Why electrons never make contact with the nucleus?

[Med242]

Hi everyone:

This concept has bothered me for a while. The concept being that two oppositely charged particles (electron and proton) are attracted to each other, but the electrons go on a orbital trajectory around the nucleus instead of directly "sticking to" the nucleus. The closest I have come to a reasonable answer lies within the theories of quantum mechanics, ie. Uncertainty Principle, Wave behavior of electrons, Kinetic energy, etc.

It all confuses me when it comes to the probability of the electron's path. A path straight towards the nucleus has to be included in that statistic. How can it deliberately avoid contact with the nucleus? It can't be centripetal force keeping it from the nucleus because that involves acceleration, which should be straight toward the nucleus.

 

[Orodruin]

but the electrons go on a orbital trajectory around the nucleus

Whether or not this is a correct statement depends on what you mean with it. Electrons most certainly do not orbit the nucleus in a classical fashion, but enter quantised energy eigenstates, states we refer to as orbitals.

It all confuses me when it comes to the probability of the electron's path. A path straight towards the nucleus has to be included in that statistic. How can it deliberately avoid contact with the nucleus? It can't be centripetal force keeping it from the nucleus because that involves acceleration, which should be straight toward the nucleus.

You simply cannot describe what happens at a subatomic level with classical mechanics. At that level, you need to describe things using quantum mechanics and any classical likenesses are doomed to be simple mental images.

 

[Med242]

Whether or not this is a correct statement depends on what you mean with it. Electrons most certainly do not orbit the nucleus in a classical fashion, but enter quantised energy eigenstates, states we refer to as orbitals

You simply cannot describe what happens at a subatomic level with classical mechanics. At that level, you need to describe things using quantum mechanics and any classical likenesses are doomed to be simple mental images.

I agree with you there. So quantum mechanics says there is absolutely no way to tell what a part is doing at a moment in time. I know that we can only guess where it is, so why can't we guess that it could be on a path towards the nucleus?

 

[Orodruin]

You seem to be stuck in a classical mindset with the assumption that the electron is actually "doing" something. This is not the case, the entire behaviour of the electron is captured by its wave function. It is not about only being able to guess what it is "doing". It is about the electron actually being something that is described better by a wave function rather than a small billiard ball.

 

[Med242]

You seem to be stuck in a classical mindset with the assumption that the electron is actually "doing" something. This is not the case, the entire behaviour of the electron is captured by its wave function. It is not about only being able to guess what it is "doing". It is about the electron actually being something that is described better by a wave function rather than a small billiard ball.

Ok, yes, it has properties of a wave, so what does this imply with its behavior?

 

[Orodruin]

Ok, yes, it has properties of a wave, so what does this imply with its behavior?

You also need to stop thinking about the wave-particle duality as if it was a particle which some times has the properties of a wave. An electron is an electron, it is well described by a quantum mechanical wave function which shares some properties with wave and some properties with particles, but it is neither a classical particle nor a wave.

 

[Med242]

You also need to stop thinking about the wave-particle duality as if it was a particle which some times has the properties of a wave. An electron is an electron, it is well described by a quantum mechanical wave function which shares some properties with wave and some properties with particles, but it is neither a classical particle nor a wave.

Ok yes I realize this.

 

[HowardTheDuck]

According to Louis de Broglie, particles can act like waves. Therefore, an electron orbiting a nucleus could be interpreted as a standing wave, with only an integer amount of wavelengths being allowed. Higher energy electrons can pack more wavelengths into their orbit. The longest wavelength is the lowest energy an electron can possess, and that represents the ground state. An electron can therefore get no nearer the nucleus.

 

[Orodruin]

According to Louis de Broglie

de Broglie published this hypothesis in 1924. Physics has advanced since then and the model you quote for the orbitals is severely antiquated. In my opinion, the use of this type of models in popular science is the reason we have people coming here who think they can do physics just by quoting ideas similar to this one. What people do not realize is that these models are old and at best analogies and approximations of the actual theory.

 

[HowardTheDuck]

I would say that the basic principles of quantum physics have not changed much since the early decades of the 20th century. De Broglie's picture basically became the Schrodinger equation, still in use today. I could say the integer wavelengths represent energy eigenstates, but it's basically the same thing. You mentioned energy eigenstates yourself - discovered in the 1920s! Nothing wrong with old stuff! I think the integer wavelength is quite an intuitive way of looking at it.

 

[Orodruin]

The problem with the de Broglie picture is that it is giving the appearance of the electron having a classical circular orbit. You will agree that this is certainly not the case. The Schrödinger equation is three-dimensional and the appropriate solutions in the angular directions are the spherical harmonics. It is certainly not about the electron "travelling" as a wave around the nucleus.

I would say that the basic principles of quantum physics have not changed much since the early decades of the 20th century,

Oh, but it has. I would claim implying that the foundations of physics have not changed in 100 years is simply not true. We have obtained significant insight in the formulation of quantum theory, including the development of quantum field theory and the standard model of particle physics, just to mention a few things. To view anti-particles as "holes" in a Dirac sea as Dirac did is no longer really a model that we work after. That things are taught in this way for historical reasons is a different matter. In a similar fashion, Einstein laid the foundation for GR, but we certainly do not teach it today as he would have 100 years ago.

 

[jtbell]

Actually the electron does sometimes "make contact with the nucleus," in some sense. See the graphs for the electron probability density for the ground state of hydrogen in figures 3.4 and 3.6 on this page:

http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_2.html

The probability density is actually largest at the origin (the nucleus)!

With hydrogen, nothing actually happens as a result of the non-zero probability of the electron being "in contact with the nucleus", because there's no outcome that satisfies energy conservation. The proton can't simply absorb the electron and convert into a neutron, because an isolated neutron has more mass than an isolated proton, and there's no place for the required additional energy to come from.

However, certain heavier nuclei can capture the electron, convert a proton into a neutron, and change the total nuclear binding energy in such a way that the new isotope has less mass than the original one, releasing energy in the process.

https://en.wikipedia.org/wiki/Electron_capture