D. The Balmer Series 1. When Balmer found his famous series for hydrogen in 1886, he was limited experimentally to wavelengths in the visible and near ultraviolet regions from 250 nm to 700 nm, so all the lines in his series lie in that region. a) Based on the entries in Table 2 and the transitions on your energy level diagram, what common characteristic do the lines in the Balmer series have? B) What would be the longest possible wavelength for a line in the Balmer series? λ = ___________nm C) What would be the shortest possible wavelength that a line in the Balmer series could have? Hint: What is the largest possible value of ΔE to be associated with a line in the Balmer series? λ = ___________nm The Ionization Energy of Hydrogen 1. In the normal hydrogen atom the electron is in its lowest energy state, which is called the ground state of the atom. The maximum electronic energy that an electron in a hydrogen atom can have is 0 kJ/mole, at which point it would essentially be removed from the atom and it would become a H+ ion. How much energy in kilojoules per mole does it take to ionize a hydrogen atom? ______________ kJ/mole a) The ionization energy of hydrogen is often expressed in units other than kJ/mole. What would it be in joules per atom? in electron volts per atom? (1 ev = 1.602 x 10-19 J) ______________J/atom; _____________ ev/atom

1. You want to design a pendulum for a grandfather clock so that it has a period of 2.00 seconds (so that one “tick” plus one “tock” occur during one complete period). The pendulum has a heavy 8.00-kg bob. (Throughout this problem, assume an ideal simple pendulum: the pendulum’s arm has negligible mass, the bob can be approximated as a point-mass, the initial angle of displacement is small, and there is negligible friction.)

a.) If you want the clock to be used on the surface of the Earth near sea level (where g = 9.80 m/s2 ), what length should you use for the pendulum arm? Show your work. (Note: How many significant figures should your final answer have? Watch your rounding!)

b.) Suppose that the temperature in the room gets much warmer, and the length of the pendulum’s arm expands by 2.50%. By what percentage will the pendulum’s period increase? Show your work. Express your final answer as either a decimal factor or a percentage (with appropriate sig. figs.).

c.) Which one or more of the following changes would (when considered separately and individually) increase the period of the pendulum, thereby making the clock run “slower”? Circle ALL that apply:

A. moving the pendulum to the top of a (fictitiously) high mountain where g = 9.70 m/s2

B. sticking some putty on the pendulum bob, thereby increasing its mass

C. decreasing the amplitude of the pendulum’s swings

An industrial process is using river water to cool 10⁵ kg/h of saturated steam in a heat exchanger at 0.1 bar. The cooled steam exits the heat exchanger as a saturated liquid at the same pressure of 0.1 bar to be used in the process. The river water has a volumetric flow rate of 500 ft³/s and is the coolant in the heat exchanger., having properties close to pure water (i.e., density – 1000 kg/m³). It exists the heat exchanger with the same mass flow rate, and is returned to the river, but at a higher temperature. The river water on a hot summer day is 20 ⁰C at the heat exchanger inlet, and near the mixing point of the discharged water from the heat exchanger. Operation is at steady state and kinetic and potential energy can be neglected. Since a higher river temperature results in lower dissolved oxygen there may be a risk of killing fish or even “stressing” them. For example, rainbow trout stop growing at sustained river temperatures of 73°F (23° C), and die at about 80 ⁰F (27 ⁰C). Should the owner of this industrial process be concerned for the fishes and local fisherman’s livelihood? Please comment by calculating the temperature rise of the river at the heat exchanger’s exit that discharges into the river.

Hint: properties of the saturated and compressed water can be found in tables: Table A-3 and Table A-5.

1. Anyone who plays or watches sports has heard of the “home field advantage.” Tournaments in many sports are designed to try to neutralize the advantage of the home team or player. Most people believe that teams tend to win more often when they play at home. But do they? If there were no home field advantage, the home teams would win about half of all games played. To test this, we’ll use the games in the Major league Baseball 2017 season. That year, there were 2430 regular-season games. It turns out that the home team won 1312 of the 2430 games, or 53.99% of the time. Is there strong evidence that there exists a “home field advantage?” Use a significance level of 5% to test your hypothesis.

a) Define the parameter of interest.

b) State the hypotheses statements.

c) Check that the conditions have been met and name the significance test to be used. (Note: Though we are not interested in just the 2017 season, and this is not randomly selected, it is reasonable that the sample is representative of all Major League Baseball games in the recent past and near future.)

d) Perform the test and show all work.

e) Interpret the P-value and state your conclusion.

f) Calculate and interpret a 95% confidence interval.

g) Describe what a Type I and Type II error would be in the context of this problem.

