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One can't take results like that too seriously at the scale at which an electron would apply. In particular, the classical general relativistic model, applied naively to a point mass electron would tell you that the electron has too large a charge and angular momentum to have a black hole horizon, and would instead be the exotic type of object called a ...


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It's not a fundamental feature of electrical potential, but: If you have a polycrystalline metal and you cut and polish a smooth surface, the differently-oriented regions will present a different lattice plane to the outside. Crystals cut along different planes may have slightly different work functions, and so the electric potential very close to such a ...


14

For static charges, the relationship is V (voltage) = Q (charge) / C (capacitance). Capacitance is a function of the shape, size and distance between objects, which are all continuous values. (Well, I suppose you could argue that shape and size are quantized to the atomic spacing of the object's material, but you can't say the same thing for distance.) So ...


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Voltage is a continuous function. If you are a certain distance from a (point) charge $q$, the potential is $$V=\frac{q}{4\pi\epsilon_0 r}$$ By adjusting the value of $r$ to anything you want (not quantized), you can get any potential you want. And so yes, when you do any analog-to-digital conversion, you will "destroy" a certain amount of information. ...


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Voltage doesn't come directly from the charge of the electron. It's the energy per charge. The charge carriers may be discrete, but the energy is not. We can easily generate a potential by moving a wire through a magnetic field. The potential is proportional to the speed of the wire, which is a continuous value. $$V = vBL\sin{\theta}$$


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How should it be “very weak”? Its field strength is immense, against macroscopic samples. Sure, one shouldn’t suppose a Maxwellian E-M fields inside a matter, especially an electric conductor – this microscopic field is uncertain. One hardly can understand it thinking about it as a vector or tensor field in the spacetime; one needs QFT. There is a related ...


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For what it's worth, I've always had the same feeling that the spin should have some sort of reason behind it. It seems so unsatisfying to be told more or less that "it just came that way." Is there any deeper sort of explanation at all? I recall a paper in AJP from years ago called "What is spin?" by Ohanian, but I didn't put in the effort to follow it. I ...


2

Spin is a wave property. It exists in classical relativistic wave theories as well. A circularly polarized wave carries an angular momentum that's related to the spin of the field. A gravitational wave (spin-2) can carry twice the angular momentum of a classical electromagnetic wave (spin-1). Being "pointlike" is a particle property. You can think of the ...


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Spin is not about stuff spinning. (Confusing, I know, but physicists have never been great at naming things. Exhibit A: Quarks.) Spin is a purely quantum mechanical phenomenon, it cannot be understood with classical physics alone, and every analogy will break down. It has also, intrinsically, nothing to do with any kind of internal structure. ...


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"The electron has no known internal structure", but since it does have a spin, does that mean that we know the electron has an internal structure but we just don't know what it is? An electron has no known internal structure simply means that nobody knows if the electron has an internal structure. So far they know none and therefore they suppose it ...


3

Actually the framework where one can describe electromagnetic fields is a classical framework. When one is talking of photons phonons etc one is in the quantum mechanical regime where the concept field, is different. A classical field in physics: A field can be classified as a scalar field, a vector field, a spinor field or a tensor field according ...


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It depends on whether you're considering only hydrogen, or whether you're considering multi-electron atoms. In hydrogen the states with different $\ell$ are (very nearly) degenerate in energy, so a transition like $2s^1 \rightarrow 2p^1$ is in principle allowed but in practice unobservable. However in Helium the $2s$ and $2p$ levels are not degenerate and ...


1

Distance. Electric fields weaken as the distance between them increases, so the force applied on the other leaf shrinks as the leaves separate. Eventually, the force from the electric field balances the force of gravity trying to pull the leaves back to their normal rest position, so the leaves cease to accelerate upwards.


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The new constant U 2.30x10 -28 J-m proves that the only diference between hydrogen atom and neutronc lays only in the distance r between the elctron and proton . Dividing constant U by the energy of hydrogen atom gives exactly the radius of hydrogen atom in any of its states , while dividing the same constant U by the nuclear energy one Mev = ...


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If you take an isolated hydrogen atom then the electron sits in well defined atomic orbitals that are eigenfunctions of the Schrodinger equation. This is a stable system that doesn't change with time. If you now introduce an oscillating electromagnetic field (i.e. light) then this changes the potential term in the Schrodinger equation and the hydrogen ...


1

Transparent media are transparent because the incoming photon does not match any of the available energy levels to transfer its energy to the atom , or molecule, or crystal. A classical analogy is thinking of energy levels as various size sieve holes which allow only certain size of particles to go through. Not any matter of knowing or adjusting, but ...


0

Energy of the electron changes with its interaction with photons, if it reaches more it gets excited, else remains in its position even though interacted with the photon, also it comes back during decay to release the photon. Hence photons don't know the energy level they produce, but it happens by interaction.


