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The angular momentum and charge of an electron are both large enough that a black hole would not form. If you believe classical general relativity all the way down to the scale of an electron (and you really shouldn't), then the electron will form a naked singularity. More exactly, for the case of a spinning body, the horizon is at the zero of $$r^{2} - ...


6

Why don't electrons collapse into black holes? Because the electron isn't a point-particle. Its field is what it is. It isn't some speck that has a field, it is that field. There's energy in that field, that energy has a mass-equivalence, and it doesn't have a zero volume. Also note that we can diffract electrons. And that the Einstein-de Haas effect ...


6

It's a good question, and one that puzzled me for a while as well. However the answer is very simple. For a massive particle like an electron the total energy is given by: $$ E^2 = p^2c^2 + m^2 c^4 $$ where $p$ is the momentum and $m$ is the rest mass of the electron. Electrons can obviously have any momentum you want, so the total energy can be any value ...


5

The electromagnetic wave is a classical theory while matter waves are quantum mechanical. The wave aspect is a mathematical abstraction which allows us to predict future quantum states of the electron with a known probability.


5

In quantum mechanics, things are not "particles" or "waves" - they may behave like both, or like neither. But a quantum object "is" neither of those - it is a quantum state, usually described as a vector in a Hilbert space. The Bohr model of the electron orbiting the atom is false (for one inconsistency, that of moving charges classically radiating, see ...


4

It's not a stupid question. In fact, Quantum Field Theory is the field of physics that seeks to answer exactly this question. In QFT, in addition to the electromagnetic field, there is a single electron field that extends throughout the universe. Stable ripples in the electron field constitute individual electrons. Every fundamental particle has a ...


2

A degenerate gas is one where more than one electron (in fact, two) occupies each possible low-energy state up to the Fermi energy. I suppose the term "degenerate" comes from the multiple occupancy of each energy level.


2

Electron is a particle with mass and a certain probability of being found at a given distance around the nucleus of an atom at a certain time. It caries a negative charge which makes chemical reactions possible since chemical reactions are driven by the electrostatic forces between electrons and positively charged protons which reside in the nucleus of the ...


2

From the famous Double-slit experiment, it is clear that electrons do behave as wave as well as particle. When it is detected by geiger counter, "click" sound appears & no matter how greatly the voltage is decreased along the cathode tube, "click" & never "half click" appears. So, electrons always arrive at lumps like bullets. However, unlike bullets ...


2

Short answer: Yes Slightly longer answer: If you scatter the wavefunction of a propagating electron from a potential (surface of a material for example), it generally splits into two parts - a transmitted part and a reflected part. As the names indicate, the reflected part represents a 'reflected' electron, the transmitted part a transmitted one. However, ...


1

The atom has some charge distribution $\rho(r)$. We don't don't know what form the function $\rho(r)$ has, but we do know it depends only on $r$ because an atom is spherically symmetric. When you have a spherical charge distribution the potential at a distance $r$ is simply due to the total charge inside the distance $r$: $$ V(r) = ...


1

Electrons accelerating due to EM fields in the presence of gravity field radiate - examples are cyclotron radiation, antenna emissions. In the absence of EM field, whether the electrons radiate in the presence of gravitational field is theoretically problematic question, because Earth is not an inertial system, so Maxwell's equations should not apply ...


1

Is it possible to decrease the mass of the object? Perhaps surprisingly the answer is yes. All you need to do is it drop it. Then some of the object's mass-energy, which we call potential energy, is converted into kinetic energy, which ends up getting dissipated. You're then left with a mass deficit. The mass of the object is reduced. It is known ...


1

Something analogous to the Fermi-Dirac distribution function will probably work pretty well for the electrons in the Sun; see for example this PDF. You may need to put in some "fudge factors" for their interaction energy with the rest of the proton soup, but you're in some luck, because the interaction energy in the Sun is actually mostly lower than the ...


1

Hmmm... I'll take a crack at it. An electron is a negatively charged subatomic particle that orbits the nucleus of an atom, which contains a positively charged subatomic particle called a proton and a neutral subatomic particle called a neutron.


1

Start by considering a long pipe with water flowing through it. We'll assume the rate of flow is slow, so the current of water is small. This means water entering the pipe at one end will take a long time to flow all the way along the pipe to the other end. However suppose we generate a pressure wave at one end of the pipe. A pressure wave in water is just ...


1

Lets run a few numbers. Go with electrons. 200keV electrons (like from a standard transmission electron microscope). These have a velocity of just about 2E8 m/sec (yes, relativistic effects need to be taken into account). One nano-ampere is a little more than 6E9 electrons per second. Dividing through, that gives you, on average, 30 electrons per meter of ...


1

The electrons do not even enter the wire, because the redox reaction between the substances in each of the nodes never occurs. Once the wire is connected to each of the nodes, electricity will flow through as electrons will be more attracted to the node with the greater reduction potential.


1

However it did pass within Δx of the electron. The Δx is not the difference in space with the electron, as the electron is bound to a nucleus with a potential simulated by "an infinite potential well" . The Δx is related to the whole system, from the center of its mass as a possible location to start with. So the problem is : "photon + atom" as a ...


1

I now come to my point, why one restricts a particle's motion to some discrete set of distances? Is it to provide a theory on the particle's stability? An attempt at an answer to your first question anyway. The electrons surrounding an atom need to obey energy level (and other) rules. As you mention distance, if you imagine that the further away the ...


1

Electron as a standing wave Yes, the electron is a standing wave. See atomic orbitals on Wikipedia: "The electrons do not orbit the nucleus in the sense of a planet orbiting the sun, but instead exist as standing waves". I couldn't understand how come Bohr who interpreted electron as a particle, formulated an equation for electron's angular ...


1

Let's look at where the electromagnetic interaction comes from in hydrogen. At first quantization you have a multiparticle system so the wavefunction is defined as $\psi=\psi(x_1,y_1,z_1,x_2,y_2,z_2,t)$ and the point is to write the Hamiltonian. And the Hamiltonian comes from the Lagrangian. For a single particle of charge $q$ in an external ...


1

this is a description of an interaction between the electron and photons, which would collapse the wavefunction (right?). No this isn't right. As long as the system stays isolated, the interaction simply means that there are cross terms in the relevant Hamiltonian and that you have a two-particle quantum system, whose state space is the tensor product ...


1

Electron and holes are Fermions (particles with spin 1/2). This means that no two particles can share the same microstate. The Fermi-Dirac distribution describes how Fermions fill the available states consistent with this property. Bosons on the other hand (particles with integer spin) can occupy the same state. The Bose-Einstein distribution describes how ...



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