Beam of electrons moving in a circle in a
Teltron tube, due to the presence of a
magnetic field. Purple light is emitted along the electron path, due to the electrons colliding with gas molecules in the bulb. The masstocharge ratio of the electron can be measured in this apparatus by comparing the radius of the purple circle, the strength of the magnetic field, and the voltage on the electron gun. The mass and charge
cannot be
separately measured this way—only their ratio.
The masstocharge ratio (m/Q) is a physical quantity that 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 spectroscopy, cosmology and mass spectrometry.^{[1]} The importance of the masstocharge ratio, according to classical electrodynamics, is that two particles with the same masstocharge ratio move in the same path in a vacuum when subjected to the same electric and magnetic fields. Its SI units are kg/C.
Some fields use the chargetomass ratio (Q/m) instead, which is the multiplicative inverse of the masstocharge ratio. The 2014 CODATA recommended value for an electron is ^{e}⁄_{me} = 7011175882002400000♠1.758820024(11)×10^{11} C/kg.^{[2]}
Contents

Origin 1

Symbols and units 2

Mass spectrometry and m/z 2.1

History 3

Chargetomass ratio 4

Significance 4.1

The electron 4.2

Zeeman Effect 4.3

See also 5

References 6

Bibliography 7

External links 8
Origin
When charged particles move 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} = m \frac{\mathrm{d}\mathbf{v}}{\mathrm{d}t}


(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 "masstocharge 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.^{[1]}
Combining the two previous equations yields:

\left(\frac{m}{Q}\right)\mathbf{a} = \mathbf{E}+ \mathbf{v} \times \mathbf{B}.
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 masstocharge ratio is an important physical quantity in those scientific fields where charged particles interact with magnetic or electric fields.
Exceptions
There are nonclassical effects that derive from quantum mechanics, such as the Stern–Gerlach effect that can diverge the path of ions of identical m/Q.
Symbols and units
The IUPAC recommended symbol for mass and charge are m and Q, respectively,^{[3]}^{[4]} however using a lowercase q for charge is also very common. Charge is a scalar property, meaning that it can be either positive (+) or negative (−). The Coulomb (C) is the SI unit of charge; however, other units can be used, such as expressing charge in terms of the elementary charge (e). The SI unit of the physical quantity m/Q is kilograms per coulomb.
Mass spectrometry and m/z
The units and notation above are used when dealing with the physics of mass spectrometry; however, the m/z notation is used for the independent variable in a mass spectrum.^{[5]} This notation eases data interpretation since it is numerically more related to the unified atomic mass unit.^{[1]} The m refers to the molecular or atomic mass number and z to the charge number of the ion; however, the quantity of m/z is dimensionless by definition.^{[5]} An ion of 100 atomic mass units (m = 100) carrying two charges (z = 2) will be observed at m/z = 50.
History
In the 19th century, the masstocharge ratios of some ions were measured by electrochemical methods. In 1897, the masstocharge ratio of the electron was first measured by J. J. Thomson.^{[6]} By doing this, he showed that the electron was in fact a particle with a mass and a charge, and that its masstocharge ratio was much smaller than that of the hydrogen ion H^{+}. In 1898, Wilhelm Wien separated ions (canal rays) according to their masstocharge ratio with an ion optical device with superimposed electric and magnetic fields (Wien filter). In 1901 Walter Kaufman measured the increase of electromagnetic mass of fast electrons (Kaufmann–Bucherer–Neumann experiments), or relativistic mass increase in modern terms. In 1913, Thomson measured the masstocharge ratio of ions with an instrument he called a parabola spectrograph.^{[7]} Today, an instrument that measures the masstocharge ratio of charged particles is called a mass spectrometer.
Chargetomass ratio
The chargetomass ratio (Q/m) of an object is, as its name implies, the charge of an object divided by the mass of the same object. This quantity is generally useful only for objects that may be treated as particles. For extended objects, total charge, charge density, total mass, and mass density are often more useful.
Significance
In some experiments, the chargetomass ratio is the only quantity that can be measured directly. Often, the charge can be inferred from theoretical considerations, so that the chargetomass ratio provides a way to calculate the mass of a particle.
Often, the chargetomass ratio can be determined from 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 chargetomass ratio. One application of this principle is the mass spectrometer. The same principle can be used to extract information in experiments involving the Wilson cloud chamber.
The ratio of electrostatic to gravitational forces between two particles will be proportional to the product of their chargetomass ratios. It turns out that gravitational forces are negligible on the subatomic level, due to the extremely small masses of subatomic particles.
The electron
The elementary chargetoelectron mass quotient, e/m_{e}, is a quantity in experimental physics. It bears significance because the electron mass m_{e} is difficult to measure directly, and is instead derived from measurements of the elementary charge e and e/m_{e}. 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.
The 2014 CODATA recommended value is e/m_{e} = 2988824117997600000♠−1.758820024(11)×10^{11} C/kg.^{[2]} CODATA refers to this as the electron chargetomass 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 Magnetron Method: Using a GRD7 Valve (Ferranti valve), electrons are expelled from a hot tungstenwire filament towards an anode. The electron is then deflected using a solenoid. From the current in the solenoid and the current in the Ferranti Valve, e/m can be calculated.

