Cyclotron equation

The frequency of the cyclic motion of ions,m, within the cell is given by the cyclotron equation ... 

In addition to high mass resolution, another important feature of FTMS is its wide mass range (7,8). From examination of the cyclotron equation (Eq. 1), the mass range of FTMS appears to have no upper limit. However, an instrumental upper limit in excess of 100,000 has been suggested (16), based on a detailed study of ion motion (30). From a practical standpoint, the cyclotron... 

Cyclotron Equation Inverse relationship between ionic mass (m)... 

Equation 4 is the cyclotron equation, coc corresponding to the cyclotron frequency (ICR frequency). The ICR frequencies are between a few kHz and several MHz. Equation 4 indicates that all ions with the same ratio of ion charge to ion mass possess the same ion cyclotron frequency. In contrast to other mass analyzers (magnetic/electric sector field, time-of-flight (TOF), quadrupol), the ion velocity has no direct influence on the relation between the measured value and the ion mass (ICR frequencies toc in equation 4 sector field radius of deflection r for magnetic selection in equation 5 TOF flight time t). 

The cyclotron equation shows that the frequency at which an ion undergoes cyclotron motion is inversely proportional to its mass-to-charge ratio. Thus, when the cyclotron frequency is measured, m/z may be calculated. 

Equation O 50.20 is the so-called cyclotron equation, and the accelerator that is based on this principle is the classical cyclotron. The accelerating electrodes are named dees after their D-shape and usually an electrostatic deflector compensating for the bending force of the magnetic field is used to extract the beam. 

Substituting the equation for kinetic energy ( = j w v ) as solved for the ion velocity, along with the cyclotron equation as solved for [Pg.375]

Fourier transform mass spectrometry is made possible by the measurement of an AC current produced from the movement of ions within a magnetic field under ultra-high vacuum, commonly referred to as ion cyclotron motion.21 Ion motion, or the frequency of each ion, is recorded to the precision of one thousandth of a Hertz and may last for several seconds, depending on the vacuum conditions. Waveform motion recorded by the mass analyzer is subjected to a Fourier transform to extract ion frequencies that yield the corresponding mass to charge ratios. To a first approximation, motion of a single ion in a magnetic field can be defined by the equation... 

The study was subsequently extended to include the radiofluorodemetallation of organogermanium compounds31. Both fluorine-18 and 18F-acetylhypofluorite were used to displace the trimethylgermyl moiety from a series of para-substituted aryltrimethyl-germanes (equation 26). The 18F was produced in a cyclotron by bombarding Ne atoms with deuterium ions (equation 27). 

Imura and Suzuki36 have prepared labelled organotin compounds from artificial tin isotopes produced in a cyclotron. The carrier-free tin-113 radioisotope was produced by irradiating indium-115 oxide with 40-MeV protons (equation 33). 

An interesting feature of this equation is that all ions of a certain m/z have the same cyclotron frequency, independent of their velocity. Hence, energy focusing is not essential for precise determination of m/z. 

Matsson and coworkers have measured the carbon-1 l/carbon-14 kinetic isotope effects for several Menshutkin reactions (equation 35) in an attempt to model the S/v2 transition state for this important class of organic reaction. These isotope effects are unusual because they are based on the artificially-made radioactive carbon-11 isotope. The radioactive carbon-11 isotope is produced in a cyclotron or linear accelerator by bombarding nitrogen-14 atoms with between 18- and 30-MeV protons (equation 36). 

The first report of this new type of kinetic isotope effect in a Menshutkin reaction was published by Matsson and coworkers in 198744. In this study, the alpha carbon kll/ku kinetic isotope effect was measured for the Menshutkin reaction between N,N-dimethyl-para-toluidine and labelled methyl iodide in methanol at 30 °C (equation 35). The carbon-11 labelled methyl iodide required for this study was prepared from the nC atoms produced in the cyclotron in three steps45 (equation 37). 

Ion cyclotron resonance (ICR) spectroscopy has been used to determine the reaction enthalphy (A//r) of hydride-transfer reaction of silanes with various hydrocarbons having known hydride affinities (Reaction 2.19). The hydride affinities of R3Si+, D//(X3Si+—H ) = Affbase, were obtained from Equation (2.20) and are summarized in Table 2.6 [30,31]-... 

