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

Si les électrons sont des particules, alors quand un faisceau d'électrons traverse deux fentes étroitement espacées, on s'attend à ce que deux faisceaux d'électrons plus petits émergent et produisent deux bandes lumineuses avec l'obscurité entre les deux. Initialement, avec seulement quelques électrons, des taches localisées apparaissent aléatoirement sur l'écran. Cela suggère un comportement semblable à une particule.Cependant, comme de plus en plus d'électrons passent à travers les fentes, un modèle d'interférence-la marque du comportement ondulatoire-émerge. Comment est-ce possible? Rappelons que le modèle de Bohr a proposé que l'électron est une particule qui orbite autour du noyau.Le physicien français Louis de Broglie a postulé que l'électron peut présenter des propriétés d'onde. Il a suggéré que l'électron se comporte comme une onde stationnaire circulaire avec une longueur d'onde, lambda. La circonférence de chaque orbite contient un nombre entier de longueurs d'onde.Certains points de l'onde ont une amplitude nulle-ce sont des nœuds. De Broglie a proposé la relation suivante, dans laquelle la longueur d'onde de l'électron dépend de sa masse et de sa vitesse, h étant la constante de Planck. Plus la vitesse de l'électron est grande, plus sa longueur d'onde est courte.L'hypothèse de Broglie s'étend à toute la matière, et ces ondes sont appelées ondes de matière"Cependant, les grands objets macroscopiques, comme une balle de golf, n'apparaissent pas comme des vagues. Si nous appliquons la relation de Broglie, la petite valeur de la constante de Planck divisée par la masse et la vitesse de la balle de golf révèle une longueur d'onde extrêmement faible qui est trop petite pour être observée. Cependant, pour les particules subatomiques avec des masses extrêmement petites-comme les électrons-leur nature ondulatoire ne peut être ignorée.Lorsque les rayons X traversent un cristal, les ondes sont diffractées, et un motif d'interférence distinctif est obtenu qui révèle la disposition des atomes dans le cristal. C'est la technique de laboratoire connue sous le nom de diffraction des rayons X.Si une expérience similaire est réalisée en faisant passer des électrons à travers le cristal au lieu de rayons X, un comportement similaire est observé. Ceci est une preuve expérimentale que les électrons sont des particules qui démontrent un comportement ondulatoire.

la longueur d'onde de de broglie

Dans le monde macroscopique, les objets qui sont assez grands pour être vus à l'œil nu suivent les règles de la physique classique. Une boule de billard qui se déplace sur une table se comporte comme une particule ; elle continue à se déplacer en ligne droite à moins qu'elle ne heurte une autre boule ou qu'une autre force ne s'exerce sur elle, telle que la friction. La boule a une position et une vitesse bien définies ou une quantité de mouvement bien définie, p = mv, qui est définie par la masse m et la vitesse v à tout moment donné. Il s'agit du comportement typique d'un objet classique. 
 
 Lorsque les ondes interagissent, elles montrent des motifs d'interférence que n'affichent pas les particules macroscopiques, comme la boule de billard. Cependant, dans les années 1920, il est devenu de plus en plus clair que de très petits morceaux de matière suivent un ensemble de règles différent des grands objets. Dans le monde microscopique, les ondes et les particules sont inséparables.  
 
 Louis de Broglie est l'un des premiers à avoir prêter attention au comportement particulier du monde microscopique. Il s'est interrogé sur le fait que si le rayonnement électromagnétique peut avoir un caractère de particule, les électrons et d'autres particules sous-microscopiques peuvent-ils présenter un caractère ondulatoire ? De Broglie a étendu la dualité onde-particule de la lumière qu'Einstein a utilisé pour résoudre le paradoxe de l'effet photoélectrique aux particules matérielles. Il prédisait qu'une particule avec une masse m et une vitesse v (c'est-à-dire avec une quantité de mouvement linéaire p) devrait aussi présenter le comportement d'une onde avec une valeur de longueur d'onde λ, donnée par cette expression dans laquelle h est la constante de Planck : 
 
