Inquiring Minds

Physics Questions People Ask Fermilab

Could you please tell me if electrons ever " fall " into the nucleus of an atom?

I have never read of this happening - not even in the depths of space where the temperature is so cold the electrons should be moving very slowly and hence should " fall " in.

If the electron of a hydrogen atom were to " fall " into the nucleus then this would produce a proton. However, I seem to recall reading that an electron has to be fired into a proton using a particle accelerator in order for us to produce a neutron.

When I was at school I was taught that electrons travel around the nucleus in a similar way to planets travelling around the sun. This doesn't seem to be quite right.

Thank you for the opportunity to ask this question.

Regards, Bob Dowe

Hello Bob,

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. ( The transistor, the basic constituent of computers works on quantum transitions.) (This makes QM produce money!!)

I hope the above takes care of your first and last question which were:

Could you please tell me if electrons ever " fall " into the nucleus of an atom ?

When I was at school I was taught that electrons travel around the nucleus in a similar way to planets travelling around the sun. This doesn't seem to be quite right.

Let me make a comment on the next question. You wrote:

I have never read of this happening - not even in the depths of space where the temperature is so cold the electrons should be moving very slowly and hence should "fall" in.

Quantum mechanics states that among all the possible energy levels an electron can sit in the presence of a nucleus, there is one, which has THE MINIMAL energy. This energy level is called the ground state. So, even if atoms are in a very very called environment, QM prohibits electrons from falling to the nucleus. The worst it can happen, is that they will sit in their ground states.

Finally we get to your last question:

If the electron of a hydrogen atom were to " fall " into the nucleus then this would produce a proton. However, I seem to recall reading that an electron has to be fired into a proton using a particle accelerator in order for us to produce a neutron.

It is possible to force electrons into the nucleus. You have to overcome certain energy barriers made by other, possibly present electrons ( the repulsive force between these electrons makes this barrier). Once you do that, electrons can enter the nucleus and can react with protons or neutrons, but that is another story. It is not anymore QM which is responsible for description of such an event, but something called the Standard Model of Particle Physics. This is the model we are verifying here at Fermilab. (And of course, at the same time we are looking for the ultimate theory of our universe.)

I hope your questions got answered. If not, please do not hesitate to write us and we will try to do our best.

Bye Arnold

Graduate Student at Fermilab

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