I am quantitating lead in a solution using anodic stripping Voltammetry. I am asked to use the Reagents as follows: 0.1 M KNO3 /50 mM HNO3 containing an unkown concentration of lead. For the purposes of preparing the method of standard additions, I am to assume the concentration in the container to be 1ppm. 0.1 M KNO3/50 mM HNO3 (take only what needed) 500 ppm Hg ^2+ in 0.1 M KNO3/50 mM HNO3 1000 ppm Pb and the preparation of standards and unknowns: 1. you will need to prepare a solution for your ASV analysis that contains the unkown Pb (us 2 mL of the stock Pb unkown) spiked with Hg ^2+ at a concentration of 50 ppm, diluted to a final volume of 5 mL in 0.1 M KNO3/50 mM HNO3. You should know precisely the diltuion of your Pb unkown as you will have to back calculate to your original concentration. 2. You will need to prepare a standard concentration of Pb for your additions. There is a Pb standard of 1000 ppm to be used for serial dilutions. Determine a standard concentration from your knowledge of standard additions and the fact that your unknown is near 1 ppm Pb. Check the standard concentration you determine before continuing with preparation of your solution. I don't understand how we are to back calculate to original concentration and how to prepare the standards and unkowns. PLEASE HELP!

Viewing the return rate of lost letters as a measure of social responsibility in neighborhoods, a social psychologist intentionally ‘loses’ self-addressed, stamped envelopes near mailboxes. Furthermore, to determine whether social responsibility, as inferred from the mailed return rates, varies with the type of neighborhood, lost letters are scattered throughout three different neighborhoods: downtown, suburbia, and a college campus.

Letters are ‘lost’ in each of the three types of neighborhoods according to procedures that control for possible contaminating factors, such as the density of pedestrian traffic and mailbox accessibility. (Ordinarily, the social psychologist would probably scatter equal numbers of letters among the three neighborhoods, but to maximize the generality of the current example, we will assume that a total of 200 letters were scattered as follows: 60 downtown, 70 in suburbia, and 70 on campus.) Each letter is cross classified on the basis of the type of neighborhood where it was lost and whether or not it was returned. For instance, of the 60 letters lost downtown, 39 were returned, while of the 70 letters lost in suburbia, 40 were not returned. When observations are cross classified according to two qualitative variables, as with the lost letter study, the test is a two-variable test. Answer the following.

A) Defined null and alternative hypothesis?

B) Obtain all expected frequencies from table of observed frequencies?

C) Find test statistic value?

D) Identify degrees of freedom?

E) Find the chi-squared value?

F) What is the conclusion?

1)

a) Prepare an EDTA solution by dissolving 0.1 g of magnesium chloride hexahydrate and 3.2g of EDTA in 1 L of water. Also prepare a standard calcium carbonate solution by weighing out 0.4 g of pure calcium carbonate and adding 500 mL of water and a few drops of 1:1 HCl:Water solution. Take 50mL aliquots of the standard calcium carbonate solution, add 10 mL of ammonia/ ammonia chloride buffer, and 5 drops of calmagite indicator, and titrate this with the EDTA solution. A color change occured when 47.8 mL, 48.2, and 49.0 mL of EDTA was added/ titrated to each aliquot. Determine the exact concentration of EDTA.

b) Weigh 0.18g of acid-soluble limestone and add 20 mL of 1:1 HCl:Water solution. Heat this solution to near dryness, add 10mL of 1:10 HCl: Water solution, and dilute to 100mL with water. Take a 50mL aliquot, add 5 mL of 10% hydroxylamine hydrochloride solution, 10 mL of ammonia/ ammonium chloride buffer and 5 mL of 5% potassium cyanide. Then add a few drops of calmagite indicator, and titrate with the same EDTA solution in part a. A color change occured when 50.0 mL, 48.7 mL, 49.5 mL, 49.2 mL of EDTA was added to each of these aliquots. Find the percentage of calcium carbonate in the unknown limestone sample.

