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They mention that Rutherford's model of an atom was wrong as in a circular orbit the electron would accelerate and hence radiate energy along with electric and magnetic fields. But why does the electron accelerate and how would it spend energy?

The displacement of the electron is perpendicular to the force so wouldn't that mean that the work done (or) energy used is 0?

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Electron according to classical physics would have centripetal acceleration. All accelerating charges emit EM waves and loose kinetic energy in classical electromagnetism. Therefore electron would fall fast into atom nucleus. This shows that Rutherford atom model is incomplete and that's why quantum mechanics was born.

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I think the OP doesnt understand why the electron undergoes acceleration.Well it does because its speed may not change , but its velocity changes.Any object in a orbits is accelerating since velocity is a vector and obviously a object in a orbit doesnt follow a straight line.

The displacement of the electron is perpendicular to the force so wouldn't that mean that the work done (or) energy used is 0?

This is true only in linear motion.In circular motion $W(work)=\tau(torque)\cdot\theta(angle)$

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  • $\begingroup$ what T and theta? $\endgroup$
    – Martin
    Commented Feb 9 at 15:21
  • $\begingroup$ torque and angle. $\endgroup$ Commented Feb 9 at 15:21
  • $\begingroup$ It should be explained in the answer's text, not in a comment. Please take into account that comments may be canceled. $\endgroup$ Commented Feb 9 at 16:15
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    $\begingroup$ Please tell it to the author of this Wikipedia page en.wikipedia.org/wiki/Lagrangian_mechanics where $T$ is the kinetic energy :-) $\endgroup$ Commented Feb 9 at 16:26
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    $\begingroup$ It is not a matter of my happiness. It is the standard rule of scientific communication. In a scientific paper, even the most obvious acronyms are explained the first time they are introduced. $\endgroup$ Commented Feb 9 at 16:41
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Electrons would be attracted to the nucleus. They would naturally fall in.

But they don't fall in. The natural guess is that the reason they don't fall into the nucleus is the same reason that the earth doesn't fall into the sun -- that they orbit fast enough to stay in a stable orbit.

But if they travel around in a circle, they are supposed to radiate electrical force. Electrons that go back and forth in a radio tower make radio waves. Electrons that travel in a circular loop radiate. Perpendicular to the loop they make circularly-polarized radiation, and in the plane of the loop they make linearly polarized radiation.

So according to electromagnetic theory the reason they don't fall into the nucleus is not that they are in an orbit that keeps them from falling.

They had a similar problem with the nucleus. If there is more than one proton in the nucleus, why don't they repel each other with tremendous force? How can they stay together?

For the nucleus, scientists invented the strong force. It's stronger than the repulsive force that would force them apart, strong enough to hold them together anyway, despite their tremendous repulsion.

They could have invented another strong force to keep the electrons from falling into the nucleus, or even decided that it was part of the first strong force. But instead of that, they invented quantum mechanics. Quantum mechanics describes statistically the way that electrons in an atom behave. It does not postulate a reason they behave that way. Since it is a clear description, physicists don't need to make up a reason. Sometimes they do make up reasons that are compatible with the math, but that is not necessary.

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From classical point of view an accelerated charged particle (the electron around the nucleus) loses energy radiating electromagnetic waves (see the power Larmor formula), thus after a certain amount of time $\Delta t$ the electron falls in the nucleus. In this way the atom isn't stable.

A person might think of introducing relativistic effects to solve the problem (giving an upper limit to the speed of electron), but even in this case the accelerated particle radiates, it loses energy (see relativistic Larmor formula) and it falls in the nucleus. If you try to calculate the fall time $\Delta t'$ of electron in this case the situation is even worse than the classic one: $\Delta t'< \Delta t$, and so the atom is "more unstable".

The matter that surrounds us is stable and these approaches cannot justify this characteristic. The only way to solve the problem is to introduce quantum mechanics, but that's a whole other story.

As Feynman would say: "Nature isn't classical, dammit, and if you want to make a simulation of nature, you'd better make it quantum mechanical, and by golly it's a wonderful problem, because it doesn't look so easy.”

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