Proton's Closest Approach to Mercury Nucleus

[dtesselstrom]

Homework Statement

A proton is fired from far away toward the nucleus of a mercury atom. Mercury is element number 80, and the diameter of the nucleus is 14.0 fm. If the proton is fired at a speed of 4.0 times 10^7, what is its closest approach to the surface of the nucleus? Assume the nucleus doesn't move

Homework Equations

Not sure

The Attempt at a Solution

I really don't know how to start this problem if anyone could give me some advice on how to approach it Id appreciate it.

 

[denverdoc]

well to begin, we need somewhere to start, and the best place is what do you know. Do you know the force on an a pair of electric charges? Do you know the energy of a particle with this mass and velocity. These are starting points.

 

[dtesselstrom]

I can calculate the Kinetic energy of the proton but I don't know how to figure out how close that will allow me to get to the mercury atom.

 

[denverdoc]

Thats a problem. Like charges repel, and so this proton bullet will be running into a force field. Ever play with magnets? When you try to push the north ends together they push back. Well think of the problem that way, these are powerful magnets, no matter how hard you try you can't push them together. Bright idea, get a running start.

Still if the magnets are strong enough if, will it keep them from touching?

 

[Dick]

Since you say you know the initial kinetic energy of the proton you are halfway there. At it's closest approach it is stopped and has no kinetic energy. Where does the energy go? Do you know an expression for potential energy that would be appropriate?

 

[dtesselstrom]

How would I find the charge on the Mercury. Wouldn't it have a neutral charge or 0 with 80 electrons and protons and even if it is a charged state which state would it be?

 

[Dick]

The problem actually says that the proton is fired towards the NUCLEUS of a mercury atom. This is a hint you should ignore the electrons. This is actually a reasonable approximation. At high energies the interaction with the nucleus takes place well inside of the electron orbits - so you can pretty much ignore them.