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A lot of text books mention that one of the reasons that classical mechanics failed to explain atomic and subatomic processes is that electrons which accelerate should release energy in the form of electromagnetic radiation, which would lower the atoms overall energy level, but this does not happen. One place where I discovered this, for example, is in the description for the Bohr model.

What I don't understand is why everyone takes for granted the fact that the electron is accelerating. I thought the electron orbits the nucleus at a, more or less, constant velocity. Are people referring to specific situations when the atom is excited? Furthermore, I was under the impression that electrons already travel at the fastest allowable speed, the speed of light.

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acceleration refers to a changing velocity, which is not always the same as a changing speed. an object moving at a constant speed around a circle is also constantly changing its direction, thus acceleration. Also electrons most assuredly do not travel at the speed of light. –  wsc Apr 28 '13 at 4:03
    
@wsc I never though a change in direction could cause radiation. Thanks –  puk Apr 28 '13 at 4:04
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Synchrotron radiation –  CodesInChaos Apr 28 '13 at 12:52
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4 Answers

up vote 3 down vote accepted

On a uniform circular orbit, even if the speed does not change in norm, it does change in direction so that the speed vector change over time and $\frac{d\vec{v}}{dt}\neq\vec{0}$. In fact, in polar coordinates, you have $$\vec{a} = \frac{d\vec{v}}{dt} = -\frac{v^2}{R}\,\vec{e_r}$$

Imagine a car taking a turn at constant speed: if the turn is left, you feel like you're pulled on the right because the car itself is exerting a force on your lower parts to make you turn left rather than continue in straight line. Thus you effectively experience an acceleration with respect to the ground even if your speed stay constant in norm.

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In uniform circular motion: $a=\frac{v^2}{r}$

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so the earth is accelerating even though it has been going the same speed for 5 billion years? –  puk Apr 28 '13 at 4:00
    
yes, $a=\frac{F}{M}$ the gravitational force of the sun –  richard Apr 28 '13 at 4:05
    
Earth isn't a charge . I mean net charge is kind of balanced and also if it isn't EM wave energy is comaparatively extremely less . And no force is doing work on earth by sun , so its KE isn't changing . However , possibly other planets are and earth is slowing down ? –  nonagon Apr 28 '13 at 4:49
    
wow, good point, the net charge doesn't matter, each positive or negative charge of earth must radiate!!! –  richard Apr 28 '13 at 4:52
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Look at it this way. An electron is a charged particle. A moving, electrically charged particle creates a magnetic field, and the particle itself already has an electric field. If the particle is accelerating, then you're going to have a ripple effect from the electric and magnetic field, or an electromagnetic ripple, ie an electromagnetic wave. So an accelerating electron does indeed release electromagnetic waves.

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The electrons should accelerate in the electric current also, since there is an electric force created by the potential difference, probably this is the cause of the magnetic field of the electric current.

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The Bohr model can be true, since the electrons are moving on equipotential curves in the atom. –  George Rajna Oct 18 '13 at 9:06
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protected by Qmechanic Oct 17 '13 at 16:52

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