# A proton and an electron

I know this question sounds... find a word for it you like... But please bear with me.

A proton. An electron. Not very high speeds...Vacuum..

A proton has an electric field, so does an electron...
They arrive into each others' fields and start to accelerate towards each other...

What happens next? What is bound to be happened? What might one expect?
May they collide if so. what would happen?

DrClaude
Mentor
They arrive into each others' fields and start to accelerate towards each other...
Electric fields extend to infinity, so they don't "enter each others' fields."

What happens next? What is bound to be happened? What might one expect?
The process can take different forms, and things may happen in various order, but basically the system proton+electron will gradually lose energy through the emission of photons, and you will eventually end up with a hydrogen atom.

May they collide if so. what would happen?
What exactly do you mean by collide? Because the above process is a collision of sorts.

Hydrogen atom

Electric fields extend to infinity, so they don't "enter each others' fields."
.

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Collision is an interaction that takes a small amount of time and involves relatively large forces.

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sophiecentaur
Gold Member
Collision is an interaction that takes a small amount of time and involves relatively large forces.

I'm not sure where you would draw the line between what could and couldn't called a collision. Does one 'collide' with a trampoline or a sponge, in your terms?
To answer the question involves Quantum Mechanics because both particles are very much quantum objects. The energy states, in close, are definite and well separated. There is a minimum possible energy state (the ground state) as the electron gets further and further away, the spacing between the energy states gets less and less until you can regard it as a continuum. The Inverse Potential Law applies ('Potential Well' with decreasing slope as you go further out). The slope is never actually zero. In practice, even in deeeeep space, there will be some other particles around to disturb this idealised, circularly symmetrical pattern and providing other attractive wells to pull against the two particles.
If their relative speed is high enough, so that the KE is greater than the Potential energy, there will never be capture. (As with asteroids and comets, in the classical world.)

I'm not sure where you would draw the line between what could and couldn't called a collision. Does one 'collide' with a trampoline or a sponge, in your terms?
To answer the question involves Quantum Mechanics because both particles are very much quantum objects. The energy states, in close, are definite and well separated. There is a minimum possible energy state (the ground state) as the electron gets further and further away, the spacing between the energy states gets less and less until you can regard it as a continuum. The Inverse Potential Law applies ('Potential Well' with decreasing slope as you go further out). The slope is never actually zero. In practice, even in deeeeep space, there will be some other particles around to disturb this idealised, circularly symmetrical pattern and providing other attractive wells to pull against the two particles.
If their relative speed is high enough, so that the KE is greater than the Potential energy, there will never be capture. (As with asteroids and comets, in the classical world.)
Interesting answer, thank you: the further away, the less energy levels differ that one can regard it as a continuum is an interesting point.

sophiecentaur
Gold Member
Interesting answer, thank you: the further away, the less energy levels differ that one can regard it as a continuum is an interesting point.
That's very basic QM when you first do the Hydrogen Atom, with only four quantum numbers involved, as I remember.

I'm not sure where you would draw the line between what could and couldn't called a collision. Does one 'collide' with a trampoline or a sponge, in your terms?
To answer the question involves Quantum Mechanics because both particles are very much quantum objects. The energy states, in close, are definite and well separated. There is a minimum possible energy state (the ground state) as the electron gets further and further away, the spacing between the energy states gets less and less until you can regard it as a continuum. The Inverse Potential Law applies ('Potential Well' with decreasing slope as you go further out). The slope is never actually zero. In practice, even in deeeeep space, there will be some other particles around to disturb this idealised, circularly symmetrical pattern and providing other attractive wells to pull against the two particles.
If their relative speed is high enough, so that the KE is greater than the Potential energy, there will never be capture. (As with asteroids and comets, in the classical world.)
Err.. another point.. When a proton and electron accelerate towards each other, and when quantum weirdness takes over.. So where does the energy go that they had?

sophiecentaur