Name: bohr’s quantized atomic orbits
Uploaded: 2020-09-03T13:38:27.000Z
Duration: 2 min 18 s
Channel: JoVE

K12 Standards

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

NC K-12 Science Standard Course of Study

9-12

Physical Science

Matter and its Interactions

PS.PSc.1.4

The Bohr Model

행성계 모형에서는 수소 원자를 전자가 양전하를 띤 핵 주위를 돌고 있는 작은 태양계로 설명합니다. 고전물리학에서는 전자가 원형 궤도에서 움직이는 전하 입자이기 때문에 양전하를 띤 핵 주위를 돌면서 지속적으로 에너지를 방출해야 한다고 제안합니다. 그렇다면 원자는 결국 붕괴될 것입니다.

그러나 이것은 관측되지 않습니다. 원자는 안정합니다. 닐스 보어는 핵으로부터 일정한 거리에 궤도가 있다고 제안했습니다.

이러한 궤도들은 주 양자수 n으로 표시된 번호가 붙은 정수들입니다. 핵에 가장 가까운 궤도는 1과 같습니다. n은 임의의 양의 정수일 수 있지만 0이 될 수 없습니다.

n이 증가하면 궤도의 반경도 증가합니다. 핵에서 멀리 떨어져 있는 전자는 정전기력이 약해지고 양성자에게 약하게 끌립니다. 각 궤도는 고유의 에너지 준위 또는 에너지 상태에 있습니다.

각 궤도의 에너지는 양자화되어 있으며, 그 사이의 어떤 에너지도 가능하지 않다는 것을 의미합니다. 전자가 가장 낮고 가장 안정된 에너지 준위 즉 n이 1일 때를 바닥 상태라고 합니다. 높은 에너지 준위, 즉 n이 1보다 큰 때를 들뜬 상태라고 합니다.

전자는 다른 에너지 준위로 이동할 수 있는데 에너지를 흡수할 때는 에너지가 높은 상태로 전이합니다. 또는 다시 낮은 에너지 상태로 돌아오면서 잉여 에너지를 광자의 형태로 방출합니다. 흡수되거나 방출되는 에너지는 마지막 에너지 준위와 초기 준위 사이의 에너지 차이와 관련됩니다.

더 높은 에너지 준위로부터 이완되는 전자는 낮은 에너지 수준에서 이완되는 전자보다 짧은 파장의 빛을 방출합니다. 보어의 모형은 수소나 단일 전자 이온에만 적합하지만, 그것은 보다 정확한 원자 모형의 토대를 마련했습니다.

보어 모델

20세기 초 어니스트 러더퍼드(Ernest Rutherford)와 그의 동료들의 연구에 따라, 더 가볍고 심지어 더 작은 전자로 둘러싸인 작고 조밀한 핵으로 구성된 원자가 핵 주위를 계속해서 이동한다는 그림이 잘 확립되었습니다. 이 그림은 원자를 태양 주위를 도는 행성처럼 핵 주위를 도는 전자가 있는 소형 “태양계”로 묘사했기 때문에 행성 모델이라고 불렸습니다. 가장 단순한 원자는 수소이며, 단일 전자가 움직이는 핵인 단일 양성자로 구성됩니다. 전자를 양성자로 끌어당기는 정전기력은 두 입자 사이의 거리에만 의존합니다. 그러나 원자에 대한 고전 역학의 설명은 불완전합니다. 왜냐하면 타원 궤도에서 움직이는 전자는 방향을 변경하여 가속되고 고전 전자기학에 따르면 전자는 지속적으로 전자기 복사를 방출해야 하기 때문입니다. 궤도 에너지의 이러한 손실은 전자의 궤도가 핵으로 나선형으로 들어갈 때까지 계속해서 작아지는 결과를 가져오며, 이는 원자가 본질적으로 불안정하다는 것을 의미합니다.

1913년에 닐스 보어(Niels 소 내 궤도를 도는 전자가 Bohr)는 수지속적으로 빛을 방출할 것이라는 고전 전자기학의 예측을 무시하고 원자 역설을 해결하려고 시도했습니다. 대신에 그는 원자에 대한 고전 역학의 설명, 즉 플랑크의 양자화 개념과 빛이 에너지가 주파수에 비례하는 광자로 구성되어 있다는 아인슈타인의 발견을 통합했습니다. 보어는 핵 주위를 도는 전자가 일반적으로 방사선을 방출하지 않지만(정지 상태 가설), 다른 궤도로 이동하면 광자를 방출하거나 흡수할 것이라고 가정했습니다. 흡수되거나 방출되는 에너지는 다음 방정식에 따라 궤도 에너지의 차이를 반영합니다.

