Electron charge to mass ratio

The charge and mass of an electron are often denoted by the letters e and m, respectively. In 1897, J. J. Thomson calculated the e/m ratio for an electron, and for this he was awarded a Nobel prize in 1905. In this activity, you will follow in Thomson s footsteps and determine the charge to mass ratio of an electron. 

In an electromagnetic tube, electrons are produced by a hot filament. Electrons are emitted from the surface of the filament in a process known as thermionic emission. 

Normally an electron beam is invisible to the human eye. However, when the electromagnetic tube contains a low-pressure gas that ionizes upon collision with an electron (emitting light when the ion recombines), the path of the electron beam can be seen. 

The velocity, v, of an electron with mass, m, that has been accelerated by a voltage, V, is given by the following equation. 

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The transition between the two centuries also saw the discovery and development of two concepts essential to the further development of the understanding of soil chemistry. One was the discovery by J. J. Thomson of the electron, a subatomic particle. This work occurred around 1897 and culminated in the determination of the electron charge-to-mass ratio, which made it possible to develop the idea of ions [21], This was basic to the concept of ions discussed and developed by Svante Arrhenius in a series of lectures given at the University of California at Berkeley in 1907 [22], In this series of lectures, he clearly describes ions of hydrogen and chlorine. The basic idea of a hydrogen ion and its application to enzyme chemistry would be further developed by S. Sorenson [13],... 

FIGURE 1.8 Thomson s apparatus to measure the electron charge-to-mass ratio, e/rOe. Electrons (cathode rays) stream across the tube from left to right. The electric field alone deflects the beam down, and the magnetic field alone deflects it up. By adjusting the two field strengths, Thomson could achieve a condition of zero net deflection. (( indicates the length of the deflection plates.)... 

The more penetrating P-rays were easily studied. In 1899 their direction of deflection in a magnetic field was observed, indicating the negative charge. Then Becquerel was able to deflect P-rays in electric and magnetic fields and thereby deterrnined the charge-to-mass ratio. This ratio showed that the mass was much smaller than that of any atom and corresponded to that of electrons. 

Thomson s momentous discovery of the electron 100 years ago this year is a story familiar to anyone who has enrolled in an undergraduate chemistry course. His experiments with cathode-ray tubes allowed him to determine the charge-to-mass ratio of the electron—with a mass some 1,000 times less than the smallest particle previously found—and to establish that it was a component of all matter. Thus Thomson earned a place in the annals of physics—and the honor of a centenary. We might also, however, take note of another contribution Thomson made, one that is not so widely known. 

What is the equation for the charge to mass ratio (e/m) in terms of the voltage (V), current (/), constant (k), electron travel radius (r), coil radius (R), and number of coil turns (/V) Use this equation and the fact that the e/m ratio will be a constant to answer questions 2-4. 

Walter Kanfmarm also reported the determination of the charge-to-mass ratio of cathode rays (abont 10 emu g- ) in a paper he submitted in April 1897 (7). Kanfmarm also based his result on magnetic deflection measurements however, he concluded that the hypothesis of cathode rays as emitted particles could not explain his data. (One of the outstanding questions in the study of cathode rays in the late 1890s was whether they were particles or electromagnetic waves. Thomson and Kanfmarm were typical of their coimtrymen most British researchers leaned toward the particulate hypothesis and most Germans toward waves.) Today Kanfmarm is better known for his careful measurements of the velocity-dependent mass of the electron published over several years beginning in 1901 these results were later explained by special relativity. 

The stationary sedimentation velocity of a particle is an experimentally accessible quantity for some systems, so item 4 summarizes much of our interest in sedimentation. Unfortunately, it is the ratio (m/f) rather than m alone that is obtained from sedimentation velocity in the general case of particles of unspecified geometry. The situation is comparable to the result of the classical experiment of J. J. Thomson in which the charge-to-mass ratio of the electron was determined. 

Measured the charge-to-mass ratio for a beam of electrons... 

By carefully measuring the amount of deflection caused by electric and magnetic fields of known strength, Thomson was able to calculate the ratio of the electron s electric charge to its mass—its charge-to-mass ratio, e/m. The modern value is... 

With the voltage on the plates and the mass of the drops known, Millikan was able to show that the charge on a given drop was always a small whole-number multiple of e, whose modern value is 1.602 176 X 10-19 C. Substituting the value of e into Thomson s charge-to-mass ratio then gives the mass m of the electron as 9.109 382 X 10-28 g ... 

Anomalous electron moment correction Atomic mass unit Avogadro constant Bohr magneton Bohr radius Boltzmann constant Charge-to-mass ratio for electron Compton wavelength of electron... 

The determination of the g factor thus requires a measurement of the Larmor and the cyclotron frequency. The electrons cyclotron frequency may conveniently be replaced by w /u> x w, where uj, is the ions cyclotron frequency. This is of advantage because the cyclotron frequency of the ion and the Larmor precession frequency can measured at the same particle. The ratio ujec/ujlc is the charge to mass ratio of the ion to the electron. For the case of Carbon it has been determined in Penning trap experiments by van Dyck and coworkers [16],... 

CPT invariance is a fundamental property of quantum field theories in flat space-time which results from the basic requirements of locality, Lorentz invariance and unitarity [1,2,3,4,5]. A number of experiments have tested some of these predictions with impressive accuracy [6], e.g. with a precision of 10-12 for the difference between the moduli of the magnetic moment of the positron and the electron [7] and of 10-9 for the difference between the proton and antiproton charge-to-mass ratio [8],... 

J. J. Thomson Plum pudding model charge-to-mass ratio of electron Work with cathode rays discovered the positive and negative nature of the atom also determined the charge-to-mass ratio for electrons... 

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