Bohr's Atomic Model: Magnetic vs Gravitational Force

[tiagobt]

My physics teacher told me that one of the innacuracies of Bohr's Atomic Model is that the nucleus (positive) would attract the electron (negative) making it move as a spiral until it collapses with the nucleus. What I don't get is why the same thing doesn't happen with a planetary system. How different is magnetic force from gravitational force?

 

[Doc Al]

The reason has to do with the fact that the electron has a charge, and that--according to classical physics--accelerating charges radiate energy. Thus the orbiting electron would quickly lose its energy and spiral into the nucleus.

That doesn't happen to planets.

 

[pervect]

My physics teacher told me that one of the innacuracies of Bohr's Atomic Model is that the nucleus (positive) would attract the electron (negative) making it move as a spiral until it collapses with the nucleus. What I don't get is why the same thing doesn't happen with a planetary system. How different is magnetic force from gravitational force?

The "spiraling" mechanism involves the emission of electromagnetic waves (for charges), or gravitational waves (for masses) which are necessary to maintain the conservation of momentum.

In theory, the Earth does spiral into the sun via the emission of gravitational radiation - it is just that this is a very weak effect. (So weak that it cannot be directly observed).

Gravity is universally attractive, so there can be no dipole terms to generate gravitational radiation. The first terms which can generate gravitational radiation are quadropole terms. This means that gravitational radiation is surpressed even more than electromagnetic radiation.

See for instance the sci.physics.faq
http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_speed.html

Since this point can be confusing, it's worth exploring a little further, in a slightly more technical manner. Consider two bodies--call them A and B--held in orbit by either electrical or gravitational attraction. As long as the force on A points directly towards B and vice versa, a stable orbit is possible. If the force on A points instead towards the retarded (propagation-time-delayed) position of B, on the other hand, the effect is to add a new component of force in the direction of A's motion, causing instability of the orbit. This instability, in turn, leads to a change in the mechanical angular momentum of the A-B system. But total angular momentum is conserved, so this change can only occur if some of the angular momentum of the A-B system is carried away by electromagnetic or gravitational radiation.

Now, in electrodynamics, a charge moving at a constant velocity does not radiate. (Technically, the lowest order radiation is dipole radiation, which depends on the acceleration.) So, to the extent that A's motion can be approximated as motion at a constant velocity, A cannot lose angular momentum. For the theory to be consistent, there must therefore be compensating terms that partially cancel the instability of the orbit caused by retardation. This is exactly what happens; a calculation shows that the force on A points not towards B's retarded position, but towards B's "linearly extrapolated" retarded position. Similarly, in general relativity, a mass moving at a constant acceleration does not radiate (the lowest order radiation is quadrupole), so for consistency, an even more complete cancellation of the effect of retardation must occur. This is exactly what one finds when one solves the equations of motion in general relativity.

 

[rbj]

The reason has to do with the fact that the electron has a charge, and that--according to classical physics--accelerating charges radiate energy. Thus the orbiting electron would quickly lose its energy and spiral into the nucleus.
That doesn't happen to planets.

what about gravitational radiation? isn't there some energy radiated as gravity waves because of the accelerated masses of the planets? (admittedly, the acceleration is far less than that in the Bohr model.)

 

[Doc Al]

what about gravitational radiation? isn't there some energy radiated as gravity waves because of the accelerated masses of the planets? (admittedly, the acceleration is far less than that in the Bohr model.)

Absolutely, as pervect explained. (I ignored such small effects in my response; pervect's post is more complete and accurate.)

 

[jtbell]

My physics teacher told me that one of the innacuracies of Bohr's Atomic Model is that the nucleus (positive) would attract the electron (negative) making it move as a spiral until it collapses with the nucleus.

Actually, this is a problem with a predecessor to Bohr's model, not with Bohr's model itself. Before Bohr entered the picture, physicists considered what one might call the "naïve planetary model" of the atom, in which the electrons are classical particles orbiting the nucleus under the influence of the electric force. This model was quickly seen to have the "radiation problem" discussed in this thread.

Bohr's model specifically postulated that atomic electrons are restricted to certain discrete orbits via quantization of orbital angular momentum, and do not undergo the classical electromagnetic radiation process while they are in these orbits.

Bohr's model does make some incorrect predictions, although it gets the basic energy levels of hydrogen right; and it couldn't be extended to multi-electron atoms. People tried to fix it by introducing elliptical orbits and relativistic corrections (try a Google search on "bohr sommerfeld atomic model"), but in the end it was superseded by Schrödinger's quantum mechanics, plus the concept of "spin".

 

[Mk]

accelerating charges radiate energy. Thus the orbiting electron would quickly lose its energy and spiral into the nucleus.
That doesn't happen to planets.

The electron is not changing its direction of movement?

 

[Doc Al]

The electron is not changing its direction of movement?

Says who? In the classical picture of an orbiting electron, the electron's direction of motion is constantly changing.