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 appears in the scientific fields of electron microscopy, cathode ray tubes, accelerator physics, nuclear physics, Auger electron spectroscopy, cosmology and mass spectrometry.

[1] 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.

[2] When charged particles move in electric and magnetic fields the following two laws apply: 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.

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.

It immediately reveals that two particles with the same m/Q ratio behave in the same way.

Charge is a scalar property, meaning that it can be either positive (+) or negative (−).

[4] This notation eases data interpretation since it is numerically more related to the dalton.

[4] An ion with a mass of 100 Da (daltons) (m = 100) carrying two charges (z = 2) will be observed at m/z 50.

This observation may be used in conjunction with other lines of evidence to subsequently infer the physical attributes of the ion, such as mass and charge.

On rare occasions, the thomson has been used as a unit of the x-axis of a mass spectrum.

In the 19th century, the mass-to-charge ratios of some ions were measured by electrochemical methods.

The first attempt to measure the mass-to-charge ratio of cathode ray particles, assuming them to be ions, was made in 1884-1890 by German-born British physicist Arthur Schuster.

He put an upper limit of 10^10 coul/kg,[5] but even that resulted in much greater value than expected, so little credence was given to his calculations at the time.

[6] By doing this, he showed that the electron was in fact a particle with a mass and a charge, and that its mass-to-charge ratio was much smaller than that of the hydrogen ion H+.

In 1898, Wilhelm Wien separated ions (canal rays) according to their mass-to-charge ratio with an ion optical device with superimposed electric and magnetic fields (Wien filter).

In 1913, Thomson measured the mass-to-charge ratio of ions with an instrument he called a parabola spectrograph.

[7] Today, an instrument that measures the mass-to-charge ratio of charged particles is called a mass spectrometer.

In some experiments, the charge-to-mass ratio is the only quantity that can be measured directly.

Often, the charge can be inferred from theoretical considerations, so the charge-to-mass ratio provides a way to calculate the mass of a particle.

Often, the charge-to-mass ratio can be determined by observing the deflection of a charged particle in an external magnetic field.

The cyclotron equation, combined with other information such as the kinetic energy of the particle, will give the charge-to-mass ratio.

The same principle can be used to extract information in experiments involving the cloud chamber.

It also has historical significance; the Q/m ratio of the electron was successfully calculated by J. J. Thomson in 1897—and more successfully by Dunnington, which involves the angular momentum and deflection due to a perpendicular magnetic field.

Thomson's measurement convinced him that cathode rays were particles, which were later identified as electrons, and he is generally credited with their discovery.

[2] CODATA refers to this as the electron charge-to-mass quotient, but ratio is still commonly used.

There are two other common ways of measuring the charge-to-mass ratio of an electron, apart from Thomson and Dunnington's methods.

The charge-to-mass ratio of an electron may also be measured with the Zeeman effect, which gives rise to energy splittings in the presence of a magnetic field B:

The shift in energy is also given in terms of frequency υ and wavelength λ as

If δD is the change in mirror separation required to bring the mth-order ring of wavelength λ + Δλ into coincidence with that of wavelength λ, and ΔD brings the (m + 1)th ring of wavelength λ into coincidence with the mth-order ring, then