Mass-to-charge Ratio - Origin

Origin

When charged particles move in electric and magnetic fields the following two laws apply:

		(Lorentz force law)
		(Newton's second law of motion)

where F is the force applied to the ion, m is the mass of the particle, a is the acceleration, Q is the electric charge, E is the electric field, and v × B is the cross product of the ion's velocity and the magnetic field.

This differential equation is the classic equation of motion for charged particles. Together with the particle's initial conditions, it completely determines the particle's motion in space and time in terms of m/Q. Thus mass spectrometers could be thought of as "mass-to-charge spectrometers". When presenting data in a mass spectrum, it is common to use the dimensionless m/z, which denotes the dimensionless quantity formed by dividing the mass number of the ion by its charge number.

Combining the two previous equation yields:

.

This differential equation is the classic equation of motion of a charged particle in vacuum. Together with the particle's initial conditions it determines the particle's motion in space and time. It immediately reveals that two particles with the same m/Q ratio behave in the same way. This is why the mass-to-charge ratio is an important physical quantity in those scientific fields where charged particles interact with magnetic or electric fields.