<img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/978/978_Equations-01.png" style="height: 40px;" />

여기서 h는 플랑크 상수이고, E_i와 E_f는 각각 초기 궤도 에너지와 최종 궤도 에너지입니다. 주파수와 파장은 항상 양수이므로 에너지 차이의 절대값이 사용됩니다. 보어는 연속적인 에너지 값을 허용하는 대신 이러한 전자 궤도의 에너지가 양자화되었다고 가정했습니다.

<img alt="Eq2" src="https://www.jove.com/files/core/CDNSource/lessons/978/978_Equations-02.png" style="height: 40px;" />

이 식에서 k는 전자질량, 전하 등의 기본상수와 플랑크상수로 이루어진 상수입니다. 궤도 에너지에 대한 표현을 ΔE 방정식에 삽입하면 다음이 제공됩니다.

<img alt="Eq3" src="https://www.jove.com/files/core/CDNSource/lessons/978/978_Equations-03.png" style="height: 40px;" />

물리학의 기본 법칙 중 하나는 물질이 가능한 가장 낮은 에너지로 가장 안정적이라는 것입니다. 따라서 수소 원자의 전자는 일반적으로 가장 낮은 에너지를 갖는 궤도인 n = 1 궤도에서 이동합니다. 전자가 가장 낮은 에너지 궤도에 있을 때 원자는 바닥 전자 상태(또는 간단히 바닥 상태)에 있다고 합니다. 원자가 외부 소스로부터 에너지를 받으면 전자가 더 높은 n 값을 갖는 궤도로 이동할 수 있으며 원자는 이제 더 높은 에너지를 갖는 들뜬 전자 상태(또는 단순히 들뜬 상태)에 있게 됩니다. 들뜬 상태(더 높은 에너지 궤도)에서 덜 들뜬 상태, 즉 바닥 상태로 전자 전이가 발생할 때 에너지의 차이가 광자로 방출됩니다. 마찬가지로, 광자가 원자에 흡수되면 광자의 에너지는 전자를 낮은 에너지 궤도에서 더 들뜬 궤도로 이동시킵니다. 우리는 원자 내 전자의 에너지를 이전에 에너지에 대해 배운 것과 연관시킬 수 있습니다. 에너지 보존의 법칙은 우리가 에너지를 생성하거나 파괴할 수 없다고 말합니다. 따라서 전자를 한 에너지 준위에서 다른 에너지 준위로 여기시키는 데 일정량의 외부 에너지가 필요한 경우 전자가 초기 상태로 돌아갈 때 동일한 양의 에너지가 방출됩니다.

보어의 모델은 단 하나의 전자만을 포함하므로 단일 전자 이온인 Hev+, Li^2+, Be^3+ 등에 적용될 수도 있습니다. 이는 수소와 핵 전하만 다릅니다. 따라서 단일 전자 원자와 이온은 집합적으로 수소 같은 원자라고 불립니다.

이 문서는 에서 발췌되었습니다 <a href="https://openstax.org/books/chemistry-2e/pages/6-2-the-bohr-model">Openstax, Chemistry 2e, Section 6.2: The Bohr Model</a>.

20 세기 초 어니스트 러더포드 (Ernest Rutherford)와 그의 동료들의 연구에 따르면, 작고 조밀 한 핵으로 구성된 원자의 그림은 ...

Education

교육

JoVE Core

Chemistry

화학

하나

Electronic Structure of Atoms

원자의 전자 구조

KEY TERMS AND CONCEPTS

주요 용어 및 개념

bohr’s quantized atomic orbits

Bohr’s quantized atomic orbits explain why hydrogen atoms can stay stable. Early in the twentieth century, Ernest Rutherford and his colleagues described atoms as tiny dense nuclei with lighter electrons moving around them. This picture was called the planetary model because it compared the atom to a miniature solar system, with electrons orbiting the nucleus like planets around the sun.

The simplest atom is hydrogen. It has one proton in the nucleus and one electron moving around it. In the classical view, the electrostatic force between the proton and electron depends only on the distance between them. That description is incomplete, though. If the electron moved in an elliptical orbit, it would be accelerating because its direction changes.

