A molecule of mass 2.0×10^-24Kg is moving along at a speed of 100±10 m/sec, where the ±10 m/sec is the statistical spread or uncertainty in the determination of its velocity or ∆v = 10 m/sec. The molecule is somewhat localized in space and is described by a travelling wave packet solution to the Schrödinger equation centered around x=0 at t=0 and moving in the positive x-direction.

1. What is the minimum statistical spread or uncertainty ∆x in the determination of its position?
2. What is the de Broglie wavelength of this molecule?
3. Determine the frequency f of this travelling wave packet.
4. Does the frequency f in part d) satisfy the relation λf = v with the given central value of v=100 m/s? Show your calculation.
5. Suppose this electron has a wavefunction given at time t=0 by Ψ(x,0) = Asin((2π/λ)x). What is the probability density at x=λ/4? (Write your answer in terms of A and λ.)

(a) Calculate the speed of an electron that is in the n = 1 orbit of a hydrogen atom, and give your answer v as a fraction of the speed of light in empty space c, for example, v = 0.5 if the answer were v = c/2 = 1.50 × 108 m/s. (It isn’t.)

(b) How many nanometers would be the wavelength of the photon emitted when the electron in a hydrogen atom jumps from the n = 3 orbit to the n = 2 orbit? This is the Hα line, and its light is scarlet, the color of fresh human blood.

(c) How many nanometers would be the wavelength of the photon emitted when the electron in a hydrogen atom jumps from the n = 2 orbit to the n = 1 orbit?

(d) How many nanometers would be the wavelength of a photon that would have the minimum amount of energy needed to ionize any hydrogen atom? (Hint: Electromagnetic radiation with this wavelength or shorter is called extreme ultraviolet radiation.

(e) How many electron-volts (eV) would the electron in part (7)(d) need to have?

A Geiger tube consists of two elements, a long metal cylindrical shell and a long straight metal wire running down its central axis. Model the tube as if both the wire and cylinder are infinitely long. The central wire is positively charged and the outer cylinder is negatively charged. The potential difference between the wire and the cylinder is 1.10 kV. Suppose the cylinder in the Geiger tube has an inside diameter of 3.64 cm and the wire has a diameter of 0.452 mm. The cylinder is grounded so its potential is equal to zero.

(a) What is the radius of the equipotential surface that has a potential equal to 545 V? Is this surface closer to the wire or to the cylinder?

(b) How far apart are the equipotential surfaces that have potentials of 195 and 245 V?

(c) Compare your result in Part (b) to the distance between the two surfaces that have potentials of 685 and 730 V, respectively.

What does this comparison tell you about the electric field strength as a function of the distance from the central wire?

Let p1,p2 denote the probability that a randomly selected male and female, respectively, has allergy to nuts. Let n1,n2 be the sample size of a random sample for male and female, respectively. Assume two samples are indepedent. Let X1,X2 be the number of male and female who have allergy to nuts in the random sample, respectively.

(1) For parameters p1,p2, and p1−p2, find one unbiased estimator for each of them. And show why they are unbiased.

(2)Derive the formula for the standard error of those estimators in (1). Note that V(X−Y)=V(X)+V(Y) for two independent rv's X,Y.

(3)For given samples, let n1=100,n2=150,x1=5,x2=9. Compute the the value of those estimators in (1).

4) For given samples, let n1=100,n2=150,x1=5,x2=9. Compute the estimated standard errors of those estimators in (2)

1.

Rock Valley Airport is beginning to experience flight congestion and backups on the one runway that is used exclusively for landings. A plane can land and be cleared in 7.3 minutes on average. Planes waiting to land are asked to circle the airport.

On average 4.6 planes arrive at the airport per hour. What is the utilization-factor U of this runway? (Two decimal places.)

2.

Rock Valley Airport is beginning to experience flight congestion and backups on the one runway that is used exclusively for landings. A plane can land and be cleared in 7.6 minutes on average. Planes waiting to land are asked to circle the airport.

On average 3.9 planes arrive at the airport per hour. Assume system V=1.

On average, how many minutes do planes circle the airport waiting for clearance to land?

(Hint: this is the WT. Use WT = V*U*PT. Get U using the same procedure for the last questsion. The V factor is almost always assumed to be 1. The procedure is similar to the face painting example in the lecture.)

Read and print parallel array - How can this be made to read parallel arrays and then print them?

