Charge-to-mass ratio

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The charge-to-mass 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 which may be treated as particles. For extended objects, total charge, charge density, total mass, and mass density are often more useful.

[edit] Significance

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 that the charge-to-mass ratio provides a way to calculate the mass of a particle.

Often, the charge-to-mass 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 charge-to-mass ratio. One application of this principle are 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 charge-to-mass ratios. It turns out that gravitational forces are comparatively negligible on the subatomic level.

[edit] The electron

The charge-to-mass ratio of an electron is commonly used for charged particles in physics and chemistry. It can be calculated experimentally or theoretically, and is simply equal to the fundamental elementary charge, $e=1.6022\times 10^{-19} C,$ divided by the electron's mass, $m_{e}= 9.109\times 10^{-31} kg.$

${e \over m}= 1.759\times 10^{11} {C \over kg}=1.759\times 10^{8} {C \over g}$

The "q/m" of an electron was successfully calculated by J.J. Thomson in 1897 and more successfully by Dunnington's Method which involves the angular momentum and deflection due to a perpendicular magnetic field.

There are two other common ways of measuring the charge to mass ratio of an electron, apart from J.J Thompson and the Dunnington Method.

1. The Magnetron Method- Using a GRD7 Valve (Ferranti valve), electrons are expelled from a hot tungsten wire 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

2. Fine Beam Tube Method- Electrons are accelerated from a cathode to a cap shaped anode. The electron is then expelled into a helium filled ray tube, producing a luminous circle. From the radius of this circle, e/m is calculated.