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 os elétrons são partículas, então quando um feixe de elétrons passa por duas aberturas bem espaçadas, espera-se que os dois feixes menores de elétrons surjam e produzam duas riscas brilhantes e escuras no meio. Inicialmente, com apenas alguns elétrons, os pontos localizados aparecem aleatoriamente no ecrã. Isto sugere um comportamento parecido com o das partículas.No entanto, à medida que mais e mais elétrons passam pelas aberturas, um padrão de interferência a marca distintiva do comportamento ondulatório emerge. Como é que isto é possível, recordemos que o modelo Bohr propôs que o elétron é uma partícula que orbita o núcleo. O físico francês Louis de Broglie postulou que o elétron pode exibir propriedades das ondas.Sugeriu que o elétron se comporta como uma onda circular de pé com um comprimento de onda, lambda. A circunferência de cada órbita contém um número inteiro de comprimentos de onda. Certos pontos da onda têm amplitude zero estes são os nodos.De Broglie propôs a seguinte relação, na qual o comprimento de onda do elétron depende da sua massa e velocidade, sendo o h a constante de Planck. Quanto maior for a velocidade do elétron, mais curto é o comprimento da sua onda. A hipótese de Broglie estende-se a toda a matéria, e estas ondas são chamadas de ondas de matéria'No entanto, objetos grandes e macroscópicos, tal como uma bola de golfe, não aparecem como ondas.Se aplicarmos a relação de Broglie, o pequeno valor da constante de Planck dividido pela massa e a velocidade da bola de golfe revela um comprimento de onda extremamente pequeno e que é demasiado pequeno para ser observado. No entanto, para partículas subatómicas com massas extremamente pequenas como os elétrons a sua natureza ondulatória não pode ser ignorada. Quando os raios X passam por um cristal, as ondas são difratadas, e é obtido um padrão de interferência distinta interferência distinta que revela a disposição dos átomos no cristal.Esta é a técnica laboratorial conhecida como difração de raios X.Se uma experiência semelhante for realizada através da passagem de elétrons pelo cristal em vez dos raios X, é observado um comportamento semelhante. Esta é uma prova experimental de que os elétrons são partículas que demonstram um comportamento ondulatório.

o comprimento de onda de de broglie

No mundo macroscópico, objetos que são suficientemente grandes para serem vistos a olho nu seguem as regras da física clássica. Uma bola de bilhar que se move em uma mesa comporta-se como uma partícula; continuará a viajar em linha reta, a menos que colida com outra bola, ou seja accionada por outra força, como a fricção. A esfera tem uma posição e velocidade bem definidas ou um momentum bem definido, p = mv, que é definido pela massa m e velocidade v em qualquer momento. Este é o comportamento típico de um objeto clássico.

Quando ondas interagem umas com as outras, elas mostram padrões de interferência que não são exibidos por partículas macroscópicas, como a bola de bilhar. No entanto, na década de 1920, tornou-se cada vez mais claro que partes muito pequenas da matéria seguem um conjunto diferente de regras do que grandes objetos. No mundo microscópico, as ondas e as partículas são inseparáveis. 

Uma das primeiras pessoas a prestar atenção ao comportamento especial do mundo microscópico foi Louis de Broglie. Ele questionou que se a radiação eletromagnética pode ter carácter semelhante a partículas, poderão os eletrões e outras partículas submicroscópicas apresentar carácter ondulatório? de Broglie ampliou a dualidade onda-partícula da luz que Einstein usou para resolver o paradoxo do efeito fotoelétrico às partículas materiais. Ele previu que uma partícula com massa m e velocidade v (isto é, com momentum linear p) também deveria apresentar o comportamento de uma onda com um valor de comprimento de onda λ, dado por esta expressão na qual h é a constante de Planck:

<img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/979/979_Equations-01.png" style="height: 40px;" />

Isto é chamado de comprimento de onda de de Broglie. Onde Bohr postulou o eletrão como sendo uma partícula orbitando o núcleo em órbitas quantizadas, de Broglie argumentou que a suposição de Bohr de quantização poderia ser explicada se o eletrão fosse em vez disso considerado uma onda circular estacionária. Apenas um número inteiro de comprimentos de onda poderia caber exatamente dentro da órbita.

Se um eletrão for visto como uma onda que se circunda ao redor do núcleo, um número inteiro de comprimentos de onda deve caber na órbita para que este comportamento de onda estacionário seja possível.

Para uma órbita circular de raio r, a circunferência é 2πr, e a condição de de Broglie é:

<img alt="Eq2" src="https://www.jove.com/files/core/CDNSource/lessons/979/979_Equations-02.png" style="height: 40px;" />

onde n = 1, 2, 3, e assim por diante. Pouco depois de de Broglie ter proposto a natureza ondulatória da matéria, dois cientistas da Bell Laboratories, C. J. Davisson e L. H. Germer, demonstraram experimentalmente que os eletrões poderiam apresentar comportamento ondulatório. Isto foi demonstrado com a finalidade de direcionar um feixe de eletrões para um alvo de níquel cristalino. O espaçamento dos átomos dentro do retículo foi aproximadamente o mesmo que os comprimentos de onda de de Broglie dos eletrões que lhe foram dirigidos, e as camadas atómicas regularmente espaçadas do cristal serviram como ‘fendas’, o que é usado em outras experiências de interferência. 

Inicialmente, quando apenas alguns eletrões foram registados, observou-se um comportamento claro semelhante a partículas. À medida que mais eletrões chegaram e foram registados, surgiu um padrão de interferência claro, que é a marca do comportamento ondulatório. Assim, parece que, enquanto que os eletrões são pequenas partículas localizadas, o seu movimento não segue as equações de movimento implícitas pela mecânica clássica. Em vez disso, o seu movimento é governado por uma equação de onda. Assim, a dualidade onda-partícula observada pela primeira vez com fotões é um comportamento fundamental, intrínseco a todas as partículas quânticas.

Este texto é adaptado de <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</a>.

O Comprimento de Onda de de Broglie

No mundo macroscópico, objetos grandes o suficiente para serem vistos a olho nu seguem as regras da física clássica. Uma bola de bilhar movendo-se em um ...

Education

JoVE Core

Chemistry

Química

Electronic Structure of Atoms

Estrutura Eletrônica dos Átomos

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

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 - Química dá vida a conceitos gerais de química usando vídeos de animação fáceis de entender. Além disso, nos vídeos Cientistas em ação, demonstramos experimentos de pesquisa clássicos e originais realizados atualmente por cientistas em laboratórios em todo o mundo.

Tennessee Academic Standards

High School

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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

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Molecules and Compounds

Atoms and Molecules

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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 ...

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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

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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

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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