Your Turn 10C = L, Verify that the function P (x) = A (e−(x-L)ƒ /kBT - 1) vanishes at x = solves the Smoluchowski equation with the potential Vtot (x) = fx, and resembles the curve sketched in Figure 10.12 between 0 and L. (Here A is some positive constant.) Substitute into Equation 10.3 to find that j(1d) (x) is everywhere constant and positive. dP |j (1d) = net number crossing per time == -MD + 1 dx KBT P dUtot dx). (10.3)

Verify the normalization equation 0f(v)dv=1 In doing the integral, first make substitution u=m2kBTv=vvp. This "scaling" transformation gives you all features of the answer except for the integral, which is a dimensionless numerical factor. You'll need the formula 0x2e x 2dx= 4 to find the numerical factor and verify the normalization.`

Compute |(x,t)|2 for the function (x,t)=(x)sint, where is a real constant.

Sketch the potential energy function of an electron in a hydrogen atom, (a) What is the value of this function at r=0 ? in the limit that r=? (b) What is unreasonable or inconsistent with the former result?

To obtain a more clearly defined picture of the FermiDirac distribution, consider a system of 20 FermiDirac particles sharing 94 units of energy. By drawing diagrams like Figure P10.11, show that there are nine different microstates. Using Equation 10.2, calculate and plot the average number of particles in each energy level from 0 to 14E. Locate the Fermi energy at 0 K on your plot from the fact that electrons at 0 K fill all the levels consecutively up to the Fermi energy. (At 0 K the system no longer has 94 units of energy, but has the minimum amount of 90E.) 1 Microstate8 others? One of the nine equally probable microstates for 20 FD particles with a total energy of 94E.

(a) A person’s blood pressure is measured to be 1202mmHg . What is its percent uncertainty? (b) Assuming the same percent uncertainty, what is the uncertainty in a blood pressure measurement of 80 mm He?

A photovoltaic array of (solar cells) is 10.0% efficient in gathering solar energy and converting it to electricity. If the average intensity of sunlight on one day is 70.00 W/m2, what area should your array have to gather energy at the rate of 100 W? (b) What is the maximum cost of the array if it must pay for itself in two years of operation averaging 10.0 hours per day? Assume that it earns money at the rate of 9.00 cents per kilowatt-hour.

Consider an infinite square well with wall boundaries x=0 and x=L. Explain why the function (x)=Acoskx is not a solution to the stationary Schrödinger equation for the particle in a box.

In 2011, artist Hans-Peter Feldmann covered the walls of a gallery at the New York Guggenheim Museum with 100,000 one-dollar bills (Fig. P1.48). Approximately how much would it cost you to wallpaper your room in one-dollar bills, assuming the bills do not overlap? Consider the cost of the bills alone, not other supplies or labor costs. FIGURE P1.48

A marathon runner completes a 42.188-km course in 2 h, 30 min, and 12s. There is an uncertainty of 25 m in the distance traveled and an uncertainty of 1 s in the elapsed time. (a) Calculate the percent uncertainty in the distance. (b) Calculate the percent uncertainty in the elapsed time. (C) What is the average speed in meters per second? (d) What is the uncertainty in the average speed?