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how does adding energy to the EM field cause the electron to to change orbitals or oscillate in a different pattern. Here one is using two frameworks, the classical and the quantum mechanical. The classical electromagnetic field is composed by an enormous number of photons each with energy=h*nu, nu the frequency of the electromagnetic field. The ...


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The photon couples to all particles with electric charge or magnetic moment. This includes all of the quarks, the charged leptons $e,\mu,\tau$, and their antiparticles. It also includes particles composed of quarks and charged leptons: the proton and neutron (though the neutron only magnetically), the charged mesons, etc. Many electrically neutral mesons, ...


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Wikipedia takes a swing at explaining this phenomenon. There it says that the velocity saturation is caused by scattering from optical phonons, with $$ \frac{1}{2}m*v_s^2 \approx \hbar \omega_o $$ where $m*$ is the effective mass of the carrier (depends on conduction band), $v_s$ is the drift velocity in saturation and $\omega_o$ is the angular frequency of ...


1

By observations we know that only whole electrons are distributed in specific hydrogen and helium areas. These areas have certain probabilities stay. For description of these areas there are a lot of rules (Hund, ...) and principles (Pauli, ...) and quantum formulas. That allows to predict more precise statements. But that can not hide the fact that the ...


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(add my comment as an answer) It all depends on the time-energy uncertainty relation $$ (\Delta t) (\Delta E) \ge ℏ/2 $$ (see for example here and here). Classicaly a particle can access only system (energy) states which are compatible with its (current) energy. Actually this is still true in quantum mechanics, the difference is the time-energy ...


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Electron's quantum jump is the same thing as an atomic electron transition. https://en.wikipedia.org/wiki/Atomic_electron_transition At the beginning, the electron has one energy and sits at some level which may be represented by some "typical distance" from the nucleus. At the end, it has another value of the energy, so a different "typical distance ...


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Luboš Motl's answer gives you all you need, so I'll just add some basics that might also help you (in future readings of similar texts): In order to interpret the statement you've copied: ...finding anywhere in space... First remember that the electron is represented by a wavefunction $\Psi(x,t)$ (simplest 1D case for now) that describes the ...


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Well, the wave function of the electron in the ground state of a hydrogen atom (and very similarly in other atoms) behaves like $$ R(r) \sim \exp(-r / a) $$ where $a$ is the Bohr radius, effectively the radius of the atom. The exponential is in principle nonzero for an arbitrarily large $r$, so the electron may be found arbitrarily far from the nucleus at a ...


1

John Rennie gave a nice answer based on the De Broglie hypothesis, however he didn't try the hard part: "Why do only a certain number of electrons occupy each shell?" so let me try! In quantum mechanics particles are described by wave functions. All the observable properties of a particle (like its position) are related to the square of the wave function, ...


7

First of all, strictly speaking, electron shells (as well as atomic orbitals) do not exist in atoms with more than one electron. Such physical model of an atom is simplified (and often oversimplified), it arises from a mathematical approximation, which physically corresponds to the situation when electrons do not instantaneously interact with each other, but ...


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A big part of it can be explained by combining the constraints of quantum mechanics with the geometry of angular momentum. For the special case of the hydrogen atom, it turns out that when you solve the equations of motion for an electron near a proton, you can't give the electron any old energy. There's a set of energies that are allowed; all others are ...


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Any answer based on analogies rather than mathematics is going to be misleading, so please bear this in mind when you read this. Most of us will have discovered that if you tie one end of a rope to a wall and wave the other you can get standing waves on it like this: Depending on how fast you wave the end of the rope you can get half a wave (A), one wave ...


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I can sniff a lot of familiarity with the ''HOW'' answers from what I interpret about you from your post, so I'll only focus on the objective point - ''WHY''. It turns out that it is possible to meaningfully describe nature by postulating that any object would tend to be in the minimum energy state possible under a given set of physical conditions. So, ...


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Your equation is considering the effective mass of electrons. The holes are lack of electrons. To talk about them, we effectively invert the energy axis, i.e. if we compute electron and hole energies with respect to valence band ceiling $E_V=0$, we have: $$E_e=-E_h.$$ Then it's straightforward to see that $m^*_e=-m^*_h$ in the same valley.


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From the askers perspective, the explanatory powers of most of these answers seem pretty bad. I prefer Emilio Pisanty's answer here: Why isn't Hydrogen's electron pulled into the nucleus? because it explains exactly how the uncertanity principle dictates the facts of this atomic reality. The summarized problem is that, if the charged and attracted ...


1

According to General Relativity, energy is equivalent to inertial mass, and all inertial mass generates gravity. Since electrons have measureable inertial mass, they should have a small influence 0.1% contribution to the gravitational force in neutral matter. That being said however, the question cannot be answered experimentally because the electrical ...



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