드가 있으며, 여기서 전자를 찾을 확률은 0입니다. 따라서 s 궤도 전자는 핵에 더 단단히 결합되어 있으며 p 전자보다 낮은 에너지를 갖습니다. d-전자는 p 오비탈 전자보다 침투력이 더 낮고 에너지는 더 높습니다.

다양한 껍질과 부 껍질에 대해 전자의 침투력 추세는 다음과 같이 나타낼 수 있습니다.

<img alt="Eq2" src="https://www.jove.com/files/core/CDNSource/lessons/985/985_Equations-02.png" style="height: 40px;" />

차폐 및 침투 효과가 크며 4s 전자는 3d 전자보다 에너지가 낮을 수 있습니다.

이 문서는 에서 발췌되었습니다 <a href="https://openstax.org/books/chemistry-2e/pages/6-4-electronic-structure-of-atoms-electron-configurations">Openstax, Chemistry 2e, Section 6.4: Electronic Structure of Atoms (Electron Configurations).</a>

원자에서 음전하를 띤 전자는 양전하를 띤 핵에 끌립니다. 다중 전자 원자에서 전자-전자 반발력은 ...

Education

교육

JoVE Core

Chemistry

화학

하나

Electronic Structure of Atoms

원자의 전자 구조

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 electrons in different shells can have different energies because they sit at different distances from the nucleus. In atoms with several energy levels, inner electrons partly block the nucleus from outer electrons. This blocking is called shielding, and it happens because of electron-electron repulsions.

The pull felt by one electron after shielding is the effective nuclear charge, or Zeff. It describes the attraction from the nucleus after repulsions are taken into account. For hydrogen, which has only one electron, Z and Zeff are the same. In atoms with more than one electron, core electrons shield outer electrons, while electrons in the same valence shell do not block the nuclear pull very well.

Orbital penetration describes how close an electron can get to the nucleus. s orbitals penetrate best because their spherical probability density is non-zero at the nucleus. p orbitals penetrate less because their dumbbell shape has a node through the nucleus, where the chance of finding an electron is zero. d orbitals penetrate even less than p orbitals.

Because of shielding and penetration, s electrons are usually bound more tightly and have lower energy than p electrons. d electrons have higher energy than p electrons. These effects can be strong enough that a 4s electron may have lower energy than a 3d electron.

Shielding and Orbital Penetration

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the uncertainty principle

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the quantum-mechanical model of an atom

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quantum numbers

Electron Orbitals and Spin

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atomic orbitals

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the energies of atomic orbitals

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 shielding, effective nuclear charge, and orbital penetration affect electron energy levels, and why s, p, and d orbitals differ in energy.

Shielding and Orbital Penetration | JoVE K12

chemistry

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

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

Alabama Course of Study Science

9-12.C.1.1.c

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

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south-carolina-college-and-career-ready-science-standards

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C-PS1-4

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HS. Chemical Reactions

HS-PS1-7.

Georgia Standards of Excellence

SC1.

electron-configuration-and-chemical-properties

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Shielding and Orbital Penetration

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