In a hydrogen atom we have an electron and a proton (2 up-quarks and one down-quark). The electron and proton are attracted to each other by gravity and electromagnetic force.
Do I have this correct so far?
If I do, what keeps the electron and proton apart? There are only two forces left, strong and weak nuclear. Or is just gravity and electromagnetic force is not powerful enough to bring them together?
I sure I have something wrong here.
Gravity is insignificant at this scale. Ignore it.
You might as well ask what keeps the planets and sun apart. The only force acting there is gravity, and that’s only attractive. Mathematically, it’s quite possible to have two things pulling on each other and not hit. You might think of it in terms of conserved angular momentum, or in terms of a centrifugal force, but there’s no need for an actual repulsive force to work.
So, basically the electromagnetic force is not strong enough to to cause the proton and electron to meet?
It’s not really a question of strength. Just because two things are attracted together doesn’t mean they’ll come together. Upping the magnitude of the electrostatic force won’t mean that they collide; it will just make the electron orbitals tighter.
I’ve always dealt with this just using the Rutherford model.
Remember that the electron possesses a total energy which must remain constant. This total energy is made up of a potential energy and a kinetic energy. The potential energy is proportional to -1/r where r is the radius. So if you move the electron closer to the nucleus (decrease r) then the potential energy decreases.
This means that the kinetic energy has to increase. The kinetic energy is equal to mv[sup]2[/sup]/2. the only way to increase this is to increase the velocity.
So as the radius of the electron decreases the electron has to move faster and faster and as the radius approaches zero the velocity of the electron has to approach infinity. And it can’t do that. So it doesn’t.
Sticking with the simple orbital model, it’s the same reason the planets don’t fall into the sun. There is a huge attractive force between the Earth and the Sun yet the Earth does not fall into the Sun because it has kinetic energy which means it orbits the Sun.
Now you may then think that an electron in it’s ground state would fall into the neutron, however it does not due to the Pauli exclusion principle which means that there is an associated kinetic energy even in the ground state. So even at absolute zero the electron and proton won’t collapse into each other. However it is possible for the Pauli exclusion principle to be overcome, this happens in the supergravity of a neutron star where electrons and protons are pushed together to form neutrons.
This is a fairly common misperception but it isn’t true. If you do the math you’ll find that the probability of this occurring is zero. What really happens is the available momentum states increase without limit and therefore no two identical fermions are forced into the same quantum state.
What it shows is that I only completed the first year of my physics degree before changing to history. But even at university I was taught that neutrons stars were formed because of the overcoming electron-degenracy pressure which led tothe overcoming of the Pauli exclusion principle.
Actually I see what your saying now the Pauli exclsuion principle isn’t overcome by the collapse and the electron and proton don’t occupy the same state.
There’s a subtle difference between the electron orbiting the nucleus and the Earth orbiting the Sun. The electron is a charged particle, while the Earth has a net charge of zero. According to classical electrodynamics, a charged particle undergoing acceleration (centripetal acceleration in the case of orbital motion) will radiate energy at a rate given by the Larmor formula. Classically, this radiation would lead to the electron spiraling into the nucleus rather than remaining in a stable orbit. A rough classical calculation would put the lifetime of the Bohr atom on the order of picoseconds.
To overcome this difficulty, Bohr invoked some premature quantum mechanics, extending classical mechanics to allow for discrete, stationary orbits in which the electron does not radiate. He required that the angular momenta of these stationary orbits be quantized in integral multiples of h-bar. The conclusions that followed from Bohr’s quantization condition agreed with the experimental data collected by spectroscopy, which led to its acceptance in the scientific community, at least until the development of quantum mechanics.
Yes the degeneracy pressure can be overcome but the exclusion principle cannot be violated, and If you’re into masochism please see below.
The Pauli Exclusion Principle
With indistinguishable particles |c[sub]mn[/sub]| = |c[sub]nm[/sub]| so c[sub]mn [/sub]= -c[sub]nm[/sub] or c[sub]mn [/sub]= c[sub]nm[/sub][sub][/sub]
Where c[sub]mn [/sub]= - c[sub]nm [/sub]represents fermions
Now exchange the particles
| psi[sup]21[/sup]> ~ [ | psi[sup]2[/sup][sub]m[/sub]> | psi[sup]1[/sup][sub]n[/sub]> - | psi[sup]2[/sup][sub]n[/sub]> | psi[sup]1[/sup][sub]m[/sub]> ] = - | psi[sup]12[/sup]>
Now put them in the same state
| psi[sub]n[/sub]> = | psi[sub]m[/sub]>
psi[sup]12[/sup]> ~ [ | psi[sup]1[/sup][sub]m[/sub]| psi[sup]2[/sup][sub]m[/sub]> - | psi[sup]1[/sup][sub]m[/sub]> | psi[sup]2[/sup][sub]m[/sub]> ] = "0"
So the probability of two fermions occupying the same state is
Zero
How about a restatement of the question:
Gravity causes particles to attract each other, and if there were no repulsive forces involved, then sun, earth, pencils people, etc., should all contract to become singular points.
So, what are the repulsive forces which prevent this from happening?
And most important: why is the Exclusion Principle not classed as a repulsive force?
This may seem obvious to you, but it is not generally true. As other people have mentioned, in the solar system, there is no repulsive force keeping the earth from falling into the sun, and yet this does not occur. The reason for this is that the earth has kinetic energy which prevents it from being pulled in closer than it is (on average). In general, if there are no repulsive forces to keep a system of particles from contracting, it will contract to a certain finite size from which it cannot contract further without losing energy. (this doesn’t apply to black holes because of relativistic effects which normally aren’t important)
If you were to take the earth and magically eliminate all forces except gravity from acting between its particles, you would find that very few particles would fall into the geometric center. The reason is that the earth is rotating, so most of its matter has tangential velocity – it has kinetic energy in the earth’s center-of-mass inertial frame. You would end up with most of the matter orbiting the center in highly-elliptical orbits. Soon you would have a cloud of particles in what is known as virial equilibrium. Over a very long time, gravitational interactions between the particles would randomly redistribute kinetic energy. Occasionally particles would escape from the system entirely, taking some kinetic energy with them, and as a result other particles would fall in closer. This is similar to the case of a very thin gas cloud in interstellar space. Repulsive forces between particles in such a cloud are so weak as to be negligible, yet such clouds do not collapse on a timescale comparable to the age of the earth.
The idea of this is that a central attractive force does not necessarily cause contraction. An electron in the ground state of an atom would need to lose energy in order to get any closer to the nucleus, but it cannot lose energy because, by the Pauli Exclusion Principle, there are no lower-energy states in which it can exist. As a result atoms do not collapse; no force is necessary to stabilize them.