Name: electron waves and standing orbits
Uploaded: 2020-09-03T13:38:27.000Z
Duration: 2 min 32 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 de Broglie Wavelength

電子が粒子であるならば 電子のビームが2つの間隔の 狭いスリットを通過するとき 2つの小さな電子ビームが現れ その間に暗闇がある 2本の明るい縞模様が生じると 予想されます 最初は数個の電子があるだけで 画面上に局所的な 斑点がランダムに現れます これは粒子のような振る舞いを していることを示唆しています しかし より多くの電子が スリットを通過すると 波のような振る舞いの特徴である 干渉パターンが現れます これはどのようにして 可能なのでしょうか？ボーアモデルでは 電子は 原子核の周りを回る粒子であると 提案していたことを 思い出してください フランスの物理学者 ルイ・ド・ブロイは 電子は波動的な性質を 示すことができると仮定しました 彼は 電子は波長λの 円形の定在波として 振る舞うことを提案しました 各軌道の円周には整数個の波長が 含まれています 波の上のある点は 振幅がゼロであり それがノードです ド・ブロイは 電子の波長は 質量と速度に依存し hをプランク定数とすると 次のような関係を示すと 提案しました 電子の速度が大きいほど 波長は短くなります ド・ブロイの仮説は すべての物質に適用され これらの波は「物質波」と 呼ばれています しかし ゴルフボールのような 大きな巨視的なものは 波としては現れません ド・ブロイの関係を適用すると プランク定数の小さな値を ゴルフボールの質量と 速度で割ったものは 観測するには小さすぎるほどの 極小の波長を持っています しかし 電子のように質量が 極端に小さい素粒子の場合は その波動性を 無視することはできません X線を結晶の中を 通過させると その波が回折され 結晶中の原子の 配列がわかる 独特の干渉縞が 得られます これがX線回折と呼ばれる 実験技術です X線の代わりに 電子を結晶に通して 同様の実験を行うと 同様の挙動が観察されます これは 電子が 波のような振る舞いをする 粒子であることを示す 実験的証拠です

ド・ブロイ波長

マクロの世界では、肉眼で見ることのできる大きさの物体は、古典物理学の法則に従っています。テーブルの上を移動するビリヤードボールは、粒子のように振る舞います。他のボールと衝突するか、摩擦などの他の力が作用しない限り、一直線に移動し続けます。ボールは、任意の瞬間に質量mと速度vで定義される、明確に定義された位置と速度、または明確に定義された運動量、p = mvを持っています。これは、古典的な物体の典型的な挙動です。 
 
 波が相互に作用すると、ビリヤードのボールのような巨視的な粒子では表示されない干渉パターンが表示されます。しかし、1920年代に入ると、非常に小さな物質は大きな物体とは異なる法則に従っていることが次第に明らかになってきました。ミクロの世界では、波と粒子は切っても切れない関係にあります。
 
 ミクロの世界の特殊な挙動に注目した最初の人物の一人がルイ・ド・ブロイです。彼は、電磁波が粒子的な性質を持つならば、電子などの微小な粒子は波動的な性質を持つのではないかと考えました。ド・ブロイは、アインシュタインが光電効果のパラドックスを解決するために用いた光の波動と粒子の二重性を、物質的な粒子にまで拡張しました。彼は、質量m、速度v（つまり、直線的な運動量p）を持つ粒子が、波長λを持つ波の挙動を示すことを予測しました。ここでhはプランク定数です。 
 
 <img alt="Eq1" src="https://www.jovecore.com/CDNSource/lessons/979/979_Equations-01.png" style="height: 40px;" />
 
 これを「ド・ブロイ波長」と呼びます。ボーアは、電子が量子化された軌道で原子核を周回する粒子であると仮定していたが、ド・ブロイは、電子が円の定在波であると考えれば、ボーアの量子化の仮定は説明できると主張しました。軌道の中に正確に収まるのは整数の波長だけです。 
 