 <img alt="Eq1" src="https://www.jovecore.com/CDNSource/lessons/979/979_Equations-01.png" style="height: 40px;" />
 
 C'est ce que l'on appelle la longueur d'onde de De Broglie. Lorsque Bohr avait postulé que l’électron était une particule en orbite autour du noyau dans des orbites quantifiées, de Broglie a soutenu que l’hypothèse de quantification de Bohr pouvait être expliquée si l’électron est plutôt considéré comme une onde circulaire stationnaire. Seul un nombre entier de longueurs d'onde peut être contenu exactement dans l'orbite. 
 
 Si un électron est considéré comme une onde décrivant des cercles autour du noyau, un nombre entier de longueurs d'onde doit s'adapter à l'orbite pour que ce comportement d'onde stationnaire soit possible. 
 
 Pour une orbite circulaire de rayon r, la circonférence est de 2πr, et la condition de Broglie est : 
 
 <img alt="Eq2" src="https://www.jovecore.com/CDNSource/lessons/979/979_Equations-02.png" style="height: 40px;" />
 
 où n = 1, 2, 3, etc. Peu après que de Broglie ait proposé la nature ondulatoire de la matière, deux scientifiques des laboratoires Bell, C. J. Davisson et L. H. Germer, ont démontré expérimentalement que les électrons pouvaient présenter un comportement de type ondulatoire. Cela a été démontré en visant un faisceau d'électrons sur une cible de nickel cristallin. L'espacement des atomes à l'intérieur du réseau était à peu près le même que les longueurs d'onde de De Broglie des électrons qui y étaient visés, et les couches atomiques régulièrement espacées du cristal servaient de ‘ fentes ’, ce qui est utilisé dans d'autres expériences d'interférence.  
 
 Au départ, lorsque seulement quelques électrons ont été enregistrés, un comportement clair de type particulaire a été observé. Au fur et à mesure que de plus en plus d'électrons arrivaient et étaient enregistrés, un motif d'interférence clair est apparu, ce qui est la marque du comportement ondulatoire. Ainsi, il semble que si les électrons sont de petites particules localisées, leur mouvement ne suit pas les équations de mouvement impliquées par la mécanique classique. Au lieu de cela, leur mouvement est régi par une équation d'onde. Ainsi, la dualité onde-particule d'abord observée avec les photons est un comportement fondamental, intrinsèque à toutes les particules quantiques. 
 
 Ce texte est adapté de <a href="https://openstax.org/books/chemistry-2e/pages/6-3-development-of-quantum-theory">Openstax, Chimie 2e, Section 6.3 : Développement de la théorie quantique</a>.

La longueur d'onde de de Broglie

Dans le monde macroscopique, les objets suffisamment grands pour être vus à l’œil nu suivent les règles de la physique classique. Une boule de billard se déplaçant sur un ...

Education

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Chemistry

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Electronic Structure of Atoms

Structure électronique des atomes

KEY TERMS AND CONCEPTS

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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

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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...

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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

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HS. Chemical Reactions

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Classifying Matter by State

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Classifying Matter by Composition

Matter: Pure Substances and Mixtures
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Elements: Chemical Symbols and Isotopes

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Solution Formation

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Colloids

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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

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Phase Transitions: Vaporization and Condensation

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Vapor Pressure

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Clausius-Clapeyron Equation

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Phase Transitions: Melting and Freezing

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Phase Transitions: Sublimation and Deposition

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Heating and Cooling Curves

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Phase Diagrams

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

PS.PSc.1.2

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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 ...

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Molecular Comparison of Gases, Liquids, and Solids

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Intermolecular vs Intramolecular Forces

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Intermolecular Forces

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

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

PS.PSc.1.3

The Atomic Theory of Matter

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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

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Emission Spectra

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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

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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

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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

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Halogens

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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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