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

Jeśli elektrony są cząstkami, to gdy wiązka elektronów przechodzi przez dwie blisko rozmieszczone szczeliny, oczekuje się, że wyłonią się dwie mniejsze wiązki elektronów i wytworzą dwa jasne paski z ciemnością pomiędzy nimi. 
Początkowo, przy zaledwie kilku elektronach, zlokalizowane plamki pojawiają się losowo na ekranie. Sugeruje to zachowanie podobne do cząsteczki.

Jednak w miarę jak coraz więcej elektronów przechodzi przez szczeliny, pojawia się wzór interferencyjny – cecha charakterystyczna zachowania przypominającego falę. Jak to możliwe?

Przypomnijmy, że model Bohra proponował, że elektron jest cząstką, która krąży wokół jądra. Francuski fizyk Louis de Broglie postulował, że elektron może wykazywać właściwości falowe. Zasugerował, że elektron zachowuje się jak kołowa fala stojąca o długości fali, lambda.

Obwód każdej orbity zawiera całkowitą liczbę długości fal. Niektóre punkty na fali mają zerową amplitudę — są to węzły. 

De Broglie zaproponował następującą zależność, w której długość fali elektronu zależy od jego masy i prędkości, gdzie h jest stałą Plancka. Im większa prędkość elektronu, tym krótsza jest jego długość fali. 

Hipoteza de Broglie'a rozciąga się na całą materię, a fale te nazywane są "falami materii". Jednak duże, makroskopowe obiekty, takie jak piłka golfowa, nie pojawiają się jako fale. Jeśli zastosujemy zależność de Broglie'a, niewielka wartość stałej Plancka podzielona przez masę i prędkość piłki golfowej ujawnia niezwykle małą długość fali, która jest zbyt mała, aby ją zaobserwować.

Jednak w przypadku cząstek subatomowych o bardzo małych masach – takich jak elektrony – ich falowa natura nie może być ignorowana.

Kiedy promienie rentgenowskie przechodzą przez kryształ, fale ulegają dyfrakcji i uzyskuje się charakterystyczny wzór interferencyjny, który ujawnia układ atomów w krysztale. Jest to technika laboratoryjna znana jako dyfrakcja promieniowania rentgenowskiego. 

Jeśli podobny eksperyment jest przeprowadzany przez przepuszczanie elektronów przez kryształ zamiast promieni rentgenowskich, obserwuje się podobne zachowanie. Jest to eksperymentalny dowód na to, że elektrony są cząstkami, które wykazują zachowanie podobne do falowego.

długość fali de broglie’a

W świecie makroskopowym obiekty, które są na tyle duże, że można je zobaczyć gołym okiem, podlegają prawom fizyki klasycznej. Kula bilardowa poruszająca się po stole będzie zachowywać się jak cząstka; będzie kontynuować podróż po linii prostej, chyba że zderzy się z inną piłką lub działa na nią inna siła, np. tarcie. Piłka ma dobrze określone położenie i prędkość lub dobrze określony pęd, p = mv, który jest określony przez masę m i prędkość v w dowolnym momencie. Jest to typowe zachowanie klasycznego obiektu.

Kiedy fale oddziałują ze sobą, wykazują wzorce interferencji, których nie widać na makroskopowych cząstkach, takich jak kula bilardowa. Jednak w latach dwudziestych XX wieku stawało się coraz bardziej jasne, że bardzo małe kawałki materii podlegają innym zestawom zasad niż duże obiekty. W mikroskopijnym świecie fale i cząstki są nierozłączne.

Jedną z pierwszych osób, która zwróciła uwagę na szczególne zachowanie mikroskopijnego świata, był Louis de Broglie. Zakwestionował on, że skoro promieniowanie elektromagnetyczne może mieć charakter cząsteczkowy, to czy elektrony i inne cząstki submikroskopowe mogą wykazywać charakter falowy? De Broglie rozszerzył dualizm falowo-cząsteczkowy światła, którego Einstein użył do rozwiązania paradoksu efektu fotoelektrycznego na cząstki materialne. Przewidział, że cząstka o masie m i prędkości v (czyli pędzie liniowym p) powinna również zachowywać się jak fala o długości fali λ, wyrażona wzorem, w którym h jest stałą Plancka:

<img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/979/979_Equations-01.png" style="height: 40px;">

Nazywa się to długością fali de Broglie’a. Tam, gdzie Bohr postulował, że elektron jest cząstką krążącą wokół jądra po skwantowanych orbitach, de Broglie argumentował, że założenie Bohra o kwantyzacji można wyjaśnić, jeśli zamiast tego elektron uzna się za kołową falę stojącą. Tylko całkowita liczba długości fal mogła zmieścić się dokładnie na orbicie.

Jeśli elektron postrzega się jako falę krążącą wokół jądra, na orbicie musi zmieścić się całkowita liczba długości fal, aby możliwe było zachowanie się fali stojącej.

Dla orbity kołowej o promieniu r obwód wynosi 2πr, zatem warunek de Broglie'a jest następujący:

<img alt="Eq2" src="https://www.jove.com/files/core/CDNSource/lessons/979/979_Equations-02.png" style="height: 40px;">

gdzie n = 1, 2, 3 i tak dalej. Wkrótce po tym, jak de Broglie zaproponował falową naturę materii, dwóch naukowców z Bell Laboratories, C. J. Davisson i L. H. Germer, wykazało eksperymentalnie, że elektrony mogą zachowywać się falowo. Wykazano to poprzez skierowanie wiązki elektronów na tarczę z krystalicznego niklu. Odstępy atomów w siatce były w przybliżeniu takie same, jak długości fal de Broglie’a skierowanych na nią elektronów, a regularnie rozmieszczone warstwy atomowe kryształu służyły jako „szczeliny”, co wykorzystuje się w innych eksperymentach interferencyjnych.

Początkowo, gdy zarejestrowano tylko kilka elektronów, zaobserwowano wyraźne zachowanie przypominające cząstkę. W miarę przybywania i rejestrowania coraz większej liczby elektronów pojawił się wyraźny wzór interferencji, będący cechą charakterystyczną zachowania falowego. Zatem wydaje się, że chociaż elektrony są małymi, zlokalizowanymi cząstkami, ich ruch nie jest zgodny z równaniami ruchu sugerowanymi przez mechanikę klasyczną. Zamiast tego ich ruchem rządzi równanie falowe. Zatem dualizm korpuskularno-falowy zaobserwowany po raz pierwszy w przypadku fotonów jest zachowaniem podstawowym, właściwym dla wszystkich cząstek kwantowych.

Długość fali de Broglie’a

W świecie makroskopowym obiekty, które są wystarczająco duże, aby można je było zobaczyć gołym okiem, podlegają zasadom fizyki klasycznej. Kula bilardowa poruszająca się na ...

Education

JoVE Core

Chemistry

Chemia

Jeden

Electronic Structure of Atoms

Budowa elektronowa atomów

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

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

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Phase Diagrams

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PS.PSc.1.2

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PS.PSc.1.3

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Subatomic Particles

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The Bohr Model

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Emission Spectra

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The Uncertainty Principle

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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

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Ionic Radii

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PS.PSc.1.6

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Covalent Bonding and Lewis Structures

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Bonding in Metals

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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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