Mass-to-charge ratio

The mass-to-charge ratio, is a physical quantity that is widely used in the electrodynamics of charged particles, e.g. in electron optics and ion optics. In the majority of the scientific fields where the mass-to-charge ratio is used, (Lithography, electron microscopy, cathode ray tubes, accelerator physics, nuclear physics, Auger spectroscopy, cosmology) the notation $m/q$ or $m/Q$ is nearly universally used. In mass spectrometry the notation $m/z$ is widely used. (See mass spectrum).

History

In the 19th century the mass-to-charge ratio of some ions was measured by electrochemical methods. In 1897 the mass-to-charge ratio $m/e$ of the electron was first measured by J.J. Thomson By doing this he showed that the electron, which was postulated before in order to explain electricity, 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 1901 Walter Kaufman measured the relativistic mass incrase of fast electrons. In 1913 J.J. Thomson measured the mass-to-charge ratio of ions with an instrument he called a parabola spectrograph [http://web.lemoyne.edu/~giunta/canal.html. Today, an instrument that measures the mass-to-charge ratio of charged particles is called mass spectrometer.

Symbols & Units

The official symbol for mass is $m$ . The official symbol for electric charge is $Q$ . However, $q$ is also very common. Therefore the official symbol for the mass-to-charge ratio is $m/Q$ or $m/q$ .

The SI unit of the physical quantity $m/q$ is kilogram/coulomb (kg/C).

^*= kg/C

In most fields dealing with particles it is much more common to use the atomic mass unit u (the former amu) or its synonym dalton, Da, and the elementary charge unit $e$ , whereby the unit of the mass-to-charge ratio becomes u/e or Da/e.

^*= u/e = Da/e

Cooks and Rockwood proposed the unit thomson (Th) for the mass-to-charge ratio:

1 Th

1 u/e

1 Da/e.

For example, for the ion C₇H₇²⁺, $m/q$ = 45.5 Th or $m/q$ = 45.5 Da/e

In mass spectrometry the notation $m/z$ is often used. (see Mass spectrum)

Origin

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

\mathbf{F} = q (\mathbf{E} + \mathbf{v} \times \mathbf{B}),

(Lorentz force law)

\mathbf{F}=m\mathbf{a}

(Newton's second law of motion)

where F is the force applied to the ion, m is the mass of the ion, a is the acceleration, q is the ionic charge, E is the electric field, and v x B is the vector cross product of the ion velocity and the magnetic field

Using Newton's third law of motion yields:

(m/q)\mathbf{a} = \mathbf{E}+ \mathbf{v} \times \mathbf{B}

This differential equation is the classic equation of motion of charged particles in vacuum. Together with the particles initial conditions it completely determines the particles motion in space and time. It immediately reveals that two particles with the same physical quantity m/q behave exactly the same. This is why mass-to-charge ratio is an important the physical quantity in those scientific fields where charged particles (represented by their mass m and their charge q) interact with magnetic (B) or electric (E) fields.

classic books on optics of charged particles

Electron and Ion Optics by Miklos Szilagyi, Plenum Press, ISBN 0-306-42717-6.: This book about ion optics and electron optics uses m for mass, Q for charge, and m/Q for the mass-to-charge ratio.

Introduction into optics of charged particles by J. Grosser, Teubner, ISBN 3-519-03050-0.: This book about particle optics uses m for mass, q for charge, and m/q for the mass-to-charge ratio.

Applied charged particle optics, edited by A. Septier, Academic Press, ISBN 0-12-014574-X.: This book uses m for mass, Q for charge, and m/Q for the mass-to-charge ratio.

References

Cooks, R. G. and A. L. Rockwood (1991). "The 'Thomson'. A suggested unit for mass spectroscopists." Rapid Communications in Mass Spectrometry 5(2): 93. PDF
NIST on units and manuscript check list
Physics Today's instructions on quantities and units
International Vocabulary of Basic Terms in Metrology (Second edition 1993: ISBN 92-67-01075-1); a guide whith contributions of the following organizations: IUPAP, IUPAC, ISO, OIML, IEC, IFCC.
IUPAP Red Book SUNAMCO 87-1 "Symbols, Units, Nomenclature and Fundamental Constants in Physics" (does not have an online version).
Symbols Units and Nomenclature in Physics IUPAP-25 IUPAP-25, E.R. Cohen & P. Giacomo, Physics 146A (1987) 1-68.
AIP style manual

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