Calculating Fraction of Electrons Removed from Iron Ball

[glpg80]

Homework Statement

A 2.0 mm diameter iron ball is charged to +48 nC. What fraction of its electrons have been removed? The density of iron is 7,870 kg/m3.

Homework Equations

Q = Ne; N = number of atoms in 1 mole, e is atomic charge, Q = point charge

N = Avagadro's Constant = 6.02E23

Proton Charge = 1.6e-19 C

Electron Charge = -1.6e-19 C

K = (9e9 Nm^2)/(C^2)

vector<E> = (K|q|)/(r^2)

A=4(pi)r^2

D=2r

55.845 is the atomic mass of Iron

The Attempt at a Solution

I know that either the surface area of a sphere, or the Area of the spherical metallic ball comes into play but i do not know which one? i know that electrons will go to the surface of the ball or protons will go to the surface of a ball, and that the conductor internally has an electric field of 0 N/C.

I also know that the density of the iron ball comes into play but have failed at connecting density with charge or even if there is a connection.

I know that it will be a fraction of two things over one another since it is asking for a comparison.

I know that 48nC is 3E11 electrons.

i attempted to solve for E as a vector but got an answer that is way off by more than double.

Q = Ne (6.02E23)(55.845)(1.6E-19) = 5.38E6

I then treated the ball and some other point source as a capacitor using the area of the surface of the sphere, plugging and chugging from this point on but got an incorrect number.

i don't know how to start or tackle this problem :(

 

[ideasrule]

You just need to find out how many electrons there are in total. So how heavy is a 2.0 mm iron ball? How many atoms does it contain? How many electrons are there per atom?

 

[glpg80]

You just need to find out how many electrons there are in total. So how heavy is a 2.0 mm iron ball? How many atoms does it contain? How many electrons are there per atom?

ok, so mass and volume relate to density. i need to find the volume of a 2mm iron ball.

V = (4/3)(pi)((0.001m)^3) = 4.19E-9

(7870kg/m^3)(4.19E-9m^3), meters cancel and 3.2976E-5kg = mass

how many atoms does it contain?

(3.2976E-5 kg)/(0.055845 kg/mol) = 1.84E-6 mol

(1.84E-6 mol)(6.022E23 atoms/mol) = 1.11E18 atoms

 

[ideasrule]

It would be, except you divided 3.2976E-5 kg by 55.845, which is in g/mol.

 

[glpg80]

It would be, except you divided 3.2976E-5 kg by 55.845, which is in g/mol.

ok, fixed the improper units conversion, kg cancels and mol becomes the correct unit which is then used to calculate the number of atoms, which is 1.11E18

 

[glpg80]

Iron has:

29 electrons
29 protons
30 neutrons

the iron ball was charged to +48E-9 C

(+48E-9)/(-1.6E-19) = -3E11 Number of Electrons from the Electrical Charge

To account for the Electrons in an atom of iron; (1.11E18 atoms)(29 Electrons per atom) = 3.219E19 Electrons total

present it as a fraction= (-3E11)/(3.219E19) = -9.32E-9; no units.

(web assign claims the correct answer for Iron is 3.24E-11 with no units. Web Assign changes the metals and the Densities each time a new browser is opened and it is now getting late - i will have to do this over with another example)

i still need help in solving this please. i do not know where i am messing up. i am stuck :(