Acceleration with Fe2+ ion and Fe3+ ion help

[alicia113]

Acceleration with Fe2+ ion and Fe3+ ion help!

A sample of two different iron ions, Fe^2+ and Fe^3+, are accelerated by the same potential and sent through the uniform magnetic field of a mass spectrometer.
a)Which ions moves faster after being accelerated. Justify with relevant equations.
b)Which ion follows the path with the largest radius. Justify your answer.

solutions

a)their masses are the same (or very close to being the same; these will differ by approximately the mass of one electron, which is quite negligible in this case compared to the atomic mass of Fe), then the main consideration is the difference in charges.

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

The mass of Fe3 ion is greater than Fe2 so it has more energy and more energy is equivalent to greater speed (e.g.momentum)
i don't know if this is a good enough explanaion or if its right

b) Fe3+ becasue it is heavier

eeekk don't know how to explain this one!

 

[Bhumble]

I think you pointed out the answer by stating that the masses are very close but that since the charges are different and they are subjected to the same electric potential that the ion with the greater charge will be subject to a greater force.

There are no numbers involved but assuming that masses are essentially the same the resultant acceleration on the greater charged ion is proportionately higher.

As far as formulas I'd just put something that relates acceleration to force and force to charge.

 

[Borek]

b) Fe3+ becasue it is heavier

If anything, it is lighter - after all, it has one electron less and electron is not a massless particle.

Curvature of the trajectory is a function of the mass/charge ratio, you should be able to find details either in your course book or to google them.