Finding the Force of Nucleus on a Single Electron of Plutonium

[anomalocaris]

Homework Statement

A particular nucleus of the element Plutonium contains 94 protons and 150 neutrons. What is the magnitude of the force from the nucleus on a single electron that is a distance of 0.563x10^-12 m from the Plutonium nucleus?

So basically this was a homework question that I got wrong, and I'm not entirely sure what the correct answer is. I'm reworking it to study for an exam, but I want to make sure this is right so I don't keep lousing it up!

Homework Equations

e=1.60x10^-19 C
and F=kQ/r²
where k is Coulomb's constant 8.99x10⁹ Nm²/C²

The Attempt at a Solution

Okay so if there are 94 protons, there should be 94 electrons.
(94)(e)=(94)(1.60x10^-19 C)=1.5x10^-17 C

Where I'm getting confused is what charge I should use to find the force? Because 1.5x10^-17 C is the charge of all 94 electrons and I need the magnitude of the force of the nucleus on just one electron. I'm not quite grasping this concept.

Anyway, if I blindly plug in numbers without really understanding completely what I'm doing here, I get:

F=(k(1.5x10^-17 C))/(0.563x10^-12 m)²
so F=4.27x10¹⁷ N

Also, how do I type fractions on this forum? I found the button but I'm not sure where to enter my numbers so it works! Thanks!

 

[tms]

and F=kQ/r²

You've left something out of that equation.

Okay so if there are 94 protons, there should be 94 electrons.

The problem asks for the force of the nucleus on a single electron. You can ignore the other 93 electrons.

 

[anomalocaris]

Okay, so should I have used F=[itex]\frac{(k(q1)(q2))}(r²){}[/itex]? And then I would use e as the charge of one electron (my q2) and the charge of all 94 electrons as my q1? Or am I completely off here? Thank you!

 

[anomalocaris]

Oh, sorry, the fraction thing still is not working for me. I meant F=(k(q1q2))/(r^2)

 

[tms]

Okay, so should I have used F=[itex]\frac{(k(q1)(q2))}(r²){}[/itex]? And then I would use e as the charge of one electron (my q2) and the charge of all 94 electrons as my q1? Or am I completely off here? Thank you!

That's the way to do it.

 

[anomalocaris]

Oh! Yay! Thank you so much,tms! I really appreciate it!

 

[tms]

Oh, sorry, the fraction thing still is not working for me. I meant F=(k(q1q2))/(r^2)

You need to put the denominator in the second set of curly braces: \frac{(k(q1)(q2))}{(r2)}
$$F=\frac{(k(q1)(q2))}{(r2)}$$
You should also use subscripts and superscripts, and you can get rid of the extraneous parentheses: F=k\frac{q_1q_2}{r^2}
$$F=k\frac{q_1q_2}{r^2}$$
If you are planning to go further in math or science, it is worth learning LaTeX. You can google for some brief introductions and tutorials.

 

[anomalocaris]

I tried doing that, but it didn't look right when I previewed it. My browser can be kind of wonky, though, so I'll keep trying. And I've never heard of LaTeX--sounds really cool. I'll definitely google that! Thanks again for all your help!