The program presented here is intended to read from the text file and build parallel arrays. Then it will print as shown. The first line will not be stored in the array. The second line will be stored in firstArray[] and the third line will then be stored in secondArray[] and the arrays will repeat until the file is read.

begin external text file:

lineone

linetwo

line three

linefour

line five

begin program code:

ifstream infile;
string filname;
string line;
int i = 0;
cout << "Enter file name: ";
cin >> filname;
infile.open(filname.c_str());
getline(infile, line);

infile >> line; // first line
infile.ignore(20, '\n');
  
while (infile && i < 5)
{
i++;
getline(infile, firstArray[i]);
getline(infile, secondArray[i]);
}

string w;
string v;
w = firstArray[0];
v = secondArray[0];

cout << "*" << w << v << "*" << endl;
cout << "*" << firstArray[0] << "*" << endl;
cout << line << endl;

write the MATLAB code for: Let ? = sin2 (?) and ? = sin(?) cos(?). Let x vary from 0 to 10? in increments of 0.1?. Plot two figures part a & b. This panel has rows, one figure per row. a. Plot x versus y. This plot is on the top of panel and the next figure (part b) is at bottom of panel. i. Give a meaningful title to this figure. ii. x-axis is time with unit of s. y-axis is voltage with unit of V. Label both x- and yaxis. iii. Add a legend to the graph. b. Plot x versus z. This figure is at bottom row. i. Give a meaningful title on graph. ii. Label x-axis is time with unit of s. y-axis is voltage with unit of V. Label both xand y- axis. iii. Change the thickness of this curve. Use any value other than default value. iv. Change curve to red dashed curve. v. Add a legend to the graph.

1. For the following C statement, write the corresponding RISC-V assembly code. Assume that the C variables a, b, and c, have already been placed in registers x10, x11, and x12 respectively. Use a minimal number of RISC-V assembly instructions. a = b + (c − 2);

2. Write a single C statement that corresponds to the two RISC-V assembly instructions below. add e, f, g add e, h, e

3. Assume that registers x5 and x6 hold the values 0xA000000000000000 and 0x2000000000000000, respectively.

(1) What is the value of x30 for the following assembly code? add x30, x5, x6

(2) For the contents of registers x5 and x6 as specified above, what is the value of x30 for the following assembly code? sub x30, x5, x6

(3) For the contents of registers x5 and x6 as specified above, what is the value of x30 for the following assembly code? add x30, x5, x6 add x30, x30, x6

1. Solve the following questions in excel using the skills from class.

1. Lindner is considering an investment with an initial cost of $122,400 and salvage value of 63,600 with the following cash flows over the next 6 years:

The discount rate is 14.8%. Find the NPV and IRR, what is the decision and what was the criteria for each rule?

2. You want to analyze the impact of a new project that will cause its cash flows to increase 12,000 over last year’s, and continue to grow at a constant rate of 7% per year for the foreseeable future. The discount rate is 13.5%. Analyze the project in three ways:
   1. Calculate the NPV and IRR of this project based on an initial investment cost of $97,000 and the change in cash flows each year, assuming the growth continues forever.
   2. Find the NPV and IRR of this project if the project only generates cash flows for 17 years.
   3. Use an embedded function in Excel to calculate the NPV of the project if the cash flows had zero growth, and the project only generates cash flows for 35 years.

UC Inc. has predicted unlevered free cash flows (FCF) of $19,800, $21,540, $25,300, and $28,900 for the next 4 years. Find the average growth rate using the predicted values. Then, assuming the growth rate persists forever at this rate, find the present value of the terminal value. Finally, find the total enterprise value. The discount rate is 18%.

Question 4

Researchers studied four different blends of gasoline to determine their effect on miles per gallon (MPG) of a car. An experiment was conducted with a total of 28 cars of the same type, model, and engine size, with 7 cars randomly assigned to each treatment group. The gasoline blends are referred to as A,B,C, and D.The MPGs are shown below in the table

Gasoline Miles Per

Blend Gallon

A 26 28 29 23 24 25 26

B 27 29 31 32 25 24 28

C 29 31 32 34 24 28 27

D 30 31 37 38 36 35 29

We want to test the null hypothesis that the four treatment groups have the same mean MPG vs. the alternative hypothesis that not all of the means are equal.

a) Before carrying out the analysis, check the validity of any assumptions necessary for the analysis you will be doing. Write a brief statement of your findings

b) Test the null hypothesis that the four gasoline blends have the same mean MPGs, i.e., Test Ho: ua=ub=uc=ud vs. the alternative hypothesis Ha: not all the means are equal.

c) If your hypothesis test in (b) indicates a significant difference among the treatment groups, conduct pairwise multiple comparison tests on the treatment group means. Underline groups of homogeneous means.

d) Briefly state your conclusions.

( Use IBM SPSS for all calculations)