Does r=mv/Bq hold true considering Maxwell's E.M wave theory?

[randomgamernerd]

Homework Statement

: [/B]This is a general conceptual doubt, not a numerical based doubt. We were taught that when an electron(or any charged particle) moving with uniform velocity enters a magnetic field(perpendicular to its direction of motion), then a force acts on the electron which makes it move along a circular track.
The radius is given by r=mv/Bq...(1)
Now, suddenly while studying limitations of Bohr’s theory, it stroke me that if his model was rejected based on the fact that an accelerated charged particle continuously emits energy in form of E.M waves, and so the radius of the atom should decrease and the atom will collapse which does not happen, then my question is does equation (1) hold true because here we also have an electron having acceleration...
[Note: I’m aware the cause of the centripetal acceleration is different in both cases, but I don't feel that should make a difference]

Homework Equations

: r=mv/Bq[/B]

The Attempt at a Solution

: [/B]As i mentioned above...
Please help.
Well, our currciulum does not cover modern physics in much depth, so may be I’m missing some point here...
Please help
And pardon my horrible english.

 

[BvU]

Hi,

Good thinking...

(1) holds true, but yes, the electron loses energy in the form of synchrotron radiation

 

[randomgamernerd]

Hi,

Good thinking...

(1) holds true, but yes, the electron loses energy in the form of synchrotron radiation

oh...never heard of that..so does it mean the radius remains constant but the electron still loses energy?

 

[vela]

The electron loses energy and slows down, so…

 

[randomgamernerd]

The electron loses energy and slows down, so…

so it does form a spiral, that means everywhere in the universe they will form a spiral unless its the case of an atom, right?where we have this fixed orbitals and stuffs, right?

 

[BvU]

On an atomic scale you are moving into the realm of quantum mechanics, where you do not have 'fixed orbits' in the sense of 'resembling planetary orbits'.

Instead, you have a wave equation to solve and the outcome are wave functions from which features like a most probable distance to the nucleus etc. can be derived.

For large-scale phenomena google betatron, cyclotron, synchrotron, etc.

 

[randomgamernerd]

okay, thanks