What causes electrons to emit and fall in atoms?

[arron]

I have a question about the electrons in atoms. This question is from quantum mechanics, but it is really a situation of classical electrodynamics. When the electron goes around the nucleus, it is said that the electron will emit electromagnetic wave and then fall to the nucleus. But in fact all the atoms we meet in the world are stable. So it is necessary to develop the new theory---quantum mechanics. My question is that why should it emit something and then fall. How can we describe it? Are there any formulas or equations for it?

Another similar question, if the electron moves in an magnetic field, you know, it goes around and follows a cycle and the velocity changes all the time just like it goes around the nucleus, will it emit something and then fall? If it does, where fall?

 

[Danger]

Welcome to PF, Arron.
I'm not by any means educated enough to give you proper explanations, but perhaps I can give you a bit of a start.
What you're thinking of in a Classical context would apply to something like orbital mechanics for planetary systems. The Quantum world just doesn't work that way. To start with, you can't really think of an electron as being a solid physical body in orbit around the nucleus. It's more of a cloud of probability functions that give the odds of an electron being in any particular place at any particular moment. For that reason, electrons are usually referred to as inhabiting 'orbitals' rather than 'orbits'.
Secondly, there are discreet energy levels allowable for electron orbitals, which doesn't apply to a Classical scenario. A satellite in orbit around Earth, for instance, can alter its altitude by any arbitrary distance. In an atom, there are distinct levels with no 'in-between' areas allowed. An electron must gain a unit of energy, such as being impacted by a photon, in order to climb to a higher level, and must lose energy, as in emitting a photon, to drop a level. That basic principle is what allows lasers to work.
I'm afraid that you'll have to wait for others with more knowledge to explain further.

 

[arron]

thank you Danger

Danger you are right. thank you . but that hasn't resolve my puzzle,
maybe i not good at expression, but it's not an orbit mechanics question really . even it's not a real question that exists, i think.

before the the birth of quantum mechanics, we use electrodynamics to resolve any movement question in electromagnetic field. but when Rutherford raised his planet model. there comes a question: according to classical electrodynamics, if the electron goes around the nucleus, it will changes its velocity all the time and emit electromagnetic wave,and lose energy and then fall...

now the most thing i want to know why it will fall, i know there is a equation or some formulas, but i can not find them in my books. and i also have a question : if it goes in a magnetic field ,we know that this situation is similar to going in cetripetal electric field, will this system emit electromagnetic waves and then fall into ruins?

 

[marlon]

before the the birth of quantum mechanics, we use electrodynamics to resolve any movement question in electromagnetic field. but when Rutherford raised his planet model. there comes a question: according to classical electrodynamics, if the electron goes around the nucleus, it will changes its velocity all the time and emit electromagnetic wave,and lose energy and then fall...

Aside the misconceptions you have on the role of electrodynamics versus QM (ie Electrodynamics still governs E and B fields and Bohr derived the "planet model") i can tell you that we covered your questions many times before. Here is the answer : https://www.physicsforums.com/showpost.php?p=862093&postcount=2

marlon

 

[Nesk]

I understand your question as "Why does the classical picture predict unstable atoms?". A body in non-linear movement, such as a classical electron orbiting a nucleus, is subject to an acceleration due to the centipetal force. For example like the gravitational field of a star where planets orbit, or the electrical field of a nucleaus where electrons orbited in the classical picture. Electrons carry a charge, and accelerated charges emit energy. I'm not entirely sure about this part, but I assume that this is because their magnetic field changes over time, and the energy stored in the field must come from somewhere - the orbital energy of the electron in this case.

When the electron looses energy, it's orbit "lowers", and this continues until it bangs into the nucleus and the atom is destroyed. This should all happen pretty fast in the classical model. We're thus saved by quantum mechanics.

 

[arron]

thank you Nesk, and then the second question? when it orbits in the magnetic field, will it fall?

 

[marlon]

Electrons carry a charge, and accelerated charges emit energy. I'm not entirely sure about this part,

Indeed, conservation of total energy explains why there is radiation in this case.

marlon

 

[arron]

thank you marlon, but ...what you said is what i am learning now. i am afraid i can not accept the ultimite truth with something uncetain in my mind. simply to say, if one body orbits another body, and they all carry charges(but they carry the opposite), will this system emits and ruins?

 

[ZapperZ]

thank you marlon, but ...what you said is what i am learning now. i am afraid i can not accept the ultimite truth with something uncetain in my mind. simply to say, if one body orbits another body, and they all carry charges(but they carry the opposite), will this system emits and ruins?

Then satisfy your own curiosity by going to a synchrotron facility. There, electrons are going around and around in circles. See why they could get something called synchrotron radiation when these electrons do that, and why they have to keep pushing these charges continuously during each cycle to preserve the motion.

Zz.

 

[arron]

marlon,when the electron orbits in the magnetic field, it also accelerates i think.is there any difference between these two movements? and the question will it fall?

 

[arron]

haha

Then satisfy your own curiosity by going to a synchrotron facility. There, electrons are going around and around in circles. See why they could get something called synchrotron radiation when these electrons do that, and why they have to keep pushing these charges continuously during each cycle to preserve the motion.

Zz.

oh i know ,thank you Zapperz.though there's still something unclear, can you tell me how can I make it more clear?
...
and the synchrotron facility you referred ,how does it work?
orbits in uniform and stable B field and then be kept by E field? so the facility is difficult to design because the electron is always trying to fall?

 

[ZapperZ]

http://www.lightsources.org/cms/

Zz.

 

[marlon]

marlon,when the electron orbits in the magnetic field, it also accelerates i think.is there any difference between these two movements?

An accelerating charge will emit EM radiation in order to conserve total energy !

and the question will it fall?

The charge will indeed spiral towards the center. Again, energyconservation explains this notion: loss of kinetic energy due to the emitted EM radiation.

This energy loss can also be due to collisions with surrounding particles for example. More specifically, When the particle enters the magnetic field in a plane perpendicular to that field, the Lorentz force will make sure that it moves in a circular orbit. Due to collisions with surrounding particles (like in an ionization chamber or a bubble chamber) the radius will decrease. The helix (three dimensions) only occurs when the initial velocity of the particle is not perpendicular to the B-field. Then the motion can be composed out of a circular motion in a plane perpendicular to the B-field lines and a constant velocity motion along a straight line. The superposition of these two motions results in the helix


marlon