An accelerated iron Ion moving through a mass spectrometer's field

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SUMMARY

The discussion centers on the behavior of two iron ions, Fe2+ and Fe3+, as they are accelerated through a mass spectrometer's magnetic field. The equations governing their motion reveal that Fe3+ moves faster due to its higher charge, despite its slightly lower mass, as indicated by the equation v = sqrt|(2qV)/m|. However, the radius of curvature in the magnetic field is determined by the relationship r = sqrt|(m2V)/(qB)|, which shows that Fe2+ has a larger radius due to its lower charge, resulting in less deflection. Thus, Fe3+ has a higher velocity while Fe2+ follows a path with a larger radius.

PREREQUISITES
  • Understanding of kinetic energy equations, specifically Ek = 1/2mv^2.
  • Familiarity with the motion of charged particles in magnetic fields, including the Lorentz force.
  • Knowledge of centripetal force and its relation to circular motion, Fc = (mv^2)/r.
  • Basic grasp of mass spectrometry principles and ion acceleration.
NEXT STEPS
  • Study the derivation of the velocity equation for charged particles in electric fields.
  • Learn about the principles of mass spectrometry and its applications in analytical chemistry.
  • Explore the effects of varying magnetic field strengths on ion trajectories.
  • Investigate the relationship between charge, mass, and radius of curvature in magnetic fields.
USEFUL FOR

This discussion is beneficial for physics students, particularly those studying electromagnetism and mass spectrometry, as well as professionals in analytical chemistry and instrumentation who require a deeper understanding of ion behavior in magnetic fields.

slybuster
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Homework Statement



A sample of two different iron ions, 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?
b) Which ion follows the path with the largest radius?

Homework Equations



a)
Ek = 1/2mv^2
v= sqrt|(2qV)/m|
??v= (qBr)/m??

b)
Fc= (mv^2)/r
r = sqrt|(m2V)/(qB)|



The Attempt at a Solution



a) Stated that Fe3+ had a stronger charge and a smaller (though negligibly) mass. Related this to the Ek and v= sqrt|(2qV)/m| equations in order to show that it would have a faster velocity. I think I'm alright here...

b) This is where I have trouble. My gut tells me that the Fe2+ should have the larger radius (when I picture the charge in my head it has a lower Ek and gets deflected more). However, relating the equations is confusing me as I keep getting tripped up by thinking that the larger charge of the Fe3+ ion will cause it to experience more force and thus a wider radius pushing it. Maybe I should be picturing it enter the field from over top? (i.e. (x) and not from the side -->). Also, I want to try and set up r(Fe+3)/r(Fe+2) = ?/? but can't figure out which equation to use on the right side...

Help is very much appreciated.
 
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Equate centripetal force to the force of a moving charge in a magnetic field. What do you get?
 

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