Fine Beam Tube Method: A heater heats a cathode, which emits electrons. The electrons are accelerated through a known potential, so the velocity of the electrons is known. The beam path can be seen when the electrons are accelerated through a helium (He) gas. The collisions between the electrons and the helium gas produce a visible trail. A pair of Helmholtz coils produces a uniform and measurable magnetic field at right angles to the electron beam. This magnetic field deflects the electron beam in a circular path. By measuring the accelerating potential (volts), the current (amps) to the Helmholtz coils, and the radius of the electron beam, e/m can be calculated.^{[8]}
Zeeman Effect
The chargetomass 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:
Derivation: qvB=m*v*v/r
or q/m=v/r*B (1)
F(electric)=F(magnetic)
E*q=q*v*B
or v=E/B (2)
using equation (1) and (2),
→ q/m=E/r*B*B

\Delta E = \frac{e\hbar B}{2m}(m_{j,f}g_{J,f}m_{j,i}g_{J,i})
Here m_{j} are quantum integer values ranging from j to j, with j as the eigenvalue of the total angular momentum operator J, with^{[2]}

\mathbf{J} = \mathbf{L} + \mathbf{S}
where S is the spin operator with eigenvalue s and L is the angular momentum operator with eigenvalue l. g_{J} is the Landé gfactor, calculated as

g_J = 1 + \frac{j(j+1) + s(s+1)  l(l+1)}{2j(j+1)}
The shift in energy is also given in terms of frequency ν and wavelength λ as

\Delta E = h\Delta\nu = h c \Delta \left( \frac{1}{\lambda} \right ) = hc \frac{\Delta\lambda}{\lambda^2}
Measurements of the Zeeman effect commonly involve the use of a Fabry–Pérot interferometer, with light from a source (placed in a magnetic field) being passed between two mirrors of the interferometer. If δD is the change in mirror separation required to bring the m^{th}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 m^{th}order ring, then

\Delta\lambda = \lambda^2\frac{\delta D}{2D\Delta D}.
It follows then that

hc\frac{\Delta\lambda}{\lambda^2} = hc\frac{\delta D}{2D\Delta D} = \frac{e\hbar B}{2m}(m_{j,f}g_{J,f}m_{j,i}g_{J,i}) \ .
Rearranging, it is possible to solve for the chargetomass ratio of an electron as

\frac{e}{m} = \frac{4 \pi c}{B(m_{j,f}g_{J,f}m_{j,i}g_{J,i})}\frac{\delta D}{D\Delta D} \ .
See also
References

^ ^{a} ^{b} ^{c} IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "masstocharge ratio, m/z in mass spectrometry".

^ ^{a} ^{b} ^{c} electron charge to mass quotient. NIST Database

^ International Union of Pure and Applied Chemistry (1993). Quantities, Units and Symbols in Physical Chemistry, 2nd edition, Oxford: Blackwell Science. ISBN 0632035838. p. 4. Electronic version.

^ International Union of Pure and Applied Chemistry (1993). Quantities, Units and Symbols in Physical Chemistry, 2nd edition, Oxford: Blackwell Science. ISBN 0632035838. p. 14. Electronic version.

^ ^{a} ^{b} Compiled by A. D. McNaught and A. Wilkinson (1997). IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Oxford: Blackwell Scientific Publications.

^ J. J. Thomson (1856–1940) Philosophical Magazine, 44, 293 (1897).

^ Joseph John Thomson (1856–1940) Proceedings of the Royal Society A 89, 1–20 (1913) [as excerpted in Henry A. Boorse & Lloyd Motz, The World of the Atom, Vol. 1 (New York: Basic Books, 1966)]

^ PASCO scientific, Instruction Manual and Experimental guide for the PASCO scientific Model SE9638, pg. 1.
Bibliography

Szilágyi, Miklós (1988). Electron and ion optics. New York: Plenum Press.

Septier, Albert L. (1980). Applied charged particle optics. Boston: Academic Press.

International vocabulary of basic and general terms in metrology =: Vocabulaire international des termes fondamentaux et généraux de métrologie. International Organization for Standardization. 1993. CC.

IUPAP Red Book SUNAMCO 871 "Symbols, Units, Nomenclature and Fundamental Constants in Physics" (does not have an online version).

Symbols Units and Nomenclature in Physics IUPAP25 IUPAP25, E.R. Cohen & P. Giacomo, Physics 146A (1987) 1–68.
External links

BIPM SI brochure

AIP style manual

NIST on units and manuscript check list

Physics Today's instructions on quantities and units
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