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Help with a Student Question: Why do Electrons not crash in the Nucleus?


mrthole

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Any suggestions in how to explain to high school chemistry students why negatively charged electrons do not crash into the positively charged nucleus? I have one student who is particularly interested in this topic, however, I am finding it difficult to put it into terms he can get his head around.

 

Some strategies I have used are the Accelerating Funnel Model and the Decreasing Box Model which have helped, however, maybe I need to explain them in an alternative way.

 

Thank you for your suggestions in advance.

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Any suggestions in how to explain to high school chemistry students why negatively charged electrons do not crash into the positively charged nucleus? I have one student who is particularly interested in this topic, however, I am finding it difficult to put it into terms he can get his head around.

 

Some strategies I have used are the Accelerating Funnel Model and the Decreasing Box Model which have helped, however, maybe I need to explain them in an alternative way.

 

Thank you for your suggestions in advance.

 

IIRC, the traditional explanation has to do with the wavelength of the electron.

 

Do your students think that the electrons "orbit" the nucleus?

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My students understand that electrons do not orbit the nucleus and are found in orbitals but predicting the exact location at any one point in time is virtually impossible. They also understand that it is the repulsive force between the negatively charged particles that keeps the orbitals "separated from each other.

 

The challenge is trying to explain why the electrons, especially in the lower energy levels, do not get pulled into the nucleus do to the attractive force between positive and negative.

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I cannot give you an easy explanation for your question but I'd like to comment on something else:

My students [...] also understand that it is the repulsive force between the negatively charged particles that keeps the orbitals "separated from each other."

From the perspective of a theoretician that is fundamentally wrong. The orbitals are one-electron solutions. Strictly speaking they would not even be valid for many-electron systems but they seem to work fine. The reason why that the number of electrons in an orbit is limited is the Pauli principle, not the negative charge of the electrons. The electrons do not crash into the nucleus (whereas it is not entirely clear what that means in QM; in some sense they do) because there is no such orbit - but that is not a good answer, of course.

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I would base your explanation around the second law of thermodynamics.

 

Electrons configure themselves around the nucleus according to the 2nd law of thermodynamics, i.e., the lowest possible energy state. As the a hypothetical electron spirals into the nucleus its kinetic energy would increase dramatically as a consequence of Heisenberg's uncertainty principal. Uncertainty in momentum would be enormous as the space allowed for the electron to move decreases severely [in the relatively tiny space that is the nucleus]. The electrostatic potential between the electron and nucleus could not collapse the electron's kinetic energy. Thus it could not remain in the nucleus as this would be a violation of the second law.

 

Another way of saying this is that the lowest energy state possible (allowed by Schrödinger's wave equation) is one that keeps the electron from being exclusively inside the nucleus. The possible wave functions have only certain exact values of energy and orbital angular momentum that are allowed, E=0 (inside the nucleus) not being one of them.

 

That's my understanding. I'm probably mixing QM with classical/Bohr modeling and whatever else. But that's the best I've got. Someone with more expertise may describe it better.

 

So far the last two posters have nitpicked and posed a one liner and a question to the OP.

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Any suggestions in how to explain to high school chemistry students why negatively charged electrons do not crash into the positively charged nucleus? I have one student who is particularly interested in this topic, however, I am finding it difficult to put it into terms he can get his head around.

 

The rules of QM do not allow the system to get rid of the energy.

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  • 3 weeks later...

Try and equate it to something they already understand. The moon is constantly moving around the earth, like the electron moving around the atom. Although they both want to fall inwards towards the earth/nucleus because they are moving so fast that they keep missing. While this isn't completely correct from a QM standpoint it would probably help a high school student grasp the concept.

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Try and equate it to something they already understand. The moon is constantly moving around the earth, like the electron moving around the atom. Although they both want to fall inwards towards the earth/nucleus because they are moving so fast that they keep missing. While this isn't completely correct from a QM standpoint it would probably help a high school student grasp the concept.

 

Except that model is very wrong — "not completely correct" is underselling it. Electrons do not move in planetary orbits.

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Except that model is very wrong — "not completely correct" is underselling it. Electrons do not move in planetary orbits.

 

Swansont is correct; electrons do not orbit the nucleus. If they did, they would be accelerating and thus would be giving off photons. The energy must be conserved, so as the photons are emitted, the electrons would lose energy. So, as you can probably see, if electrons orbited the nucleus, then they WOULD crash into it!

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Swansont is correct; electrons do not orbit the nucleus. If they did, they would be accelerating and thus would be giving off photons. The energy must be conserved, so as the photons are emitted, the electrons would lose energy. So, as you can probably see, if electrons orbited the nucleus, then they WOULD crash into it!

That's not a (complete) argument:

 

If planets orbited the sun as they do they would be giving off gravitational wells. The energy must be conserved, so as the gravitational waves are emitted, the planets would lose energy. So, as you can probably see, if planets orbited the sun, then they WOULD crash into it!

 

You are at least missing a time-scale in your argument (alternatively you can of course deny the existence of gravitational waves). I am not sure to what extent it is a good idea to mix a non-QM model of atomic structure with a quantized electromagnetic field (->photons).