Classical electromagnetism says an accelerating charged particle should continually emit electromagnetic radiation. If that happened, the electron would lose orbital energy. Its orbit would keep shrinking until it spiraled into the nucleus. That would make atoms unstable, so the classical picture creates an atomic paradox.

In 1913, Niels Bohr proposed a different model to address this problem. He ignored the classical prediction that the orbiting electron in hydrogen should constantly emit light. Instead, he used classical mechanics together with Planck’s idea of quantization and Einstein’s idea that light is made of photons with energy proportional to frequency. Bohr also proposed the stationary state hypothesis, which says the electron does not normally emit radiation while it stays in one orbit.

Bohr said light is emitted or absorbed only when the electron moves between orbits. The energy change follows the difference between the initial and final orbital energies, and the absolute value is used because frequency and wavelength are always positive. He also assumed the allowed electron energies are quantized, not continuous. In his energy equation, k is a constant that includes fundamental constants such as electron mass, electron charge, and Planck’s constant.

For hydrogen, the n = 1 orbit has the lowest energy. Because matter is most stable at the lowest possible energy, the electron usually stays in this orbit. This is the ground electronic state, or ground state. If the atom absorbs energy from outside, the electron can move to a higher n orbit. The atom then enters an excited electronic state, or excited state.

When an electron drops from an excited state to a less excited state or back to the ground state, the energy difference is released as a photon. The reverse also happens. If the atom absorbs a photon, that photon’s energy can move the electron from a lower orbit to a more excited one. This matches the law of conservation of energy, which says energy is neither created nor destroyed.

Because Bohr’s model was built for a single electron, it also applies to single-electron ions such as He+, Li2+, and Be3+. These species differ from hydrogen only in their nuclear charges. For that reason, hydrogen and these one-electron ions are called hydrogen-like atoms.

Bohr’s Quantized Atomic Orbits

the wave nature of light

Measuring Light with Wavelength and Frequency

Light can be described as an electromagnetic wave, and its behavior helps explain many patterns seen in science. For centuries, scientists have tried to understand light. Newton used lenses and prisms to show that white light is made of the colors of the rainbow mixed together. He explained light as tiny particles moving at high speed. Other scientists, including Christiaan Huygens, showed that reflection and refraction could also be explained by treating light as a wave. At the time, people...

the electromagnetic spectrum

Electromagnetic Waves: Uses Across the Spectrum

The electromagnetic spectrum includes all electromagnetic radiation arranged by frequency and wavelength. Visible light is only a small part of it, and each color of visible light has its own frequency and wavelength. Different parts of the spectrum also use different units. Radio waves are usually measured in MHz, while the visible range is often measured in nm or angstroms. The spectrum is organized from radio waves to gamma rays as frequency increases and wavelength decreases. Radio waves...

interference and diffraction

Wave Patterns from Light and Slits

Light can form wave patterns through interference and diffraction. When two electromagnetic waves meet with their peaks and troughs lined up, they combine into a larger wave. This is constructive interference, and the waves are in phase. When a peak of one wave meets a trough of the other, the waves reduce each other. This is destructive interference, and the result has a much lower amplitude. Diffraction is another wave behavior. When light passes through a slit that is about the same size as...

photoelectric effect

Why Light Ejects Electrons from Metals

Light can eject electrons from a metal surface when it has the right frequency. This process is called the photoelectric effect. Each metal has its own threshold frequency, which is the minimum light frequency needed to free electrons. Light below the threshold frequency cannot cause emission, even if it is very bright. When the light frequency is above the threshold, electrons are ejected. In that case, the number of electrons released is directly proportional to the intensity, or brightness,...

the bohr model

Bohr’s quantized atomic orbits explain why hydrogen atoms can stay stable. Early in the twentieth century, Ernest Rutherford and his colleagues described atoms as tiny dense nuclei with lighter electrons moving around them. This picture was called the planetary model because it compared the atom to a miniature solar system, with electrons orbiting the nucleus like planets around the sun. The simplest atom is hydrogen. It has one proton in the nucleus and one electron moving around it. In the...

emission spectra

Line Spectra from Heated Gases

Line spectra are produced when heated gases give off light at specific wavelengths. In contrast, hot solids, liquids, or condensed gases radiate excess energy as a continuous spectrum. That spectrum contains an unbroken range of wavelengths. A gas at low partial pressure can produce a line spectrum when it is excited by an electric current or heated. Fluorescent light bulbs and neon signs work in this way. Each element has its own characteristic set of lines, and molecules can also produce...