 電子を原子核の周りを回る波とみなすと、この定在波の振る舞いをするためには、整数の波長が軌道に収まる必要があります。 
 
 半径 r の円軌道の場合、円周は 2π r であり、 ド・ブロイの条件は次のようになります。 
 
 <img alt="Eq2" src="https://www.jovecore.com/CDNSource/lessons/979/979_Equations-02.png" style="height: 40px;" />
 
 ここで、nは1、2、3......となります。ド・ブロイが物質の波動性を提唱した直後、ベル研究所のC.J.デビソンとL.H.ゲルマーの2人は、電子が波動的な振る舞いをすることを実験的に示しました。これは、結晶質のニッケルに電子ビームを照射して実証したものです。格子内の原子の間隔は、電子のド・ブロイ波長とほぼ同じであり、結晶の規則的な原子層は、他の干渉実験で用いられるスリットの役割を果たしたのです。
 
 最初、数個の電子が記録されたときには、明らかな粒子状の挙動が観察されました。しかし、より多くの電子が記録されるようになると、波動的な振る舞いの特徴である明確な干渉パターンが現れてきました。このように、電子は局所的な小さな粒子ではあるが、その運動は古典力学が意味する運動方程式には従わないようです。その代わり、電子の運動は波動方程式に支配されています。このように、光子で初めて観測された波動と粒子の二重性は、すべての量子粒子に内在する基本的な振る舞いなのです。 
 
 この文章は <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 に基づい</a>ています。

巨視的な世界では、肉眼で見るのに十分な大きさの物体は、古典物理学の法則に従います。ビリヤードボールが上を動く...

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 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 patterns. These patterns do not appear in the motion of a billiard ball. By the 1920s, scientists saw that very small pieces of matter do not always follow the same rules as large objects.

Louis de Broglie was one of the first to study this difference. He asked whether electrons and other submicroscopic particles could also show wavelike behavior if light can act like both a wave and a particle. He extended the wave-particle duality of light, which Einstein used to explain the photoelectric-effect paradox, to material particles. De Broglie predicted that a particle with mass m and velocity v, and therefore momentum p, should have a wavelength λ given by a formula that includes Planck’s constant h. This is called the de Broglie wavelength.

De Broglie also offered a way to explain Bohr’s quantized electron orbits. He suggested that an electron could be treated as a circular standing wave instead of only as a particle. In that model, only an integer number of wavelengths can fit exactly around the orbit. For a circular orbit of radius r, the circumference is 2πr, so de Broglie’s condition requires n whole wavelengths, where n can be 1, 2, 3, and so forth.

The wave nature of electrons was later shown in an experiment at Bell Laboratories by C. J. Davisson and L. H. Germer. They aimed a beam of electrons at a crystalline nickel target. The spacing of atoms in the crystal lattice was about the same as the de Broglie wavelengths of the electrons. The regularly spaced atomic layers acted like slits used in other interference experiments.

At first, when only a few electrons were recorded, the result looked particle-like. As more electrons were collected, a clear interference pattern appeared. That pattern is a sign of wavelike behavior. The experiment showed that electrons are localized particles, but their motion does not follow classical mechanics. Instead, it is described by a wave equation. This wave-particle duality, first seen with photons, is a basic feature of quantum particles.

Electron Waves and Standing 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

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 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 de Broglie linked electrons to waves, explained Bohr’s quantized orbits with standing waves, and how electron interference confirmed the idea.

Electron Waves and Standing Orbits | 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。

Tennessee Academic Standards

High School

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

Physics

PH.9

PH.9.a

Texas Essential Knowledge and Skills

CHEM.6

CHEM.6.A

CHEM.6.B

Florida Department of Education

SC.912.P.8

SC.912.P.8.3

SC.912.P.10

SC.912.P.10.9

PHYS.9

PHYS.9.C

PHYS.9.D

Chemistry and Physics

IPC.7

IPC.7.E

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 ...

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 ...

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 ...

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 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

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 ...

Ionic Bonding and Electron Transfer

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 ...

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 ...

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 ...

Construct an explanation to classify the type of chemical bond that occurs (covalent, ionic, or metallic) in a given substance.

PS.PSc.2.1

Understand types, properties, and structure of matter.

Electron Waves and Standing Orbits

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