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

Se gli elettroni sono particelle, quando un fascio di elettroni passa attraverso due fessure ravvicinate, ci si aspetta che due fasci di elettroni più piccoli emergano, e producano due strisce luminose separate dall'oscurità nel mezzo. Inizialmente, con solo pochi elettroni, le macchie localizzate appaiono casualmente sullo schermo. Questo suggerisce un comportamento simile alle particelle.

Tuttavia, man mano che sempre più elettroni passano attraverso le fessure, emerge un modello di interferenza, il segno distintivo del comportamento ondulatorio. Com'è possibile? Ricordiamo che il modello di Bohr proponeva che l'elettrone fosse una particella che orbitava attorno al nucleo.

Il fisico francese Louis de Broglie ipotizzò che l'elettrone potesse esibire proprietà ondulatorie. Lo scienziato suggerì che l'elettrone si comportasse come un'onda stazionaria circolare con una lunghezza d'onda, lambda. La circonferenza di ciascuna orbita contiene un numero intero di lunghezze d'onda.

Alcuni punti sull'onda hanno ampiezza zero:questi sono definiti nodi. De Broglie propose la seguente relazione, in cui la lunghezza d'onda dell'elettrone dipende dalla sua massa e velocità, dove h è la costante di Planck. Maggiore è la velocità dell'elettrone, minore è la sua lunghezza d'onda.

L'ipotesi di de Broglie si estende a tutta la materia e queste onde sono definite onde della materia"Tuttavia, oggetti grandi e macroscopici, come una pallina da golf, non appaiono come onde. Se applichiamo la relazione di de Broglie, il minuscolo valore della costante di Planck diviso per la massa e la velocità della pallina da golf rivela una lunghezza d'onda estremamente piccola, che è troppo esigua per poter essere osservata. Tuttavia, per particelle subatomiche con masse estremamente piccole, come gli elettroni, la loro natura ondulatoria non può essere ignorata.

Quando i raggi X attraversano un cristallo, le onde vengono diffratte e si ottiene un modello di interferenza distintivo, che rivela la disposizione degli atomi nel cristallo. Questa è una tecnica di laboratorio nota come diffrazione dei raggi X.Se un esperimento simile viene eseguito facendo passare elettroni attraverso il cristallo invece dei raggi X, si osserva un comportamento simile. Questa è una prova sperimentale che gli elettroni sono particelle che dimostrano un comportamento simile a un'onda.

la lunghezza d'onda di de broglie

Nel mondo macroscopico, gli oggetti abbastanza grandi da essere visti ad occhio nudo seguono le regole della fisica classica. Una palla da biliardo che si muove su un tavolo si comporterà come una particella; continuerà a viaggiare in linea retta a meno che non entri in collisione con un'altra palla o subisca l'azione di qualche altra forza, come l'attrito. La palla ha una posizione e una velocità ben definite o una quantità di moto ben definita, p = mv, che è definita dalla massa m e dalla velocità v in un dato momento. Questo è il comportamento tipico di un oggetto classico.

Quando le onde interagiscono tra loro, mostrano schemi di interferenza che non vengono visualizzati dalle particelle macroscopiche, come la palla da biliardo. Tuttavia, a partire dagli anni '20, divenne sempre più chiaro che pezzi di materia molto piccoli seguono un insieme di regole diverse da quelle degli oggetti di grandi dimensioni. Nel mondo microscopico, le onde e le particelle sono inseparabili.

Una delle prime persone a prestare attenzione al comportamento speciale del mondo microscopico fu Louis de Broglie. Ha messo in dubbio che se la radiazione elettromagnetica può avere un carattere simile a una particella, gli elettroni e altre particelle submicroscopiche possono mostrare un carattere ondulatorio? De Broglie estese alle particelle materiali la dualità onda-particella della luce che Einstein usò per risolvere il paradosso dell'effetto fotoelettrico. Predisse che una particella con massa m e velocità v (cioè con momento lineare p) dovrebbe mostrare anche il comportamento di un’onda con valore di lunghezza d’onda λ, dato da questa espressione in cui h è la costante di Planck:

<img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/979/979_Equations-01.png" style="height: 40px;" />

Questa è chiamata lunghezza d'onda di De Broglie. Laddove Bohr aveva postulato che l’elettrone fosse una particella in orbita attorno al nucleo in orbite quantizzate, de Broglie sostenne che l’ipotesi di quantizzazione di Bohr potrebbe essere spiegata se l’elettrone fosse invece considerato un’onda stazionaria circolare. Solo un numero intero di lunghezze d'onda potrebbe rientrare esattamente nell'orbita.

Se un elettrone viene visto come un'onda che gira attorno al nucleo, affinché questo comportamento di onda stazionaria sia possibile, è necessario che un numero intero di lunghezze d'onda si adatti all'orbita.

Per un’orbita circolare di raggio r, la circonferenza è 2πr, quindi la condizione di de Broglie è:

<img alt="Eq2" src="https://www.jove.com/files/core/CDNSource/lessons/979/979_Equations-02.png" style="height: 40px;" />

dove n = 1, 2, 3 e così via. Poco dopo che de Broglie propose la natura ondulatoria della materia, due scienziati dei Bell Laboratories, C. J. Davisson e L. H. Germer, dimostrarono sperimentalmente che gli elettroni potevano mostrare un comportamento ondulatorio. Ciò è stato dimostrato puntando un fascio di elettroni su un bersaglio di nichel cristallino. La spaziatura degli atomi all'interno del reticolo era approssimativamente la stessa delle lunghezze d'onda di De Broglie degli elettroni puntati su di esso, e gli strati atomici regolarmente distanziati del cristallo fungevano da "fessure", utilizzate in altri esperimenti di interferenza.

Inizialmente, quando venivano registrati solo pochi elettroni, si osservava un chiaro comportamento simile a quello delle particelle. Man mano che sempre più elettroni arrivavano e venivano registrati, emergeva un chiaro schema di interferenza, che è il segno distintivo del comportamento ondulatorio. Sembra quindi che, sebbene gli elettroni siano piccole particelle localizzate, il loro movimento non segua le equazioni del moto implicite nella meccanica classica. Invece, il loro movimento è governato da un'equazione d'onda. Pertanto, la dualità onda-particella osservata per la prima volta con i fotoni è un comportamento fondamentale, intrinseco a tutte le particelle quantistiche.

La lunghezza d'onda di de Broglie

Nel mondo macroscopico, gli oggetti che sono abbastanza grandi da essere visti ad occhio nudo seguono le regole della fisica classica. Una palla da biliardo che si muove su un ...

Education

Didattica

JoVE Core

Chemistry

Chimica

Electronic Structure of Atoms

Struttura elettronica degli atomi

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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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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

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the quantum-mechanical model of an atom

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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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Waves and Their Applications in Technologies for Information Transfer

CHEM1.PS4.1

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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

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Classifying Matter by Composition

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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

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

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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

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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

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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

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Periodic Classification of the Elements

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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

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Ionization Energy

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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


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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

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Ionic Bonding and Electron Transfer

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Covalent Bonding and Lewis Structures

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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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