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That's not a (complete) argument:

 

If planets orbited the sun as they do they would be giving off gravitational wells. The energy must be conserved, so as the gravitational waves are emitted, the planets would lose energy. So, as you can probably see, if planets orbited the sun, then they WOULD crash into it!

They do, eventually. The photons, however take up a far greater percentage of the electron's energy than the gravity waves do of the planets.

 

You are at least missing a time-scale in your argument (alternatively you can of course deny the existence of gravitational waves).
We've seen accelerating charges radiate. :P
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Except that model is very wrong — "not completely correct" is underselling it. Electrons do not move in planetary orbits.

 

yes, But newtonian gravity is completely wrong as well but because it helps people understand a basic concept.

 

planets orbit because they have a high enough energy to escape the pull of the planet; if you increase an orbiting objects velocity it moves farther from what its orbiting.

 

Electrons in ground state have a high enough energy to escape the pull of nucleus, if you increase energy of an electron it moves farther from the nucleus.

 

 

I would think that this example would be better suited for a high school student who probably hasn't taken calculus and thus doesn't have the understanding of why orbitals are solutions of the wave function.

 

I was just trying to make it as simple as possible and while no model is perfect if it does what you want it to, that is all you need

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I struggle to understand why some people think that we are benefiting students by teaching them something which is outright false and nonrepresentative. It's as if folks are willing to replace what is "right" with what is "easy."

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your right lets start off teaching kids Quantum mechanics in kindergarten see how well they pass their first final

Totally agree. We should teach kids the MOST accurate information we have, regardless of their age. That's one of the absolute best things we can do for the progress of humanity. The stronger their foundation, the stronger the structure they will be able to build on top of it.

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Totally agree. We should teach kids the MOST accurate information we have, regardless of their age. That's one of the absolute best things we can do for the progress of humanity. The stronger their foundation, the stronger the structure they will be able to build on top of it.

 

It wouldn't actually be that bad. Our standards for education, at least in my part of the world, are ridiculously low. 10 or 11 years of school before calculus is taught? That's outrageous.

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yes, But newtonian gravity is completely wrong as well but because it helps people understand a basic concept.

 

Newtonian gravity is not "completely wrong." It is far less wrong than the Bohr model, which basically only gets the energy correct. Newtonian gravity is valid until you get into relativistic effects. The Bohr model is wrong as soon as you look at any parameter other than energy.

 

planets orbit because they have a high enough energy to escape the pull of the planet; if you increase an orbiting objects velocity it moves farther from what its orbiting.

 

Electrons in ground state have a high enough energy to escape the pull of nucleus, if you increase energy of an electron it moves farther from the nucleus.

 

A pull is a force and is not the same as energy. In neither case does the object in question have enough energy to escape; both represent bound systems.

 

Increasing the energy does not necessarily move you further away. That assumes a circular orbit in the planetary case. And s orbitals overlap with the nucleus, and can have a higher energy than other orbitals.

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I still don't agree with the "tell the students the complex model even if they can't comprehend it." When you start out by teaching students the "wrong" version, but a version of the rule they can understand, it helps them build off of that onto other concepts. In addition, you are pretty much teaching them what mankind initially knew. As they get deeper into chemistry studies, the will learn the more complex concepts and understand them better because they at least had a grasp of it before hand.

 

While we all now know that the thought of electrons orbiting the nucleus is wrong, by teaching that to us initially it helped us understand the behavior of electrons a little bit better and gave us a method for understanding WHY they don't fall into the nucleus. (Because they are moving around at such speeds to overcome the attractive force of the nucleus). If you tried teaching kids quantum mechanics right from the get go, they would VERY quickly get INCREDIBLY frustrated and have no desire to get deeper into the field of chemistry, and thus they would lose all interest in the subject. That is far, FAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAR worse than teaching them something that isn't completely true just so they can at least grasp the idea and then build upon that later.

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And teaching people inaccurate/wrong information makes it more challenging for them to correct those inaccuracies later in life. This is especially apparent with children.

 

While I agree that we have to find ways to make information more accessible to people with limited knowledge, I disagree that teaching inaccurate/wrong information is a reasonable method to achieve that.

 

We'll just have to disagree on this one. No worries.

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Any suggestions in how to explain to high school chemistry students why negatively charged electrons do not crash into the positively charged nucleus? I have one student who is particularly interested in this topic, however, I am finding it difficult to put it into terms he can get his head around.
The first thing you need to tell your students is that it is impossible to explain the existance of stable atoms in terms of classical mechanics. This is one of the facts that motivated the creation of quantum mechanics. Classically an electron orbiting a positive nucleus should continuously radiate electromagnetic energy and spiral into the nucleus thus collapsing. Classically atoms can't exist. That's one of the reasons quantum mechanics was created. What you now need to do is to find the simplest way to explain this to highschool students in a way that they'll be able to grasp without first learning quantum mechanics in its entirety. Since the terminology of quantum mechanics uses the term "orbital" you will need to explain that this term is not what it means in classical mechanics.

 

As far as the description goes I suppose you can simply relate the following postulate made by Bohr (as phrased by Hans C. Ohanian)

When an electron is in one of the quantized orbits, it does not emit any electromagnetic radiation; thus the electron is said to be in a stationary state. The electron can make a discontinuous transition, or quantum jump, from one stationary state to another. During this transition it does emit radiation.

I hope that helps.

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