Charged Aluminum Spheres: Calculating Electrons and Attractive Force

[Gaupp]

I'm having difficulty with a problem on MasteringPhysics (such wonderful software...) and as a last resort I'm posting on here. This is, I'm sure, a really simple problem but I'm getting no kind of feedback from MP and there isn't an example problem like this in the book.

Homework Statement

Two aluminum spheres of mass .025 kg are separated by 80 centimeters.

A) How many electrons does each sphere contain?

B)How many electrons would have to be removed from one sphere and added to the other to cause an attractive force between the spheres of magnitude 1.00 x 10^4 (roughly one ton)? Assume that the spheres may be treated as point charges.

C)What fraction of all the electrons in one of the spheres does this represent?

Homework Equations

F=K*q1*q2/(r^2)

q=e*(#protons-#electrons)

The Attempt at a Solution

A) I found Part A to be 7.25 x 10^24 electrons.

B) This is where I'm stuck.

If you were to remove electrons from one sphere and put them on the other I understand that their charges are to be equal but opposite, as in q1 = -q2. So using Coloumb's Law (F=K*q1*q2/(r^2)) I've set the Force to 1*10^4, divided that by K=9*10^9.

10000/(9*10^9) = q1*q2/(.8^2)

Then multiplying that by .8^2, I have just the charges on the other side of the equation. Since the charges in the formula are absolute value I can set q1=q2 and have q1^2. Taking the square root of the entire thing I have:

q=8.4327*10^-4.

So now I can use the formula q=e(#protons-#electrons). So:

8.4237*10^-4 = 1.6*10^-19(7.25*10^24-#electrons). Solving from this I get 7.249*10^24 electrons as my final answer.

However, MP says I'm wrong but there isn't any feedback as to where I went wrong, and it seems straightforward enough to me that no matter how I rework it I get the same thing every time.

Can anyone help me out here?

C) Can't do this one until B is done.

Any help is greatly appreciated.

 

[rootX]

how you did 'a'?
I am getting something different [5.58E20]

 

[Gaupp]

how you did 'a'?
I am getting something different [5.58E20]

.025 kg x [U]1000g[/U] x [U]1mol[/U] x [U]6.023*10^23 atoms in a mol[/U] x [U]13 electrons[/U] = #electrons
           1kg  26.982g               1 mol             1 atom Al

 

[rootX]

oops, I forgot units...
but do you get 7. something when you do this cal. on calculator?

my cal's giving me 5.something

and you getting

A) I found Part A to be 7.25 x 10^24 electrons.

 

[Gaupp]

oops, I forgot units...
but do you get 7. something when you do this cal. on calculator?

my cal's giving me 5.something

and you getting

How much does each ball weigh in your problem? It could be different, especially if you're doing this in MP.

 

[learningphysics]

oops, I forgot units...
but do you get 7. something when you do this cal. on calculator?

my cal's giving me 5.something

and you getting

multiply by the atomic number of aluminimum (ie number of protons in an atom which equals the number of electrons in an atom)

 

[learningphysics]

I'm confused by what you did in part B... the charge you calculated looks correct... you just need to divide by 1.6*10^-19 to get the number of electrons.

 

[rootX]

multiply by the atomic number of aluminimum (ie number of protons in an atom which equals the number of electrons in an atom)

You have to? I think maybe not. (We never did that)

oo..O you don't know that part A is correct try without multiplying by #13, hopefully, you may get the right answer

 

[learningphysics]

You have to? I think maybe not. (We never did that)

oo..O you don't know that part A is correct try without multiplying by #13, hopefully, you may get the right answer

Gaupp did... he didn't write it out..

Remember you need the number of electrons... not the number of atoms...

So number of atoms * (number of electrons/atom) gives the answer... I get the same answer as Gaupp.

 

[rootX]

Gaupp did... he didn't write it out..

Remember you need the number of electrons... not the number of atoms...

So number of atoms * (number of electrons/atom) gives the answer... I get the same answer as the Gaupp.

ooo.. yea you are right.. that gives the # of atoms, not the # of electrons

 

[Gaupp]

I'm confused by what you did in part B... the charge you calculated looks correct... you just need to divide by 1.6*10^-19 to get the number of electrons.

q=e(#protons-#electrons).

Ok I see now. The difference between the #protons and the #electrons would be the number of electrons lost or gained. I kept solving for just the number of electrons, by moving around the #protons in the equation. DOH!

Thanks for the help there learningphysics.