Name: shielding and orbital penetration
Uploaded: 2020-09-03T13:38:28.000Z
Duration: 3 min 21 s
Channel: JoVE

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The Energies of Atomic Orbitals

Orbitale atomowe mają różne energie, co jest racjonalizowane przez oddziaływania kulombowskie, efekt ekranowania i penetrację orbity.

Prawo Coulomba wskazuje, że siła przyciągania lub odpychania między dwiema naładowanymi cząstkami ma relację odwrotną do kwadratu z odległością między nimi. 

Rozmiary orbitali atomowych zwiększają się wraz z liczbą powłok, a elektrony są odpychane od przestrzeni zajmowanej przez orbitale o niższej powłoce. Tak więc prawo Coulomba sugeruje, że wraz ze wzrostem liczby powłok elektrony doświadczają mniejszego przyciągania do jądra, co odpowiada wyższym energiom orbitalnym.

Ponadto elektrony, które znajdują się mniej więcej w tej samej odległości od jądra lub bliżej niego, mają efekt ekranowania, który dodatkowo zmniejsza przyciąganie do jądra. Im większe ekranowanie, tym mniejsze przyciąganie do jądra jest odczuwalne. Jest to jeden z powodów różnic w energiach orbitalnych w powłokach elektronowych. Na przykład elektrony 3s i 3p znacznie osłaniają elektrony 3d.

Efektywny ładunek jądrowy odczuwany przez elektron oblicza się, odejmując od liczby atomowej stałą ekranowania S, która zależy od liczby atomowej liczby ekranowanych elektronów i zajmowanych przez nie podpowłok.

Na przykład dwa elektrony 1s w litu, który ma liczbę atomową trzy, ekranują jego elektron 2s. Stała ekranowania dla tego elektronu jest określana na podstawie reguł półempirycznych na 1,7. Stąd efektywny ładunek jądrowy odczuwany przez elektron 2s wynosi 1,3.

Kształty orbitali również dyktują ich energię. Jeśli elektrony na zewnętrznej orbicie mogą przemieszczać się daleko w obszary zajmowane przez elektrony wewnętrzne, aby być blisko jądra, będą tam znacznie mniej ekranowane. Stąd energia tego zewnętrznego orbitalu jest niższa.

Można to zobrazować za pomocą funkcji rozkładu radialnego opisującej prawdopodobieństwo znalezienia elektronu w danej odległości od jądra.

Wykresy funkcji rozkładu radialnego dla podpowłok 1s, 2s i 2p pokazują, że elektrony 2s mają niewielkie prawdopodobieństwo przebywania w pobliżu jądra, podczas gdy elektrony 2p w większości pozostają na zewnątrz lub na zewnętrznej krawędzi obszaru 1s. Mówi się zatem, że orbital 2s ma większą zdolność penetracji. W trzeciej powłoce 3 elektronys przenikają najwięcej, a 3 elektronyd przenikają najmniej.

Ogólnie rzecz biorąc, energia orbitalna atomów wzrasta wraz z liczbą powłoki, a na poziomie podpowłoki od s do f. Jednak efekt penetracji staje się tak znaczący w czwartej i piątej powłoce, że orbitale 4s i 5s często mają niższe energie względne niż orbitale 3d i 4d.

energie orbitali atomowych

W atomie ujemnie naładowane elektrony są przyciągane do dodatnio naładowanego jądra. W atomie wieloelektronowym obserwuje się dodatkowo odpychanie na linii elektron-elektron. Siły przyciągania i odpychania zależą od odległości między cząstkami, a także od znaku i wielkości ładunków na poszczególnych cząstkach. Kiedy ładunki na cząstkach są przeciwne, ma miejsce przyciąganie. Jeśli obie cząstki mają ten sam ładunek, obserwuje się odpychanie.

