# Understanding the atom

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I had some questions about the atom that hopefully some of you may be able to answer.

First question: How is it that electrons don't attract to protons within the nucleus and just annihilate with each other? They both have 1.6*10^-19 C charge that would attract one another. The only thing I could think of is there is some other type of force repelling the the electrons from the nucleus? This is just a guess at trying to explain this phenomenon.

Second question: Why are electrons confined to specific energy levels? I don't understand how an electron can only be at specific distances from the nucleus.

Third question: Why do neutrons even need to be paired within the nucleus to balance protons? The charge of an electron and the charge of a proton already cancel each other out to form a neutral atom. Why is the neutron even necessary?

Fourth question: I'm having trouble wrapping my head around non-integral spin. What exactly does it mean for a fermion not to have an integer spin? Maybe spin doesn't mean exactly what is traditionally associated with the word spin. Is this the rotation of the particle or does spin denote a special property about the particle, similar to how the term isospin is used simply because its properties are easier to explain in terms related to spin.

Fifth question: I understand there are two types of particles fermions and bosons, but could someone explain some of the intuitive differences in these particles. How can a force carrier be a particle. I think perhaps fermions are more intuitive because they represent the building blocks of what we see everyday constituting hadrons and leptons, but bosons seem a little less intuitive. For instance, how does a gluon transfer color charge? does it pass through quarks carrying the color charge/anticolor charge with it? are photons and W+ W- bosons inside of fermions waiting to be released through particle interactions?

Hopefully these questions don't sound too elementary or absurd, but I am a new physics student simply trying to gain a little more intuitive clarity on some of these concepts. Math is welcome, however I only have a basic understanding of calculus 1. Thanks in advance.

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First question: How is it that electrons don't attract to protons within the nucleus and just annihilate with each other? They both have 1.6*10^-19 C charge that would attract one another. The only thing I could think of is there is some other type of force repelling the the electrons from the nucleus? This is just a guess at trying to explain this phenomenon.

Second question: Why are electrons confined to specific energy levels? I don't understand how an electron can only be at specific distances from the nucleus.

Electrons and protons do attract each other, which is why they can be energetically bound together. Electrons don't just fall into the nucleus and stay there because that's not energetically possible — the energy states of the system are only allowed to have certain values. The electron does not have a specific orbit, like a planet (i.e. it's not a particular distance away from the nucleus). When you look at all of the restrictions on where the electron can be (i.e. you solve the Schrödinger equation), it turns out that only specific energies are valid solutions.

Third question: Why do neutrons even need to be paired within the nucleus to balance protons? The charge of an electron and the charge of a proton already cancel each other out to form a neutral atom. Why is the neutron even necessary?

Protons repel and are in much closer proximity than the electrons. Even though protons attract via the strong nuclear interaction, you can't form a bound system with just protons. Neutrons act as a sort of glue, since they attract but do not repel. And there's a lot more detail of nuclear structure that comes into play because neutrons and protons can decay onto each other, depending on their energy inside the nucleus.

Fourth question: I'm having trouble wrapping my head around non-integral spin. What exactly does it mean for a fermion not to have an integer spin? Maybe spin doesn't mean exactly what is traditionally associated with the word spin. Is this the rotation of the particle or does spin denote a special property about the particle, similar to how the term isospin is used simply because its properties are easier to explain in terms related to spin.

Spin is not physical motion, it's intrinsic angular momentum. There's no way an electron, for example, could physically spin fast enough to have the angular momentum it has, so it has to be interpreted as an intrinsic property. Non-integral spin merely means that the z component of the angular momentum is $\frac{\hbar}{2}$ or some multiple of that, rather than just integer multiples of hbar.

Fifth question: I understand there are two types of particles fermions and bosons, but could someone explain some of the intuitive differences in these particles. How can a force carrier be a particle. I think perhaps fermions are more intuitive because they represent the building blocks of what we see everyday constituting hadrons and leptons, but bosons seem a little less intuitive. For instance, how does a gluon transfer color charge? does it pass through quarks carrying the color charge/anticolor charge with it? are photons and W+ W- bosons inside of fermions waiting to be released through particle interactions?

You can cram as many Bosons into a volume as you want, but because of the Pauli exclusion principle you can't do this to Fermions. In this sense, Fermions take up space while Bosons do not.

Hopefully these questions don't sound too elementary or absurd, but I am a new physics student simply trying to gain a little more intuitive clarity on some of these concepts. Math is welcome, however I only have a basic understanding of calculus 1. Thanks in advance.

Quantum mechanics (and, by extension, all theories stemming from it) takes a bit of getting used to. A deeper understanding of some of these concepts might have to wait until you get a handle on QM.

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Fourth question: I'm having trouble wrapping my head around non-integral spin. What exactly does it mean for a fermion not to have an integer spin? Maybe spin doesn't mean exactly what is traditionally associated with the word spin. Is this the rotation of the particle or does spin denote a special property about the particle

...

I believe that the concept of spin originated in spectroscopic work with atoms. Physicists looked at how spectral lines split in the presence of a magnetic field, and from the splittings deduced that electrons have half integral spin

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I had some questions about the atom that hopefully some of you may be able to answer.

First question: How is it that electrons don't attract to protons within the nucleus and just annihilate with each other? They both have 1.6*10^-19 C charge that would attract one another. The only thing I could think of is there is some other type of force repelling the the electrons from the nucleus? This is just a guess at trying to explain this phenomenon.

