Collision cross section diameter

The mean free path is the average distance a molecule travels before colliding with another molecule. The mean free path, X, is given by X = kT/ jr2 itP). where k is Boltzmann s constant, Tis the temperature (K), P is the pressure (Pa), and cr is the collision cross section. For a molecule with a diameter d, the collision cross section is ltd2. The collision cross section is the area swept out by the molecule within which it will strike any other molecule it encounters. The magnetic sector mass spectrometer is maintained at a pressure of 10-5 Pa so that ions do not collide with land deflect) each other as they travel through the mass analyzer. What is the mean free path of a molecule with a diameter of 1 nm at 300 K in the mass analyzer ... 

Collision Cross-Section The model of gaseous molecules as hard, non-interacting spheres of diameter o can satisfactorily account for various gaseous properties such as the transport properties (viscosity, diffusion and thermal conductivity), the mean free path and the number of collisions the molecules undergo. It can be easily visualised that when two molecules collide, the effective area of the target is no1. The quantity no1 is called the collision cross-section of the molecule because it is the cross-sectional area of an imaginary sphere surrounding the molecule into which the centre of another molecule cannot penetrate. 

Stefan-Boltzmann constant, = 5.67 x 10 W/rn K ) alternative total (scattering) collision cross section rn ) collision diameter used in kinetic theory (m) differential scattering cross section rn ) surface tension N/m)... 

Figure 8.10 The growth rate of the mass median diameter is much greater for low values of Df, due to the increased collision cross section (results are for Opo = 5 nm, = 10 , T = 1500K, Pp = 2g/cm ). (After Wu and Friediander, 1993b.)...

The collision cross-section a is related to effective molecular diameters by a = nd2 so d =, a(ji)112... 

Schematic diagram of a supersonic free jet expansion. Shown below the diagram is a scale indicating distance in units of nozzle diameters, and the characteristics of the expansion at various points downstream. For this illustration, it is assumed that the reservoir pressure is 10 atmospheres of He at 300°K for the last row a collision cross section of 50 is assumed.

FIGURE 10.13. In a cx)lloidal system, the rate of particle flocculation will depend on the rate of particle collision. That rate, in turn, wiU depend on the diffusion coefficients of the respective particles and their effective particle diameters (or collision cross sections). 

In order to ensure that the target species thermalizes before impinging on the wall of the cell, it is necessary that the density of the buffer gas be large enough to allow for thermalization on a path smaller than the size of the cell. Cells are typically of order 1 cm in diameter. Assuming an elastic collision cross-section of about 10 cm between the target species and helium (an assumption accurately borne out by numerous experiments [3-6]), the minimum density required is typically 3 X 10 cm . This requirement puts a lower limit on the temperature of the buffer gas. Figure 13.3 shows the dependence of number density on temperature for He [7] and He [8] at about 1K. One can see that He can be used at temperatures as low as 180 mK and He as low as 500 mK. 

FIGURE 5.5 The two smaller bodies represent colliding molecules with an infinitely hard surface. The collision cross section, xd, also includes the larger surface with twice the diameter. 

The expanded beam from a HeNe laser at A = 3.39 p,m with lOmW power is sent through a methane cell T = 300 K, / = 0.1 mbar, beam diameter 1 cm). The absorbing CH4 transition is from the vibrational ground state (r 00) to an excited vibrational level with r 20 p,s. Give the ratios of Doppler width to transit-time width to natural width to pressure-broadened linewidth for a collision cross section CTj = 10 cm. ... 

Calculation of binary diffusion coefficients based on Eqs. (3.1.69),(3.1.71),(3.1.72) and (3.1.79) is limited because estimations of the collision cross-section of the molecules cr (and of the influence of the temperature on kinetic theory of gases. The so-called Hirschfelder equation is frequently presented in many textbooks and used in the literature, but values of parameters such as the collision diameters of the molecules and characteristic energies are needed. Instead, many authors have developed empirical relations. For non-polar gas pairs, D B.g is in good approximation (deviation <10%) given by the equation of Slattery and Bird (1958) ... 

Suppose we consider a sample of a pure gas. (We will consider gas mixtures later, briefly.) How often does any one gas particle collide with other gas particles, and how far does the particle travel between collisions We can answer these questions by considering the hypothetical situation of one gas particle moving while all other particles are stationary. As the moving particle P travels through space, it will collide with any gas particle whose center gets within 2r (twice the radius) of the center of particle P. This is illustrated two-dimensionally in Figure 19.7. In three dimensions, the path of particle P sweeps out a cylinder of space, and any other particle whose center is in that space will collide with particle P. The radius of that cylinder, which is equal to twice the radius (2r) or the diameter (d) of the particle, is called the collision diameter of the particle. In three dimensions, the cross section of this cylinder is a circle whose area is this area is called the collision cross section of the gas particle. 

To find expressions for X and z, we need a slightly more elaborate version of the kinetic model of gases. The basic kinetic model supposes that the molecules are effectively pointlike however, to obtain collisions, we need to assume that two points score a hit whenever they come within a certain range d of each other, where d can be thought of as the diameter of the molecules (Fig. 7.20). The collision cross-section, a (sigma), the target area presented by one molecule to another, is therefore the area of a circle of radius d, so O = nd. When this quantity is built into the kinetic model, we find that... 

As the moving particle travels along, it sweeps out a cylindrical volume as shown in Figure 9.19. The radius of this collision cylinder is equal to twice the radius of the molecules and is equal to d. We call d the collision diameter. The cross-sectional area of the collision cylinder is called the collision cross section... 

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