Wraz ze wzrostem wielkości ładunków wzrasta wielkość siły. Jednakże, gdy separacja ładunków jest większa, siły maleją. Zatem siła przyciągania między elektronem a jego jądrem jest wprost proporcjonalna do odległości między nimi. Jeśli elektron znajduje się bliżej jądra, jest ściślej związany z jądrem; dlatego elektrony na różnych powłokach (w różnych odległościach) mają różne energie.

W przypadku atomów o wielu poziomach energii elektrony wewnętrzne częściowo osłaniają elektrony zewnętrzne przed przyciąganiem jądra w wyniku odpychania elektron-elektron. Elektrony rdzeniowe osłaniają elektrony w powłokach zewnętrznych, podczas gdy elektrony w tej samej powłoce walencyjnej nie blokują tak skutecznie wzajemnego przyciągania jądrowego. Można to wyjaśnić koncepcją efektywnego ładunku jądrowego Zeffa. Jest to przyciąganie wywierane na konkretny elektron przez jądro, biorąc pod uwagę wszelkie odpychania elektron-elektron. W przypadku wodoru istnieje tylko jeden elektron, zatem ładunek jądrowy (Z) i efektywny ładunek jądrowy (Zeff) są równe. W przypadku wszystkich pozostałych atomów elektrony wewnętrzne częściowo osłaniają elektrony zewnętrzne przed przyciąganiem jądra, a zatem:

<img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/985/985_Equations-01.png" style="height: 40px;">

Penetracja orbity opisuje zdolność elektronu do zbliżenia się do jądra. Elektrony na orbicie s mogą zbliżyć się do jądra i mieć większą zdolność penetracji. Gęstość prawdopodobna dla sferycznej orbitalu s jest różna od zera w jądrze. Różne podpowłoki mają różne orientacje przestrzenne. Ze względu na orbital w kształcie hantli, elektron p penetruje znacznie mniej. Jego funkcja falowa ma węzeł przechodzący przez jądro, gdzie prawdopodobieństwo znalezienia elektronu wynosi zero. Zatem elektron orbitalny s jest ściślej związany z jądrem i ma niższą energię niż elektron p. Elektron d ma jeszcze niższą penetrację i wyższą energię niż elektron orbitalny p.

Dla różnych powłok i podpowłok trend siły penetracji elektronu można przedstawić w następujący sposób

<img alt="Eq2" src="https://www.jove.com/files/core/CDNSource/lessons/985/985_Equations-02.png" style="height: 40px;">

Efekt ekranowania i penetracji jest duży, a elektron 4s może mieć niższą energię niż elektron 3d.

Energie orbitali atomowych

W atomie ujemnie naładowane elektrony są przyciągane do dodatnio naładowanego jądra. W atomie wieloelektronowym odpychania elektron-elektron są ...

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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 electrons in different shells can have different energies because they sit at different distances from the nucleus. In atoms with several energy levels, inner electrons partly block the nucleus from outer electrons. This blocking is called shielding, and it happens because of electron-electron repulsions.

The pull felt by one electron after shielding is the effective nuclear charge, or Zeff. It describes the attraction from the nucleus after repulsions are taken into account. For hydrogen, which has only one electron, Z and Zeff are the same. In atoms with more than one electron, core electrons shield outer electrons, while electrons in the same valence shell do not block the nuclear pull very well.

Orbital penetration describes how close an electron can get to the nucleus. s orbitals penetrate best because their spherical probability density is non-zero at the nucleus. p orbitals penetrate less because their dumbbell shape has a node through the nucleus, where the chance of finding an electron is zero. d orbitals penetrate even less than p orbitals.

Because of shielding and penetration, s electrons are usually bound more tightly and have lower energy than p electrons. d electrons have higher energy than p electrons. These effects can be strong enough that a 4s electron may have lower energy than a 3d electron.

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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...

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Learn how shielding, effective nuclear charge, and orbital penetration affect electron energy levels, and why s, p, and d orbitals differ in energy.

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Shielding and Orbital Penetration

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