Electron attract to protons electromagnetically. In fact, the electromagnetic interaction is the main interaction that describes electronic structure in atoms and molecules. There are not forces F in the Schrödinger equation.

Second question: Why are electrons confined to specific energy levels? I don't understand how an electron can only be at specific distances from the nucleus.

Electrons in atoms are confined to specific levels because energy is quantized. Atoms absorb or emit quanta of energy when electrons jump from a given energy level to another. An electron in a stationary level in an atom is not "at specific distances from the nucleus". In fact, the electron does not have even a well-defined position. You cannot imagine an electron in an atom as a little billiard ball. It is all more sophisticated.

Third question: Why do neutrons even need to be paired within the nucleus to balance protons? The charge of an electron and the charge of a proton already cancel each other out to form a neutral atom. Why is the neutron even necessary?

The more common isotope of Hydrogen does not have neutrons.

Fourth question: I'm having trouble wrapping my head around non-integral spin. What exactly does it mean for a fermion not to have an integer spin? Maybe spin doesn't mean exactly what is traditionally associated with the word spin. Is this the rotation of the particle or does spin denote a special property about the particle, similar to how the term isospin is used simply because its properties are easier to explain in terms related to spin.

Effectively, quantum mechanical spin is different than classical spin. Quantum spin has nothing to see with electron rotating around an hypothetical axis. In fact recall that electrons are not little billiard balls! Quantum spin is a purely quantum effect that defines one of the fundamental properties of the electron (together with mass and charge).

Spin 1/2 means that the magnitude of its projection is $s = \hbar/2$. Note that 1/2 is only the projection of the spin, the magnitude of the total spin is $S=(\sqrt{3}/2) \hbar$.

Fifth question: I understand there are two types of particles fermions and bosons, but could someone explain some of the intuitive differences in these particles. How can a force carrier be a particle. I think perhaps fermions are more intuitive because they represent the building blocks of what we see everyday constituting hadrons and leptons, but bosons seem a little less intuitive. For instance, how does a gluon transfer color charge? does it pass through quarks carrying the color charge/anticolor charge with it? are photons and W+ W- bosons inside of fermions waiting to be released through particle interactions?

Fermions have half-integer spin and verify the Fermi & Dirac statistics. Bosons have integer spin and verify the Bose & Einstein statistics. Fermions cannot occupy a particular quantum state at the same time.

Bosons can be also 'intuitive'. Think on photons. Light is made of photons. You cannot say that bosons are inside fermions as the electron. Electrons and quarks are elementary particles, which means that in the Standard Model they are the ultimate building blocks of nature.

Edited by juanrga
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How is it that electrons don't attract to protons within the nucleus and just annihilate with each other?

They do attract. Writing it as an energy rather than a force simply fits better the wave equation. Protons and electrons don't annihilate because they can't: this would not keep the baryonic number. (Less old formulations would put other numbers here). Protons annihilate with antiprotons, electrons with positrons, that's it.

...some other type of force repelling the the electrons from the nucleus?

No repulsion, and in fact, spherical orbitals (1s, 2s, 3s...) have their maximum density of probability (per volume unit, not per radius unit) right at the nucleus. But non-spherical ones have a zero density there.

Now, atoms have a diameter because electrons, as any particle, are waves. An electron crammed into a smaller volume means a shorter wave which has more kinetic energy. You can consider orbitals as an minimization of the electron's energy: electrostatic (=nucleus attraction) plus kinetic (=electron confinement). Feynman makes a short calculation this way in this (recommended) course and gets a reasonable atom diameter.

This is the most obvious success of quantum mechanics: it explains why matter has a volume.

Why are electrons confined to specific energy levels?

They aren't. The fixed energy levels correspond only to stationary solutions, where the amplitude of the orbital does not evolve over time. So to say, these orbitals don't "vibrate" and accordingly don't radiate light - what a vibrating electron would do. This is one other early success of quantum mechanics: it explains why electrons in a atom don't radiate. Interestingly, these solutions which don't radiate are the ones where the electron's energy is constant: it's consistent.

Now, if an electron bound to an atom is absorbing or emitting light for instance, its wave function is a combination of several stationary solutions. This combination is not stationary but does vibrate, at (or near) the frequency of the light. The proportion of the stationary solutions in the combination evolves over time, more or less quickly depending on the light's intensity. Here quantum mechanics is not so abstract.

The quantization of orbital momentum is easier to understand. It corresponds to the number of 360° phase turns the wave makes in a 360° geometric turn. Since the wave function is identical after a geometric turn, the phase of the wave function makes an integer number of turns, and the orbitam momentum is integer. (Spin cannot be understood that way)

Why do neutrons even need to be within the nucleus...

I ignore it, and so do many people.

For sure, neutrons and protons can transform in an other by emitting an electron (beta minus radioactivity), emitting a positron (beta plus radioactivity), or absorbing an electron (electron capture). So if a nucleus has too many protons or neutrons, radioactivity will correct this in order to put the baryons in a favourable number, which is nearly as many protons as neutrons for small nuclei.

BUT.

Nothing would oppose a di-neutron or even a di-proton from the little I've read, and these are not observed, though we have huge amounts of free neutrons in uranium reactors. Experimentators seek them in vane. Apart that the neutron itself is radioactive (quarter hour life) a di-neutron would put both nucleons in the ground state as efficiently as a deuterium nucleus.

Could it be that only neutrons and protons attract an other, but not neutron and neutron, nor proton and proton? This is NOT standard theory; on the other hand, could it be that these interactions are not known with enough detail? No idea.

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