The range of applicability of equation 11.122 depends on the limits of detection of in the sample. The current maximum age attained by direct radioactivity counting is about 4 X 10" a. To measure residual radioactivity, the total carbon in the sample is usually converted to CO2 and counted in the gas phase, either as purified CO2 or after further conversion to C2H2 or CH4. To enhance the amount of counted carbon, with the same detection limit (about 0.1 dpm/g), counters attain volumes of several liters and operate at several bars. More recent methods of direct detection (selective laser excitation Van de Graaif or cyclotron acceleration) has practically doubled the range of determinable ages (Muller, 1979). 

Equations (A9) show that the electron exhibits the expected cyclotron motion in the presence of the magnetic field. However, collisions must also be taken into account. Let N(t) be the number of particles that have not experienced a collision for time t (after some arbitrary beginning time, t = 0). Then it is reasonable to assume that the rate of decrease of N(t) will be given by dN oc —Ndt = —Ndt/1. The solution of this equation is N(t) = N0 exp (—t/ ), where N0 is the total number of particles. It can easily be shown that x is simply the mean time between collisions. The probability of having not experienced a collision in time t is, of course, N(t)/N0 = exp(—t/ ). The... 

This type of mass spectrometer, which is not widely used, allows mass determination with a high precision. An ion cyclotron resonance spectrometer is basically an ion trap ions formed by electron impact, for example, are subjected to the orthogonal magnetic field B, which induces cyclotronic movement in the. rv plane (Fig. 16.8). The radius of the circular movement, which depends on kinetic energy, is given by equation (16.2). If the velocity v is small and the magnetic field B is intense, the radius of the trajectory will be small and the ions will be trapped in the ionisation... 

The gas-phase heats of formation obtained from pulsed ion cyclotron resonance (ICR) spectroscopy showed that the tertiary 1-cyclopropyl-1-methylethyl cation (20) is more stable than the 1-phenyl-1-methylethyl cation by 0.8 kcalmol 1, while the secondary 1-cyclo-propylethyl cation (18) is less stable than the 1 -phenylethyl cation by 4.8 kcal moT125. Thus a substantial reversal of the stabilization of the phenyl over cyclopropyl groups is observed. The results were also rationalized by STO-3G calculations for the isodesmic reaction involving proton transfer (equation 71). 

The proton affinities, PA (equation 44), are not determined directly from ICR (ion cyclotron resonance) spectrometry, but entropy terms were instead evaluated in SCF ab initio calculations209. These absolute PA values and those relative to ammonia, APA, are summarized in Table 27209, which also contains the theoretical proton affinities obtained at different levels of theory. 

This prototype drug208, 217, has been 11 C-labelled209 for assessment of serotonin uptake sites in depressed patients by reaction of [nC]iodomethane with desmethylcitalopram, 218, in 18-66% radiochemical yield (equation 114). 217 has been obtained also by Dan-nals and coworkers210 by reacting freshly prepared desmethylcitalopram dissolved in DMF with [nC]methyl iodide. The radiochemical yield based on [nC]CH3l was about 20% the overall radiochemical yield was about 9% based on the initial activity of [UC]CC>2 produced by 16 MeV proton irradiation of nitrogen gas in biomedical cyclotron. 

Accurate measurements of the electron affinity of simple Ge and Sn radicals have been obtained by threshold photodetachment experiments carried out in ion cyclotron resonance experiments183. In these experiments, measurement of the threshold frequency for removing the electron from the anion yields an upper limit for the electron affinity of the species, as shown for GeH3- in equation 28. 

Concerning the first field of application, the kinetics and equilibrium constants for several halide transfer reactions (equation 1) were measured in a pulsed electron high pressure mass spectrometer (HPMS)4 or in a Fourier transform ion cyclotron resonance mass spectrometer (FT-ICR)5. From measurements of equilibrium constants performed at different temperatures, experimental values were obtained for the thermochemical quantities AG°, AH° and AS° for the reaction of equation 1. The heat of formation (AH°) of any carbocation of interest, R+, was then calculated from the AH0 of reaction and the AH° values of the other species (RC1, R Cl and R +) involved. 

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