How close can two protons get if....

In summary: I was just trying to see if something could be done with the equation.In summary, the problem states that two protons will have kinetic energy when they are at the closest distance. The kinetic energy of the "at rest" proton is not given, but is supposed to be 1/r.
  • #1
PAK108
11
2
Mentor note: Thread got moved to the homework section

How close can two protons get if one is at rest and the other has a kinetic energy equal to the average energy at T =107 K?

I know that the kinetic energy of the moving proton is 3/2kT, but what is the kinetic energy of the proton
at rest? This question is from my book in astronomy. The answer are supposed to be r= r = 1.1 × 10−12m

Any help appreciated
 
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  • #2
PAK108 said:
but what is the kinetic energy of the proton
at rest?
Zero. What else?

At the moment of closest approach, both protons will move and have non-zero kinetic energy.

Is this homework?
 
  • #3
PAK108 said:
I know that the kinetic energy of the moving proton is 3/2kT, but what is the kinetic energy of the proton
at rest?
In your opinion what should be kinetic energy of a body which is not in motion?
the other protons kinetic energy is given so by virtue of its energy it can approach the other proton -in spite of repulsion from it so you must calculate the net work done by it in getting closer...
 
  • #4
mfb said:
Zero. What else?

At the moment of closest approach, both protons will move and have non-zero kinetic energy.

Is this homework?

Aha, I think I understand now, that means that all the kinetic energy becomes potential energy when the electron
are at the closest approach...thank you :)

Yes, this is homework (I realized that this should be posted at the homework section after posting. I am sorry for posting here)
 
  • #5
PAK108 said:
Aha, I think I understand now, that means that all the kinetic energy becomes potential energy when the electron
are at the closest approach...thank you :)
No it does not.
For that to occur, both would have to stop at the same time, which violates momentum conservation.

I moved the thread to the homework section.
 
  • #6
It's not clear from the problem statement that the "at rest" proton is meant to be able to move, or if it is to remain at rest (fixed in place). Is the problem statement complete and exactly as it was given?
 
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  • #7
gneill said:
It's not clear from the problem statement that the "at rest" proton is meant to be able to move, or if it is to remain at rest (fixed in place). Is the problem statement complete and exactly as it was given?

Yes this is the complete problem statement

I tried to solve the problem like this:

3/2kT + mc2=k(e2/r2), solving for r gave r=1.2*10-9, which is like 1000 order bigger than the correct answer :(
 
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  • #8
That does not even have matching units, and I don't understand where you got that equation from.
 
  • #9
PAK108 said:
mc2
what this energy term ( equivalent to mass) is doing there -is the problem talks about velocities comparable to velocity of light
 
  • #10
mfb said:
That does not even have matching units, and I don't understand where you got that equation from.

The equation was just put together from the equation for "thermal energy and rest energy" = "potential energy"

the k's on the left hand side is not the same on the right hand side
LHS k=1,38065*10-23 J/K
RHS k=8,99*109 Nm2/C2
 
  • #11
drvrm said:
what this energy term ( equivalent to mass) is doing there -is the problem talks about velocities comparable to velocity of light

No, the problem does not talk about velocities comparable to light...basically I was just trying something since the units matched...the chapter mentions the rest energy of a proton (E=mc2) so I just gave it a shot
 
  • #12
PAK108 said:
The equation was just put together from the equation for "thermal energy and rest energy" = "potential energy"
Why should that be true? Do you annihilate a particle to extract its rest energy? Even if that would be true, why one and not both?

PAK108 said:
the k's on the left hand side is not the same on the right hand side
That is clear and no problem. The potential energy still does not follow a 1/r2 law.
 
  • #13
PAK108 said:
o, the problem does not talk about velocities comparable to light...basically I was just trying something since the units matched...
well you can not do these things as physics theory does not mixes Newtonian and sTR -it will be a mess.
 
  • #14
mfb said:
The potential energy still does not follow a 1/r2 law.
Ah of course, it is supposed to be 1/r, that means that the calculations are completely off
 

Related to How close can two protons get if....

1. How close can two protons get if they have the same charge?

According to Coulomb's law, two protons with the same charge will repel each other with an electrostatic force. This force decreases as the distance between the protons increases. Therefore, the closer the protons get, the stronger the repulsive force will be. At a certain point, the repulsive force will be equal to the attractive strong nuclear force, preventing the protons from getting any closer. This distance is known as the strong force range and is approximately 10-15 meters.

2. How close can two protons get if they have opposite charges?

If two protons have opposite charges, they will attract each other with an electrostatic force. This force also decreases as the distance between the protons increases. However, unlike in the case of same charges, there is no repulsive strong nuclear force to counteract the attraction. Therefore, the protons can get infinitely close to each other, but they will not actually touch due to the uncertainty principle in quantum mechanics.

3. How close can two protons get if they are in a vacuum?

In a vacuum, there are no external forces or particles to interfere with the motion of the protons. This means that the protons will continue to accelerate towards each other until they reach a speed close to the speed of light. At this point, the relativistic effects of time dilation and length contraction will prevent the protons from getting closer than a certain distance, known as the Compton wavelength. For protons, this is approximately 10-15 meters.

4. How close can two protons get if they are in a material?

When two protons are in a material, they will interact with the atoms and molecules in the material. These interactions will cause the protons to lose energy, and therefore, they will not be able to get as close to each other as they would in a vacuum. The exact distance will depend on the properties of the material, such as its density and composition.

5. How close can two protons get if they are in a particle accelerator?

In a particle accelerator, protons are accelerated to very high speeds, allowing them to come closer to each other than they would in a material or a vacuum. However, even in a particle accelerator, there is a limit to how close the protons can get. This is due to the presence of other particles and the energy loss that occurs during collisions. The distance that protons can get to each other in a particle accelerator is typically on the order of 10-18 meters.

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