Name: bohr’s quantized atomic orbits
Uploaded: 2020-09-03T13:38:27.000Z
Duration: 2 min 18 s
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The Bohr Model

惑星モデルでは 水素原子を 小さな太陽系に見立て 電子が正電荷を帯びた 原子核の周りを 回っていると説明しています 古典物理学では 電子は円軌道上を移動する 荷電粒子であるため 正電荷を帯びた原子核に 螺旋を描きながら エネルギーを放射し続けると 考えられています 最終的に原子は 崩壊すると考えられました しかし これは 観測されていません 原子は安定しているのです ニールス・ボーアは 原子核から一定の距離に 軌道があることを提案しました これらの軌道は 主量子数nで ラベル付けされた整数です 原子核に最も近い軌道は nが1の場合です nは任意の正の整数ですが 0になることはありません nが大きくなると軌道の 半径も大きくなります 原子核から離れた電子は 静電力が弱くなり 陽子に 引きつけられる力が弱くなります それぞれの軌道は 特定のエネルギー準位や 状態に対応しています これらのエネルギー準位は 量子化されており その間のエネルギーは 存在しないことを意味します 最も低く 最も安定なエネルギー 状態（n=1の状態）の電子は 基底状態にあると言われます nが1よりも大きい 高エネルギー状態は 励起状態と呼ばれます 電子は エネルギーを吸収して より高い準位にジャンプするか あるいはエネルギーが 低い状態に遷移して 余分なエネルギーを 光子の形で放出するときにのみ 異なるエネルギー準位に 移動することができます 吸収されたエネルギー または 放出されたエネルギーは 最終的なエネルギー準位と 初期のエネルギー準位の間の エネルギーの差に関連しています 高いエネルギー準位から 緩和した電子は 低いエネルギー準位から 緩和した電子よりも 波長の短い光を放出します ボーアのモデルは 水素または 単電子イオンにのみ 適していますが より正確な原子モデルの 基礎を築きました

ボーア理論

20世紀初頭のアーネスト・ラザフォードらの研究により、原子は密度の高い小さな原子核と、その周りを絶えず動き回る軽くて小さな電子で構成されているという図式が確立されました。 この図式は、太陽の周りを回る惑星のように、原子核の周りを電子が回っているという太陽系のミニチュアのような図式で、惑星モデルと呼ばれました。最も単純な原子は水素で、1個の陽子が核となり、その周りを1個の電子が動きます。電子を陽子に引き付ける静電力は、2つの粒子の距離にのみ依存します。しかし、この古典力学による原子の記述は不完全です。というのも、楕円軌道上を移動する電子は（方向を変えて）加速しており、古典電磁気学によれば電磁波を放出し続けているはずだからです。このように軌道エネルギーが失われると、電子の軌道はどんどん小さくなり、やがて核の中に入り込んでしまうので、原子は本質的に不安定であることがわかります。 
 
 1913 年、ニールズ・ボーアは、水素中の電子が絶えず光を放射するという古典的な電磁気学の予測を無視して、原子のパラドックスを解決しようと試みました。 その代わりに、古典力学による原子の記述、プランクの量子化の考え方、アインシュタインの「光は光子で構成され、そのエネルギーは周波数に比例する」という発見を取り入れました。 ボーアは、原子核を周回する電子は通常、どのような放射線も放出しません ( 定常状態仮説 ) が、別の軌道に移動した場合に光子を放出したり吸収したりすると仮定しました。 吸収または放出されるエネルギーは、次の式に従って軌道エネルギーの違いを反映します。 
 
 <img alt="Eq1" src="https://www.jovecore.com/CDNSource/lessons/978/978_Equations-01.png" style="height: 40px;" />
 
 ここで、 h は プランク定数、 EiとEf は初期軌道エネルギーと最終軌道エネルギーです。 周波数と波長は常に正の値であるため、エネルギー差の絶対値が用いられます。ボーアは、エネルギーの連続値を許容する代わりに、これらの電子軌道のエネルギーを量子化されていると仮定しました。 
 
 <img alt="Eq2" src="https://www.jovecore.com/CDNSource/lessons/978/978_Equations-02.png" style="height: 40px;" />
 
 この式で k は、電子質量、電荷、プランク定数などの基本的な定数で構成される定数です。 Δ E の方程式に軌道エネルギーの式を挿入すると、次のようになります。
 
 <img alt="Eq3" src="https://www.jovecore.com/CDNSource/lessons/978/978_Equations-03.png" style="height: 40px;" />
 
