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Concept
Mass-to-charge ratio
Summary
The mass-to-charge ratio (m/Q) is a physical quantity relating the mass (quantity of matter) and the electric charge of a given particle, expressed in units of kilograms per coulomb (kg/C). It is most widely used in the electrodynamics of charged particles, e.g. in electron optics and ion optics.
It appears in the scientific fields of electron microscopy, cathode ray tubes, accelerator physics, nuclear physics, Auger electron spectroscopy, cosmology and mass spectrometry. The importance of the mass-to-charge ratio, according to classical electrodynamics, is that two particles with the same mass-to-charge ratio move in the same path in a vacuum, when subjected to the same electric and magnetic fields.
Some disciplines use the charge-to-mass ratio (Q/m) instead, which is the multiplicative inverse of the mass-to-charge ratio. The CODATA recommended value for an electron is Q/m =
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 flux density.
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 equations yields:
This differential equation is the classic equation of motion of a charged particle in a 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.
Official source
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