Atomic Structure Problem

Well we all know that the rutherford's atomic structure has a drastic limitation. According to classical electrodynamics an accelerated charged particle will emit radiation.The electron being accelerated and charged it would have to emit radtiation and thus lose enegy,this would cause it to spiral down and collide with the nucleus. Then Bohr came with the theory of stable orbits. My question is why can't the classical electrodynamics theory be applied and a similar argument be posed? Is it just because Bohr told that some specific orbits would be stable?

Note by Soham Chanda
6 years, 6 months ago

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If I understand correctly, your question is this:

Electrons classically couple to electromagnetism, and so the orbit of electrons moving in a circle around a nucleus is unstable to emission of radiation. We then throw quantum mechanics into the picture, which says that only some orbits are allowed. However, electrons STILL couple to electromagnetism. So why are those orbits not also unstable in the same way that they were classically?

There are different ways to answer this question. One is "just calculate the orbital dynamics using quantum mechanics!" Not very helpful, but it's one complete way to see it. The second way is more intuitive. Consider an electron classically. It's in an orbit, it emits radiation out to infinity and moves to a new orbit. By energy conservation this new orbit has a lower total energy - the electron spirals down. Now, ask what happens if we use quantum mechanics which only allows for SPECIFIC, discrete orbits. If an electron emits electromagnetic energy it must move down to a lower energy orbit. If the electron is in an excited state this is exactly what happens and we get a burst of light (neon lights are quantum mechanics in action). However, what happens if the electron is in its lowest energy state? There is NO state of lower energy by definition, so the electron has no way to lose energy and emit light. Therefore, it doesn't!

David Mattingly Staff - 6 years, 6 months ago

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Sir,can you suggest me any book which vastly deals with the atomic theory starting from the rutherford's model?

Soham Chanda - 6 years, 6 months ago

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If classical electrodynamics theory can be applied, then the electrons will have to emit radiation and spiral down. You argue that the stable orbit theory is still compatible with classical electrodynamics. Then we have to ask ourselves: What is the mechanism behind the stable orbit? How do we quantify the stable orbits? Quantum Mechanics is able to provide an explanations (or at least a 'formula') for the orbits.

Jiahai Feng - 6 years, 6 months ago

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Let us start from the beginning.

First I have to tell you that there are usually two ways people think about our world. 1) The classical (the NON-QUANTUM) approach. 2) The quantum physics approach.

When we talk about macroscopic objects, the quantum effects are negligible, and our intuition gives usually the right answer to problems. ( Example: if one kicks a ball to a wall, one expects that the whole ball will bounce back. Classically it is so. This is what we see in our everyday life. The intuition works.)

However, in the quantum physics world, e.g. the microscopic world, our intuition usually fails, because many times the predictions of equations contradict our everyday life experience. ( Example: if you shoot a particle to a wall, it is not anymore true, that the whole particle will bounce back. There is a certain probability that the particle will go through the wall.)

Answer number 1: Electrons do not fall into the nucleus! Why?

If one thinks about the electron-nucleus system classically, one gets confusing, untrue results. The key to the solution is hidden in quantum mechanics. I will explain everything in details in a minute, but first let us see the electron-nucleus system from the classical point of view and try to explain how atoms work.

If one takes a positive nucleus and a stationary negative electron, everybody knows that the nucleus will attract the electron, electron will start moving towards the nucleus until the electron falls to the nucleus. According to answer number 1, this cannot be a model for an atom. So the electrons cannot just be hanging above the nucleus. They must be moving.

What kind of motion one thinks about?

Yes, circular motion, just as the planets do around the sun. This circular motion protects the planets against falling into the Sun. So one might think, this would work for electrons as well. Answer number 2: This does not work for electrons! Why?

Classical mechanics teaches us that if a charged object moves with an acceleration (in other words, the magnitude or the direction of its velocity is changing in time), this object RADIATES ELECTROMAGNETIC WAVES!!!!

So, if an electron ( obviously a charged object) would be doing a circular motion around a nucleus, the direction of its velocity would be changing, therefore it would radiate out energy, therefore it would loose energy, which means it would spiral down to the nucleus.

Does this make sense? Good.

Answer number 3: Classical mechanics does not give a satisfactory answer, why atoms are stable.

Solution came early of this century. In fact, the kind of question you are asking me, were the ones that triggered the development of fundamentally new ideas, the ideas QUANTUM MECHANICS.

First, based on observation, physicists POSTULATED that electrons are allowed to move around the nucleus ONLY ON CERTAIN SPECIFIC orbits, called Sommerfeld orbits. If so, the electrons DO NOT RADIATE!!!! (for consistency, I will tell you how to find these specific orbits. The Sommerfeld orbits are the ones, for which the angular momentum of electrons is the Planck's constant "h" multiplied by an INTEGER number.) The electrons radiate only when jumping from one orbit to another one.

They did not know why, but this postulate seemed to be working. The results were in a good agreement with the experiment for very simple atoms ( one electron atoms). But for more complicated cases, such as multielectron atoms, it did not work!

The real solution came, when people introduced QUANTUM MECHANICS (QM). I think this is not the right place to give an introduction to quantum mechanics. I will just state the results relevant to your question. From the fundamental ideas of QM people obtained the following results:

1) If an electron is in the electric field of a nucleus, the electron can occupy only certain energy levels. When it is sitting on one of these energy levels, it does not radiate, it does not loose energy. QM shows the way how to calculate these energy levels.

1a) It is possible for electrons to change energy levels, but they have to either absorb, or emit a quantum of energy. This energy is an INTEGER number multiplied by a Planck's constant.

2) The electrons are not localized in certain, well defined and precise positions around the nucleus. In fact, there is a nonzero probability of finding an electron anywhere in our universe. Quantum mechanics gives a prediction and shows how to calculate the probability of finding an electron at a given space point of our universe. (This makes QM VERY appealing.)

3) It turns out, the probability of finding an electron in the field of a nucleus PEAKS in the Sommerfeld orbits mentioned above. (This makes QM EXTREMELY appealing)

4) Quantum Mechanics makes possible that our computers are working.


A Former Brilliant Member - 6 years, 6 months ago

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i was goint to appreciate you for your hard work.. well,since u cited this, .. :P i think you got my question wrong..

Soham Chanda - 6 years, 6 months ago

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coudnt underdstand ur problem i.e question

superman son - 6 years, 6 months ago

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