A. Sustainability of Approach. To the degree job growth (and increased car sales that come from more competitive labor costs) is based on two-tier wage structures, how sustainable is this approach? Consider, for example, that Fiat and Chrysler CEO Sergio Marchionne stated that “Long term, (the system) is not a viable structure. It creates two classes of workers within the plant. It doesn’t work in the same direction we are working . . . to get this organization to work in unison.” Why would Mr. Marchionne make this statement? What are the potential drawbacks of a two-tier structure? When would we expect any such drawbacks to materialize?

B. Use of Non-GM Workers. What about the use of non-GM workers at the Chevy Sonic plant? What might Mr. Marchionne think about that approach? How do you think the UAW and the workers it represents will react to Marchionne’s plan?

C. Summarizing the Pressures. Will the two-tier wage structure go away in the near future? Summarize the pressures to eliminate it as well as the pressures to keep it. Be sure to consider labor costs and productivity of workers and plants at other companies and in other parts of the world. You may wish to do some research on the new Volkswagen plant in Chattanooga, Tennessee. Also, consider that the Automotive News estimates that the Ford Fiesta (a competitor to the Chevy Sonic) plant in Cuautitlan, Mexico may have labor costs as low as $150 per vehicle.

Consider the function f(x)=2e2sin(x). In this question, we will first use a linear approximation to estimate the value of f(0.1). Then, we will use a Taylor polynomial of degree three to estimate de value of f(0.1).

a) What is a good choice for the base point a of the linear approximation and the Taylor polynomial?

Answer: a=

b) Compute the derivative of f and evaluate it at x=a.

Answer: f′(x)=

               f′(a)=

c) The linear approximation L(x) of f(x) based at a is:

Answer: L(x)=

d) Use the linear approximation that you have found in (c) to estimate f(0.1).

Answer: f(0.1)≈    

e) Compute the second and third derivatives of f.

f′′(x)=

f′′′(x)=

f) Compute f′′(a) and f′′′(a).

f′′(a)=

f′′′(a)=

g) Find the Taylor polynomial of order three of f at the base point a.

T3(x)=

h) Use the Taylor polynomial that you found in (g) to estimate f(0.1).

Answer: f(0.1)≈   

i) Compute the error (in absolute value) of the two approximations of f(0.1) that you have found. Give your answer with an accuracy of five decimal places.

Answer: Error for the linear approximation:    

Error for the Taylor polynomial of order three:   

To appreciate the improvement in the approximation provided by the Taylor polynomial of degree three over the linear approximation, you should sketch the graph of f, L, and T3 near a.

An economist with a major bank wants to learn, quantitatively, how much spending on luxury goods and services can be explained based on consumers’ perception about the current state of the economy and what do they expect in the near future (6 months ahead).  Consumers, of all income and wealth classes, were surveyed.  Every year, 1500 consumers were interviewed.  The bank having all of the data from the 1500 consumers interviewed every year, computed the average level of consumer confidence (an index ranging from 0 to 100, 100 being absolutely optimistic) and computed the average dollar amount spent on luxuries annually.  Below is the data shown for the last 24 years.

Date                 X                     Y (in thousands of dollars)

1994                79.1                 55.6

1995                79                    54.8

1996                80.2                 55.4

1997                80.5                 55.9

1998                81.2                 56.4

1999                80.8                 57.3

2000                81.2                 57

2001                80.7                 57.5

2002                80.3                 56.9

2003                79.4                 55.8

2004                78.6                 56.1

2005                78.3                 55.7

2006                78.3                 55.7

2007                77.8                 55

2008                77.7                 54.4

2009                77.6                 54

2010                77.6                 56

2011                78.5                 56.7

2012                78.3                 56.3

2013                78.5                 57.2

2014                78.9                 57.8

2015                79.8                 58.7

2016                80.4                 59.3

2017                80.7                 59.9

Question:

1. Construct the linear regression model for the dollar amount spent on luxury goods and services.