5 ms·

> they don't make it all the way there because they are repelled by some other force A repulsive force is not the best way to think about it. The potential of

> they don't make it all the way there because they are repelled by some other force A repulsive force is not the best way to think about it. The potential of the nucleus is the usual -1/r, and goes to (negative) infinity at zero. A repulsive force would be incorporated into the potential and appear as a bump around the nucleus, and would mess up the electron orbital. A hand-wavy explanation of why the electron doesn't fall in: if you try to push the electrons into the nucleus, you necessarily localize the electron into a smaller volume; this means its wavefunction must get "spikier" and therefore it has more kinetic energy. This kinetic energy rises faster than the potential energy drops, so the state of lowest energy is actually found at an average radius > 0. Note that it took quantum mechanics to rescue the atom. A classical electron could fall into the nucleus. I do not see any problem with a negative-mass particle accelerating towards the force. The analogy with opposite charges seems right to me.

btilly 8y ago
A different hand-wavy explanation. The places that an electron can be found are described by a wave pattern. If the electron is staying in place around a nucleus, that wave pattern has to be a standing wave that reinforces itself. To reinforce itself it has to wrap around the nucleus an integer number of times. This explanation doesn't just explain why it doesn't fall in, it also explains why there are discrete shells that it could be found in, corresponding to how many times it wraps around the nucleus. (It doesn't explain why only a finite number can fit in each shell though. Or why bigger shells can have more electron orbitals. Or...well the actual theory has to be good for something!)
- drjesusphd 8y ago
  This is the Bohr model of the atom, but was replaced by a proper quantum theory.
  - btilly 8y ago
    Yes. Which is why I called it "a different handwavy theory". And also listed some of the things that it didn't explain.
- thaumasiotes 8y ago
  I'm not really interested (here) in the reality of the interaction between the electron and the nucleus. I don't think the existence of an electromagnetic field is a good argument against its own existence as argued by FabHK further up. I also don't think FabHK's argument works as an analogy to my problem with negative mass. The electromagnetic field is not self-reinforcing in the same way. Imagine that you're holding a marble of negative glass in your fist. Negative glass is indistinguishable from ordinary glass except that its mass is negative rather than positive. As we all know, the first step in solving any physics problem is to draw a free-body diagram. ( http://www.smbc-comics.com/comics/20130616.png http://www.smbc-comics.com/comics/20130616.png ) Let's draw one here. First, we'll do one for an ordinary marble: 1. The enormous mass of the earth attracts the marble downward proportionately to the marble's mass. 2. The marble cannot accelerate downward, because it's stuck in your fist. Your fist experiences a downward force equal to the weight of the marble. 3. By Newton's third law, your fist exerts an upward force on the marble equal to the force exerted by the marble on your fist. This is exactly equal to the weight of the marble, but in the opposite direction. The two forces cancel, and the marble is at rest. Now for the negative marble: 1. The enormous mass of the earth attracts the marble downward proportionately to the marble's mass. Because that mass is negative, the marble attempts to accelerate upward. 2. The marble can't accelerate upward, because it's stuck in your fist. Your fist experiences an upward force equal to the weight of the marble. 3. By Newton's third law, your fist exerts an downward force on the marble equal to the force exerted by the marble on your fist. This is exactly equal to the weight of the marble, and in the same direction, effectively doubling the marble's weight. The marble is now trying twice as hard to accelerate upward into your fist. 2. (Again.) The marble can't accelerate upward, because it's stuck in your fist. Your fist experiences an upward force equal to double the weight of the marble. Nothing has moved; we're still just trying to work out the balance of forces within the system at rest. 3. (Again.) You can see where this is going. What is the conceptual breakthrough that rescues negative mass from this trap? (Note that saying the marble has negative inertial and gravitational mass, as opposed to negative inertial mass and positive gravitational mass, doesn't help: the marble will be trying to accelerate downward instead of upward, but it will still be doing it with infinite force.)
  - petre 8y ago

btilly 8y ago

A different hand-wavy explanation. The places that an electron can be found are described by a wave pattern. If the electron is staying in place around a nucleus, that wave pattern has to be a standing wave that reinforces itself. To reinforce itself it has to wrap around the nucleus an integer number of times. This explanation doesn't just explain why it doesn't fall in, it also explains why there are discrete shells that it could be found in, corresponding to how many times it wraps around the nucleus. (It doesn't explain why only a finite number can fit in each shell though. Or why bigger shells can have more electron orbitals. Or...well the actual theory has to be good for something!)

drjesusphd 8y ago
This is the Bohr model of the atom, but was replaced by a proper quantum theory.
- btilly 8y ago
  Yes. Which is why I called it "a different handwavy theory". And also listed some of the things that it didn't explain.
thaumasiotes 8y ago
I'm not really interested (here) in the reality of the interaction between the electron and the nucleus. I don't think the existence of an electromagnetic field is a good argument against its own existence as argued by FabHK further up. I also don't think FabHK's argument works as an analogy to my problem with negative mass. The electromagnetic field is not self-reinforcing in the same way. Imagine that you're holding a marble of negative glass in your fist. Negative glass is indistinguishable from ordinary glass except that its mass is negative rather than positive. As we all know, the first step in solving any physics problem is to draw a free-body diagram. ( http://www.smbc-comics.com/comics/20130616.png http://www.smbc-comics.com/comics/20130616.png ) Let's draw one here. First, we'll do one for an ordinary marble: 1. The enormous mass of the earth attracts the marble downward proportionately to the marble's mass. 2. The marble cannot accelerate downward, because it's stuck in your fist. Your fist experiences a downward force equal to the weight of the marble. 3. By Newton's third law, your fist exerts an upward force on the marble equal to the force exerted by the marble on your fist. This is exactly equal to the weight of the marble, but in the opposite direction. The two forces cancel, and the marble is at rest. Now for the negative marble: 1. The enormous mass of the earth attracts the marble downward proportionately to the marble's mass. Because that mass is negative, the marble attempts to accelerate upward. 2. The marble can't accelerate upward, because it's stuck in your fist. Your fist experiences an upward force equal to the weight of the marble. 3. By Newton's third law, your fist exerts an downward force on the marble equal to the force exerted by the marble on your fist. This is exactly equal to the weight of the marble, and in the same direction, effectively doubling the marble's weight. The marble is now trying twice as hard to accelerate upward into your fist. 2. (Again.) The marble can't accelerate upward, because it's stuck in your fist. Your fist experiences an upward force equal to double the weight of the marble. Nothing has moved; we're still just trying to work out the balance of forces within the system at rest. 3. (Again.) You can see where this is going. What is the conceptual breakthrough that rescues negative mass from this trap? (Note that saying the marble has negative inertial and gravitational mass, as opposed to negative inertial mass and positive gravitational mass, doesn't help: the marble will be trying to accelerate downward instead of upward, but it will still be doing it with infinite force.)
- petre 8y ago