# Mass Spectrometer problem

I understand that in a mass spectrometer, a particle will first pass through an accelerometer to pick up speed (presumably starting from rest).
Let's say you have an electron starting from rest being passed through a difference of 1000V, it should have a kinetic energy of 1000eV right before it enters the mass spectrometer.
Once it is in the upper chamber, where there is no electric force to counteract the magnetic force, it will curve in circular motion. Does it acquire additional KE due to the centripetal acceleration? Or is it just a change of direction? Thanks

The engineering answer is that its kinetic energy is not changed by the magnetic force (which acts perpendicular to its velocity at all times). But rigorously speaking the kinetic energy will be lessened slightly, owing to the synchrotron radiation emitted by any charged particle that accelerates, regardless of whether that acceleration is parallel to the velocity or perpendicular to it.

Yeah I figured there would be some sort of energy loss but this is a simple problem that assumes no losses anywhere. Thank you very much. Although I don't quite understand, if it is experiencing a force, it will experience acceleration, therefore increased velocity. Increased velocity should give it more KE because the mass is constant. No?

It's important to bear in mind that there are two kinds of acceleration: radial and longitudinal. Your thinking is correct for longitudinal acceleration, where the magnitude of the object's velocity is changing in time. In the case of radial acceleration, the velocity vector's direction changes in time, but its magnitude remains constant in time. This is typically the case of a particle that travels in a circle with constant speed (and KE). Somewhat amazingly, Newton's 2nd law, F=ma, applies to both types of acceleration. But the applied force does no work when it acts perpendicular to the object's velocity.

There are many type of mass spectrometers, it is a general term. I spent over 14 years designing control, pulsing, HV circuits for all different mass spectrometers!!! Only one I designed had magnetic lens which I think is what you refer to. Mostly we deflected the ions into circular path by electrostatic lens only.

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yungman, that is very interesting, but not relevant. I am clearly talking about a situation that DOES use magnetism.
GRDixon, thanks for your help. So let me get this straight, since v and B are orthogonal, the cross product is 90 degrees to both of them, giving rise to the circular motion. The magnetic force is changing the direction only, not the velocity? Therefore, the starting KE is the final KE (once again, ignoring the energy loss).

Correct. P.S. yungman: Thanks for the info. I must confess I thought that mass spectrometers all used magnetic lensing.

Thanks

Redbelly98
Staff Emeritus