Why?

[CuriousMan]

We all know that electron is negative and the nucl is positive and that they attract to each other. My question is why the electron ORBITS the nucl? What are the fources influencing that behavior of the electron?

Thank you

[reyam200]

well. isn't the nuclius spinning? that would make the electron orbit, the earth does the same around the sun.

im just guessing.

[CPL.Luke]

The classical reason for this is beacause the electron will be drawn in towards the proton, the odds of it hitting the proton are low so it ends up just circling around it in an orbit, now according to classical mechanics the electron will continue falling into the nucleus emitting electromagnetic radiation all the way down, Idk how they tried to rationalize this with the experimental observation that the electron does not rest on the nucleus before black body radiation and QM however

 

when plank created the theory of black body radiation he found that the energy of a photon is equal to hf, so the electron could not just emit a continuous stream of radiation as it dropped down through the nucleus, so there are certain destinct energy levels that the electron can occupy. eventually (forgot by whom) it was found that there is a ground energy which the electron can have, this is what prevents it from falling all the way into the nucleus.

[Locrian]

We all know that electron is negative and the nucl is positive and that they attract to each other. My question is why the electron ORBITS the nucl? What are the fources influencing that behavior of the electron?

Thank you

 

This will be almost entirely answered in your first quantum mechanics class. Get excited!

[swansont]

well. isn't the nuclius spinning? that would make the electron orbit' date=' the earth does the same around the sun.

im just guessing.[/quote']

 

No, the nucleus isn't spinning, and that's not what would make the electron orbit it. It would be the electron having orbital angular momentum, but as we find in QM, that's not it, either - you can have electrons with L=0.

[CPL.Luke]

swansont, last time I read anything on QM (it was a real text book) it taled extensively about the uncertainty relationship. How could you ssay an electron has 0 angular momentum without saying that it could be anywhere in the universe?

[Mart]

Originally Posted by CPL.Luke

according to classical mechanics the electron will continue falling into the nucleus emitting electromagnetic radiation all the way down

Couldn't the nucleus reflect back the radiation and keep the electron in it's orbit?

[CPL.Luke]

if it did do that it would still reflect less radiation back to the electron than the electron emited.

[Locrian]

swansont, last time I read anything on QM (it was a real text book) it taled extensively about the uncertainty relationship. How could you ssay an electron has 0 angular momentum without saying that it could be anywhere in the universe?

 

First, look at the total angular momentum operator in spherical coordinates. Now, see if it commutes with the spherical coordinate r. You'll see that they commute just fine.

[DQW]

How could you ssay an electron has 0 angular momentum without saying that it could be anywhere in the universe?

The canonical conjugate variable for angular momentum is angular position, not position.

[JonM]

so whats the answer?

[Severian]

Even if the atom were perfectly classical, the electron would orbit the nucleus. This would just be analagous to the way the Earth orbits the Sun. The Earth is attracted to the Sun by gravity, but the Earth has enough angular momentum to counterbalance the attraction and orbit (it is falling toward the Sun but is going so fast that it keeps missing). classically the elctron is attracted to the nucleus by electromagnetism in almost exactly the same way.

 

In QM it is slightly different since there is a quantization of energy. Particle-wave duality tells us that the electron is also a wave, so it has a associated wavelength. Only certain wavelengths of the electron can fit around the nucleus, so it cannot just fall in.

[swansont]

Even if the atom were perfectly classical' date=' the electron would orbit the nucleus. This would just be analagous to the way the Earth orbits the Sun. The Earth is attracted to the Sun by gravity, but the Earth has enough angular momentum to counterbalance the attraction and orbit (it is falling toward the Sun but is going so fast that it keeps missing). classically the elctron is attracted to the nucleus by electromagnetism in almost exactly the same way.

 

In QM it is slightly different since there is a quantization of energy. Particle-wave duality tells us that the electron is also a wave, so it has a associated wavelength. Only certain wavelengths of the electron can fit around the nucleus, so it cannot just fall in.[/quote']

 

But classically you have Bremsstrahlung, which would make the orbit collapse, and is one of the reasons quantum theory was necessary.

[Manifold]

I think you could also show it this way:

 

1. An electron is attracted towards the nucleus by the force:

[math]\vec{F}=\frac{q_e{q_p}}{4\pi{\epsilon_0}r^3}\vec{r}[/math] where [math]\vec{F}\cdot\vec{r}=1[/math];

 

2. On the other side [math]\frac{q_e{q_p}}{4\pi{\epsilon_0}r^3}\vec{r}=m\vec{a}[/math], since the electric field is non-homogeneous, and [math]\frac{q_e{q_p}}{4\pi{\epsilon_0}mr}=\vec{a}\vec{r}\neq{0}[/math], the electron gets in the electric field of the nucleus an acceleration with the normal component directed towards the nucleus, which is in the extreme case has a zero angle with the radius-vector (radial acceleration);

 

3. It is now clear that the trajectory of the electron is anyway curvilinear. Since it moves in the non-homogeneous electric field with increasing force gradient directed towards the nucleus, it gets angular acceleration, moment of inertia and hence orbital moment of force [math]L=rmv[/math].

 

This is that classical model, which allows the electron to fall on the nucleus.

[Jacques]

I understand the QM explaination but it bring me to an other question:

Why doesn't an electron orbit a positron, instead of anilating each other ?

[Severian]

But classically you have Bremsstrahlung, which would make the orbit collapse, and is one of the reasons quantum theory was necessary.

 

Yes, that is why I pointed out that the quantum case was a bit different - you don't get bremstrahlung in the quantum situation because there is no lower energy state to occupy.

 

Interestingly, a gravitational mass must presumably emit real gravitons too, so even if there were no frictional/dissipative forces all planetary orbits will eventually decay...

[CanadaAotS]

I understand the QM explaination but it bring me to an other question:

Why doesn't an electron orbit a positron' date=' instead of anilating each other ?[/quote']

 

maybe it's not positively charged enough?

*shrugs*

[Xyph]

An electron and positron can orbit each other for a short while, but the system isn't at all stable. I'm not exactly sure why, though.

[swansont]

An electron and positron can orbit each other for a short while, but the system isn't at all stable. I'm not exactly sure why, though.

 

 

From an energy standpoint, the system is very much like Hydrogen, but with a different reduced mass. But the ground state has the particles annihilating.

[Jacques]

the ground state has the particles annihilating

Can you explain a little more? The ground state in an ordinary atom keep the electron far from the nucleus. What difference is there with the electron-positron system ?

[J.C.MacSwell]

Can you explain a little more? The ground state in an ordinary atom keep the electron far from the nucleus. What difference is there with the electron-positron system ?

 

Isn't the electron-positron system the simpler case, and the "regular" ordinary atom the mystery?

[Jacques]

Simpler in what sense ?

electron-positron system must be very hard to create: create a positron, bring it to the velocity and good distance to an electron...

Maybe simpler mathematicaly

[swansont]

Can you explain a little more? The ground state in an ordinary atom keep the electron far from the nucleus. What difference is there with the electron-positron system ?

 

The ground state has the orbitals centered around the center-of-mass. In hydrogen, that's within the proton, but in positronium, the electron and positron share the same orbital - classically, they would be orbiting like a binary star (i.e nothing physically there at the COM), since they have equal mass, but the QM description doesn't have classical orbits, as we all know. Their wave functions coincide/overlap, and "poof*," two photons come out.

 

*Which is why pair production goes "foop"