Application of Electromagnetism question

[kittyNoel]

Homework Statement

A sample of two different irons, Fe2+ and Fe3+, are accelerated by the same potential and then sent through the uniform magnetic field of a mass spectrometer.
a) Which ion moves faster after being accelerated? Justify your answer by referring to equations used in this lesson.
b) Which ion follows the path with the largest radius? Justify your answer.

Homework Equations

m = q(B^2)(r^2)/2

The Attempt at a Solution

a)
Ee = Ek
Ee1 = 1/2 m1v1^2
Ee2 = 1/2 m2v2^2
1/2m1v1^2 = 1/2 m2v2^2

This means that the two particles both have the same potential energy... but one of the particles has more mass than the other... since it has more mass it takes more energy to move it and so moves slower...

This makes sense to me but how do I know which one has more mass? This answer also doesn't use the equation I included above which is the one from the unit that I think they want us to use...

c) The equation m = q(B^2)(r^2)/2 tells us that the heavier particles are deflected in an arc with a larger radius than lighter particles. This means that ____ (again I need to know which one is heaver) follows a path with a larger radius.

 

[ehild]

What do 2+ and 3+ mean? What is the difference between the Fe2+ and Fe3+ ions?

ehild

 

[kittyNoel]

I think I typed that funny, probably should be Fe^2+ and Fe^3+ With the 2+ and 3+ being tiny and up at the top. I believe it is the charge of the element.

 

[ehild]

It is right, you have double charged and triple charged Fe ions. Is the mass of these ions appreciably different?

ehild

 

[kittyNoel]

I'm not really sure... that's pretty much where I am stuck... they have to be different somehow otherwise why ask this question... I guess one has more protons than the other right because its more positive... so I guess it comes down to the tiny amount of extra mass that one of them has... you can't add protons to something... so to get the +2 charge you would have to have more electrons on it than the +3 charge... which would make it just a little bit heaver... right?

 

[tiny-tim]

hi kittyNoel!

(ehild is offline, so i'll continue where he left off …)

sorry, but in concentrating on the mass you're completely missing the point …

the difference in mass is negligible …

what else is different about them that will affect the electromagnetic force?

 

[ehild]

I am back. The number of protons, the "atomic number" identifies an element. It is very hard to add a proton to a nucleus, and if you succeed, you get a different element. But it is easy to remove one or more outer electrons. If two or three electrons are removed, the Fe atom gains 2e or 3e positive charge. If the charge of the ions are different, their potential energies are different in an electric field. And check the equation for m in your first post: it is wrong.

ehild

 

[kittyNoel]

I'm not sure about the equation that's what I see in my textbook.
What you said about the element is what I meant I just didn't explain it very well...

so where does this leave me? Is comparing them by there mass incorrect? I don't really know what's different about them except like you said one has more electrons than the other.

 

[ehild]

At potential V, what is the electric potential energy Ee of a charge q? How do you calculate the kinetic energy of a charged particle which is accelerated through a given potential difference?

ehild

 

[tiny-tim]

hi kittyNoel!

… one has more electrons than the other.

exactly! … so how does that effect the way it moves in an electric field?