Molecules, number crossing unit area

The beam intensity is given by / = ni v, the incident number of molecules 1 per unit area per unit time. The nt, n2, are particle number densities. The total cross section Q12 = Qn(vn) has units of area it is a function of the relative speed, vn, which in this case is given by v. 

For molecules in three-dimensional random motion, the number of molecules striking a unit area per unit time is Nc. If X is the average distance from the control surface at which the molecules crossing the x surface originated, then the left-to-right flux of painted molecules is cN (x - X), while the right-to-left is cN (x -f X). 

The membrane viscometer must use a membrane with a sufficiently well-defined pore so that the flow of isolated polymer molecules in solution can be analyzed as Poiseuille flow in a long capillary, whose length/diameter is j 10. As such the viscosity, T, of a Newtonian fluid can be determined by measuring the pressure drop across a single pore of the membrane, knowing in advance the thickness, L, and cross section. A, of the membrane, the radius of the pore, Rj., the flow rate per pore, Q,, and the number of pores per unit area. N. The viscosity, the maximum shear stress, cr. and the velocity gradient, y, can be calculated from laboratory measurements of the above instrumental parameters where Qj =... 

This distance is often called the mean free path. As we can see, it is inversely proportional to the number of particles per unit volume, or the density, and inversely proportional to the collision cross section. The mean free path is most commonly discussed for the ordinary elastic collisions of two molecules in a gas. For such collisions, the collision cross sections come out of the order of magnitude of the actual cross sectional areas of the molecules that is, of the order of magnitude of... 

It may be expected that on the average molecules crossing the plane 2 = 21 from the 21 — I side will transfer the property ipzi-i and those crossing from the 2i +1 side will transfer the property ipzi+i- Hence, Fz = T (V )mUi- — r > )m zi+i, where Fz- -i denotes the number of molecules per unit area per second crossing the plane 2 = 21 from the 21 — / side and Fz +i denotes the number of molecules per unit area per second crossing the plane 2 = 21 from the 2i + / side. 

Stability), the area per molecule is determined by the cross-sectional area of the sulphate group, which is in the region of 0.4 mn With nonionic surfactants consisting of an alkyl chain and a poly(ethylene oxide) (PEO) head group, adsorption onto a hydrophobic surface is determined by the hydrophobic interaction between the alkyl chain and the hydrophobic surface. For the vertical orientation of a monolayer of surfactant molecules, the area per molecule will depend on the size of the PEO chain, which is in turn directly related to the number of ethylene oxide (EO) units in the chain. If the area per molecule is smaller than that predicted from the size of the PEO chain, the surfactant molecules may associate on the surface to form bilayers and hemimicelles (as discussed in detail in Chapter 5). This information can be related directly to the stability of the suspension. 

For a wavelength interval dA, the photodissociation coefficient of molecule A is proportional to the actinic flux qvdA, the absorption cross section photodissociation quantum efficiency ca(A). The actinic flux q dA represents the number of photons per unit area and... 

All molecules within a distance u of a given unit cross-sectional area will cross that area in unit time (see Figure 11.10). The number of molecules in that volume is cv, which is therefore the flux J ... 

How many molecules pass the base, 1 m, of the parallelepiped in Fig. 30.2 in unit time If all the molecules were moving downward with an average velocity , then each travels a distance dt in the time interval dt. Therefore all the molecules in the parallelepiped of height dt will pass the bottom face in the interval dt. The volume of the parallelepiped is dt m if N is the number of molecules per cubic metre, then the number crossing the base in dt is iV dt. In unit time the number crossing 1 m area is... 

Consider the diffusion system illustrated in Fig. lA. Assume that the cross section A is a unit area and consider a layer of thickness dx. Taking the concentration in that layer to be C, the number of molecules in that element equals iVC,dx where N represents Avogadro s number. Suppose that each surface, A., is readily... 

For a Maxwell-Boltzmann distribution of molecular velocities, the number of molecules of species i crossing a unit area per unit time is... 

Show that the number of molecules which cross a plane of unit area in a gas in unit time, and which have a component of velocity normal to this plane greater than a value is given by... 

Figure 3.22. Flux j is defined as the number of solute molecules that pass the cross section of a unit area in a unit time. The solute molecules in the cyhnder of height v pass the cross section in the next unit time.

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