Define London dispersion forces. Draw a picture showing how London forces arise. Are London forces relatively strong or relatively weak? Explain. Although London forces exist among all molecules, for what type of molecule are they the only major intermolecular force?

Define London dispersion forces. Draw a picture showing how London forces arise. Are London forces relatively strong or relatively weak? Explain. Although London forces exist among all molecules, for what type of molecule are they the only major intermolecular force?

Which member in each pair has the stronger intermolecular dispersion forces?

$$\mathrm { CH } _ { 3 } \mathrm { CH } _ { 2 } \mathrm { CH } _ { 2 } \mathrm { Cl } \text { or } \left( \mathrm { CH } _ { 3 } \right) _ { 2 } \mathrm { CHCl }$$

For each question, select the best answer from the four alternatives.

Hexane, $\mathrm{C}_6 \mathrm{H}_{14}(\mathrm{l})$, boils at $69^{\circ} \mathrm{C}$ and heptane, $\mathrm{C}_7 \mathrm{H}_{16}(\mathrm{l})$, boils at $98^{\circ} \mathrm{C}$. Which would best account for the difference in the boiling points of these substances?

(a) London dispersion forces

(b) dipole-dipole forces

(c) hydrogen bonding

(d) all of the above

What is solvation? What factors influence the extent to which solvation occurs? Give two examples of solvation; include one that involves ion-dipole interaction and one in which dispersion forces come into play.

What is solvation? What factors influence the extent to which solvation occurs? Give 2 examples of solvation; include one that involves ion-dipole interaction and one in which dispersion forces come into play.

The total delay time $\delta \tau$ due to both modal distortion and material dispersion is given by

$$(\delta \tau)^2=\left(\delta \tau_{\text {mod }}\right)^2+\left(\delta \tau_{\text {mat }}\right)^2$$

Determine the total delay time in a $1-\mathrm{km}$ fiber for which $n_1=1.46, \Delta=1 \%, \lambda=820 \mathrm{~nm}$, and $\Delta \lambda=40 \mathrm{~nm}$.

Each week. Damien records the miles per gallon for his car, to the nearest whole number. Over a period of 10 weeks, the data are 18,17,19, 18, 18, 25, 29, 30, 26,19. He wants to arrange and summarize his data so that he can analyze It.
Damien thinks that the standard deviation is a more reliable measure of dispersion than the interquartile range. Is he correct? Explain.

Waveguide dispersion is measured in a silica fiber at various wavelengths using laser diode sources with a spectral width of $2 \mathrm{~nm}$. The results are

a. Plot the waveguide parameter $M^{\prime}$ versus $\lambda$ in the range $0.70$ to $1.70 \mu \mathrm{m}$. b. Determine the waveguide dispersion in $\mathrm{ps} / \mathrm{km}$ at $\lambda=1.27$ and $1.55 \mu \mathrm{m}$ for a source with a spectral width of $1 \mathrm{~nm}$.

The dispersed phase of a certain colloidal dispersion consists of spheres of diameter 1.0 $\times$ 102 nm.

(a) What are the volume $(\text{V} = \dfrac{4}{3}\pi\text{r}^3)$ and surface area $\text{(A} = 4\pi\text{r}^2)$ of each sphere?

(b) How many spheres are required to give a total volume of 1.0 cm$^3$? What is the total surface area of these spheres in square meters?

True or False: When comparing two populations, the larger the standard deviation, the more dispersion the distribution has, provided that the variable of interest from the two populations has the same unit of measure.

Solutes in an aquifer are transported by two separate mechanisms. The process by which a solute is transported by the bulk motion of the flowing groundwater is called advection. In addition, the solute is spread by small-scale fluctuations in the groundwater velocity along the tortuous flow paths within individual pores, a process called mechanical dispersion. The one-dimensional form of the advection-dispersion equation for a nonreactive dissolved solute in a saturated, homogeneous, isotropic porous medium under steady, uniform flow is

$$c_t+v c_x=D c_{x x}, \quad 0<x<L, \quad t>0,$$

where $c(x, t)$ is the concentration of the solute, $v$ is the average linear groundwater velocity, $D$ is the coefficient of hydrodynamic dispersion, and $L$ is the length of the aquifer. Suppose that the boundary conditions are

$$c(0, t)=0, \quad c_x(L, t)=0, \quad t>0$$

and that the initial condition is

$$c(x, 0)=f(x), \quad 0<x<L,$$

where $f(x)$ is the given initial concentration of the solute.

Let $v=1, D=0.5, L=10$, and $f(x)=\delta(x-3)$, where $\delta$ is the Dirac delta function. Using the solution found in the previous part, plot $c(x, t)$ versus $x$ for several values of $t$, such as $t=0.5,1,3,6$, and 10. Also plot $c(x, t)$ versus $t$ for several values of $x$. Note that the number of terms that are needed to obtain an accurate plot depends strongly on the values of $t$ and $x$.

Light containing a mixture of two wavelengths, 500 and $600 \mathrm{~nm}$, is incident normally on a diffraction grating. It is desired $(1)$ that the first and second maxima for each wavelength appear at $\theta \leq 30^{\circ}$, $(2)$ that the dispersion be as high as possible, and $(3)$ that the third order for the $600 \mathrm{~nm}$ light be a missing order. What is the largest order of maxima produced by the grating?

Light containing a mixture of two wavelengths, 500 and 600 nm, is incident normally on a diffraction grating. It is desired (1) that the first and second maxima for each wavelength appear at θ ≤ 30°, (2) that the dispersion be as high as possible, and (3) that the third order for the 600 nm light be a missing order. (a) What should be the slit separation? (b) What is the smallest individual slit width that can be used? (c) For the values calculated in (a) and (b) and the light of wavelength 600 nm, what is the largest order of maxima produced by the grating?