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 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...

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 Bohr explained hydrogen stability with quantized orbits, ground and excited states, and photon absorption and emission in hydrogen-like atoms.

Bohr’s Quantized Atomic Orbits | JoVE K12

chemistry

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

ohios-learning-standards-and-model-curriculum

Ohio’s Learning Standards and Model Curriculum

Study Of Matter

Atoms

Structure And Properties Of Matter

Atomic structure

Tennessee Academic Standards

High School

Matter and Its Interactions

CHEM1.PS1.11

waves-and-their-applications-in-technologies-for-information-transfer

Waves and Their Applications in Technologies for Information Transfer

CHEM1.PS4.1

Virginia  Standards of Learning

HIgh School

CH.2

CH.2.e

PS.2

PS.2.a

Arizona Science Standards

HS.P1

HS.P1U1.1

HS+C.P1

HS+C.P1U1.2

Texas Essential Knowledge and Skills

CHEM.6

CHEM.6.A

CHEM.6.B

CHEM.6.C

Alabama Course of Study Science

Earth and Space Science

Earth's Place in the Universe

9-12.ESS.1.2.c

Next Generation Science Standards

Earth’s Place in the Universe

HS-ESS1-2

Florida Department of Education

SC.912.P.8

SC.912.P.8.3

SC.912.P.10

SC.912.P.10.9

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

South Carolina College and Career Ready Science Standards

C-PS1-4

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Chemical Reactions

HS-PS1-7.

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 ...

Elements: Chemical Symbols and Isotopes

A chemical symbol is an abbreviation used to indicate an element or an atom of an element. For example, the symbol for mercury is Hg. The same symbol is ...

Molecules and Compounds

Atoms and Molecules

Everything in the universe is made up of matter, and matter is composed of a combination of elements. An atom is the smallest unit of ...

Solution Formation

There is no one solvent that can dissolve every type of solute. Some substances that readily dissolve in a certain solvent might be insoluble in a ...

Colloids

Children at play often make suspensions such as mixtures of mud and water, flour and water, or a suspension of solid pigments in water known as tempera ...

Construct an explanation to classify matter as a pure substance or mixture; homogeneous or heterogeneous; element or compound; solution, colloid or suspension.

PS.PSc.1.1

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 ...

Vapor Pressure

When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase molecules move randomly about, they will occasionally ...

Clausius-Clapeyron Equation

The equilibrium between a liquid and its vapor depends on the temperature of the system; a rise in temperature causes a corresponding rise in the vapor ...

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 ...

Heating and Cooling Curves

When a substance&#8212;isolated from its environment&#8212;is subjected to heat changes, corresponding changes in temperature and phase of the substance ...

Phase Diagrams

A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. ...

Use models to compare the phases of matter and the physical changes they undergo.

PS.PSc.1.2

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 ...

molecular-comparison-of-gases-liquids-and-solids

Molecular Comparison of Gases, Liquids, and Solids

Particles in a solid are tightly packed together (fixed shape) and often arranged in a regular pattern; in a liquid, they are close together with no ...

Intermolecular vs Intramolecular Forces

Intermolecular forces (IMF) are electrostatic attractions arising from charge-charge interactions between molecules. The strength of the intermolecular ...

Intermolecular Forces

Atoms and molecules interact through bonds (or forces): intramolecular and intermolecular. The forces are electrostatic as they arise from interactions ...

comparing-intermolecular-forces-melting-point-boiling-point

Comparing Intermolecular Forces: Melting Point, Boiling Point, and Miscibility

Intermolecular forces are attractive forces that exist between molecules. They dictate several bulk properties, such as melting points, boiling points, ...

Carry out investigations to compare physical and chemical properties of matter.

PS.PSc.1.3

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 ...

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 de Broglie Wavelength

In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a ...

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that ...

Use models to interpret the data presented in Bohr diagrams and electron dot diagrams for neutral atoms of elements 1 through 18.

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 ...

Use models to compare representations of atoms, ions, and isotopes.

PS.PSc.1.5

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 ...

Use the Periodic Table as a model to predict the relative properties (metallic/nonmetallic character, ionic charge, and reactivity) and arrangement of elements based on the pattern of valence electrons in the outermost energy levels of atoms.

PS.PSc.1.6

Understand types, properties, and structure of matter.

Bohr’s Quantized Atomic Orbits

Description

Transcript

More videos by Standards