# Tag Info

15

The electron is stable because there is no allowed process in the quantum field theory it can undergo that would lead to its decay. Its mass is the smallest among the electron/muon/tauon, so it doesn't have enough energy on its own to turn into one of those, and all other processes you could imagine are forbidden by conservation laws - either those of energy ...

5

The electrons from the battery are not in the ends of the wires, no. The wires do contain electrons, however. Conductors have free electrons which can "float" around in the metal. There is an electric field between the two terminals of the battery. The electrons experience a force due to this field. When the wire is not connected, the electrons don't go ...

5

Electrons move because they are in a region of space with a non-zero electric field. They don't accelerate to high speed in a wire because they keep bumping into things; a kind of friction which dissipates energy much like the friction you are used to that explains why resistors get hot. In effect their speed depends on the strength of the local electric ...

4

If an electron is an excitation of the electron field, what causes the excitation to be stable? I think the best way to say it is to take a tip from topological quantum field theory: "Although TQFTs were invented by physicists, they are also of mathematical interest, being related to, among other things, knot theory and the theory of four-manifolds in ...

4

The options 1,2 are actually physically identical because the electrons are identical particles. Once we have two electrons, we can't say which of them is "Paul" and which of them is "Peter". When the addition is slow etc., the option 1=2 violates the conservation law for the angular momentum. So it is indeed 3 that has to happen: the ion will refuse to ...

3

Electron degeneracy does not lead to an infinitely hard equation of state. The Pauli exclusion principle does not say that two fermions cannot occupy the same space; it says they cannot occupy the same quantum state. What this means is that as you squish the electrons together they have to occupy higher and higher momentum states. It is this non-zero ...

3

The claim "Entangled electrons share the same quantum state" is not correct. In an entangled state there is no well-defined notion of the states of the individual components, this is the very definition of an entangled state: A composite state $\chi\in\mathcal{H}_1\otimes\mathcal{H}_2$ is called entangled, if it cannot be written as $\chi=\psi\otimes\phi$ ...

3

Take the commutator acting on a function $f$. Then \begin{split} [ P_i , P_j ] f &= [ - i \partial_i - q A_i , - i \partial_j - q A_j ]f \\ &= ( i \partial_i + q A_i )( i \partial_j + q A_j ) f -( i \partial_j + q A_j ) ( i \partial_i + q A_i ) f \\ &= - \partial_i \partial_j + i q A_i \partial_j \, f + i q \partial_i ( ...

2

If you would measure the electron at one of the slits, then the interference patterns would no longer be formed. That is because the pattern is produced by interference of an electron amplitudes diffraction from slits 1 and 2. If you know that electron is at slit 1, it is of course no longer at slit 2, and therefore you wouldn't get the interference pattern. ...

2

The quantity that determines what a particle beam may be used for is called gamma ($\gamma$). It is defined as $$\gamma = \frac{1}{\sqrt{1-\left(\frac{v}{c}\right)^2}}.$$ As $v$ gets closer to $c$, $\gamma$ gets larger without bound and equals infinity when $v = c$. Since particles in a synchrotron are moving at very close to the speed of light ...

2

I'm researching synchrotrons for a class project, but I can't seem to find a decent answer to one of my questions. It appears that most synchrotrons use electrons as opposed to some other charged particle, while the Large Hadron Collider uses protons instead.. The first thing that you should know is that there are two completely different uses for ...

2

Ionizing radiation is radiation that is strong enough so that, when it hits an atom or molecule, will knock off electrons. This happens even if the target object doesn't have freely mobile electrons, which leaves free radicals and broken bonds, both of which are harmful to complex biological processes. There's no selection based on electron binding energy; ...

2

As long as you provide a power source to a circuit, whether it is closed or not, electrons will definitely begin to move to a small amount. There are two specific cases which I think would best demonstrate this point. Case 1: A circuit with a capacitor. A simple capacitor contains two electrically conducting plates separated by an insulator, which could ...

2

BEWARE THE SANDWICHES!!! :) In the spirit of math-avoidance sandwich-juggling, here's a better analogy, a visible one. The movable charges within conductive circuits are like silver bead-chains, like those little chains which attach the pens to desks in old-school banks. (Growing up I always played with these when mom was in the teller line. Do those ...

2

Potential energy is wrong. Even in Newtonian Mechanics it only works if the force is 1) purely a function of position and also 2) is conservative. Magnetic forces depend on velocity so they fail. And electric forces are not conservative if you aren't in statics. What you really have is kinetic energy and rest energy for the charged particle, some energy ...

1

One has to keep in mind 1) that it is the complex conjugate square of the eigenfunction that gives the probability of finding the electron with energy E at a specific radius. 2) There are no fixed orbits in the quantum mechanical solution, only a locus of probability called orbital 3)orbitals overlap in space, it is the energy that is keeping the electron ...

1

Don't forget about the rest energy, $E=mc^2$. Since a particle's intrinsic spin cannot be changed, it doesn't make sense to distinguish "intrinsic spin energy" $\frac12 I\omega^2$ (as you would compute for, say, a spinning flywheel) and the rest energy. A particle which is moving in an electric field will see a motional magnetic field. Charged particles ...

1

The question is ill-posed; the electrons "know" nothing, and voltage is not a property of the electron (other than e.g. charge, which is a property). In fact, voltage is a pretty abstract concept; it is energy divided by charge. And that means explaining an abstract term by another abstract term. Let's be more fundamental: nature shows that charges exert ...

1

I was told that electrons do not begin flowing unless the circuit is closed. This is true. Broadly speaking. The electrons from the battery are not in the ends of wire when it is open, The electrons involved in electric current are present throughout the metal wire. They are not supplied by the battery into an "empty" wire. The metal in the wire ...

1

This isn't really how it works. A photon doesn't interact with a single electron, it interacts with the entire molecule. Suppose you take the example of ozone photolysis to $O_2$ and an oxygen atom. We can do a calculation for ozone and come up with a series of molecular orbitals, then put two electrons in each orbital. So far so good. But if you remove an ...

1

Use the equation E=hc/λ. In case you don't know, h is Planck's constant and λ is the wavelength in nano meters. convert electron volts to joules (E) using 1 electron volt = 1.60217662 × 10^-19 joules. Planck's constant is 6.62607004 × 10^-34 m2 kg / s

1

It depends on what you want how you choose the polarization of the light. The polarization of your light determines the recoil of your electron and your ion. In photoelectron vmi you would like to see the angular distribution of how the electron detaches from the molecule, so you should select the polarization of your light such that the velocity vector of ...

1

The principal advantage of using electrons is that the electron is a fundamental particle so electron-electron (or electron-positron) collisions are are well defined process that is relatively eay to describe mathematically, and very accurate measurements can be made. By contrast the proton is a composite particle. We normally describe the proton as being ...

1

People have certainly measured the electron's charge and mass more than once in the last 100 years. See for example this table from the Particle Data Group, where you can find the constants you want to around 8 significant digits, much more than what was possible for Millikan. For comparison, Wikipedia claims that Millikan and Fletcher measured $e$ to be ...

1

One has to distinguish between, on one hand, an orbit and an orbital motion, which are classical notions; and on the other hand, an orbital, which is a quantum mechanical notion, cf. above comment by dmckee. If the question is really Why quantum mechanics?, then have a look at e.g. this Phys.SE post and links therein. Here we will assume that OP accepts ...

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