 物理学の基本原理の 1 つは、物質が可能な限り低いエネルギーで最も安定していることです。 このように、水素原子の電子は通常、最も低いエネルギーを持つ軌道である n =1 軌道で移動しています。 電子がこの最も低いエネルギー軌道にある場合、原子は基底電子状態（または単に基底状態）と言われます。 原子が外部からエネルギーを受け取ると、電子は n の値が大きい軌道に移動し、原子がより高いエネルギーで励起電子状態（または単に励起状態）になる可能性があります。 励起状態（高エネルギー軌道）から低励起状態（または基底状態）への電子遷移が発生すると、エネルギーの差が光子として放射されます。 同様に、光子が原子に吸収されると、光子のエネルギーは電子を低エネルギー軌道からより励起された軌道に移動します。 原子の電子のエネルギーを、以前に学んだエネルギーと関連付けることができます。 エネルギー保存則では、エネルギーの創造も破壊もできないと定められています。 したがって、あるエネルギーレベルから別のエネルギーレベルに電子を励起するために一定量の外部エネルギーが必要な場合、電子が初期状態に戻ると、同じ量のエネルギーが解放されます。 
 
 ボーアのモデルは単一の電子のみを含むため、原子電荷の水素のみとは異なる単一電子イオン、He+、 Li2+ 、 BE3+ などにも適用できます。したがって、単電子原子とイオンは、総称して水素様原子と呼ばれます。  
 
 このテキストは <a href="https://openstax.org/books/chemistry-2e/pages/6-2-the-bohr-model">、 Openstax, Chemistry 2e, Section 6.2: The Bohr Model から引用</a>しています。

20世紀初頭のアーネスト・ラザフォードと彼の同僚の研究に続いて、小さな密集した原子核からなる原子の写真が取り囲まれました...

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KEY TERMS AND CONCEPTS

主要用語と概念

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 classical view, the electrostatic force between the proton and electron depends only on the distance between them. That description is incomplete, though. If the electron moved in an elliptical orbit, it would be accelerating because its direction changes.

Classical electromagnetism says an accelerating charged particle should continually emit electromagnetic radiation. If that happened, the electron would lose orbital energy. Its orbit would keep shrinking until it spiraled into the nucleus. That would make atoms unstable, so the classical picture creates an atomic paradox.

In 1913, Niels Bohr proposed a different model to address this problem. He ignored the classical prediction that the orbiting electron in hydrogen should constantly emit light. Instead, he used classical mechanics together with Planck’s idea of quantization and Einstein’s idea that light is made of photons with energy proportional to frequency. Bohr also proposed the stationary state hypothesis, which says the electron does not normally emit radiation while it stays in one orbit.

Bohr said light is emitted or absorbed only when the electron moves between orbits. The energy change follows the difference between the initial and final orbital energies, and the absolute value is used because frequency and wavelength are always positive. He also assumed the allowed electron energies are quantized, not continuous. In his energy equation, k is a constant that includes fundamental constants such as electron mass, electron charge, and Planck’s constant.

For hydrogen, the n = 1 orbit has the lowest energy. Because matter is most stable at the lowest possible energy, the electron usually stays in this orbit. This is the ground electronic state, or ground state. If the atom absorbs energy from outside, the electron can move to a higher n orbit. The atom then enters an excited electronic state, or excited state.

When an electron drops from an excited state to a less excited state or back to the ground state, the energy difference is released as a photon. The reverse also happens. If the atom absorbs a photon, that photon’s energy can move the electron from a lower orbit to a more excited one. This matches the law of conservation of energy, which says energy is neither created nor destroyed.

Because Bohr’s model was built for a single electron, it also applies to single-electron ions such as He+, Li2+, and Be3+. These species differ from hydrogen only in their nuclear charges. For that reason, hydrogen and these one-electron ions are called hydrogen-like atoms.

Bohr’s Quantized Atomic Orbits

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the bohr model

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...

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key terms and concepts

Learn how Bohr explained hydrogen stability with quantized orbits, ground and excited states, and photon absorption and emission in hydrogen-like atoms.

Bohr’s Quantized Atomic Orbits | JoVE K12

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Phase Transitions

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Heating and Cooling Curves

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Physical Properties of Matter

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Molecular Comparison of Gases, Liquids, and Solids

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Intermolecular vs Intramolecular Forces

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

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The Atomic Theory of Matter

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Subatomic Particles

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Following the work of Ernest Rutherford and his colleagues in the early twentieth century, the picture of atoms consisting of tiny dense nuclei surrounded ...

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The Uncertainty Principle

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The Periodic Table

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Understand types, properties, and structure of matter.

Bohr’s Quantized Atomic Orbits

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