Consider a pair of molecules: They have an energy (u) that is a function of their...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Consider a pair of molecules: They have an energy (u) that is a function of their distance (r). There are two possibilities for this function: a. u= 0.0073 +12 0.41 b. u 2.5 exp(-0.68r2) Here, u is in zepto-Joules [zJ], whilst r is in nano-meters [nm]. In the vicinity of r = 1.0, formulate a Taylor Series for each of these functions: Specifically, present the first-order and second-approximations in terms of r (as such, invoke an intermediate variable here). Then employing Python, prepare the appropriate graph for each of these (there will be two graphs in total). Each graph should have the exact function, together with its first-order and second-order approximations. Except for lines for the functions themselves, also have symbols that emphasize r = 0.6 and r = 0.8; use the options for dashed or dotted lines, for diamond or square symbols, etc. Also, make sure that you display a legend. Ultimately in each case, discuss which approximation you recommend for r = 0.6 and r = 0.8 (just based on their appearance on the graph). Consider a pair of molecules: They have an energy (u) that is a function of their distance (r). There are two possibilities for this function: a. u= 0.0073 +12 0.41 b. u 2.5 exp(-0.68r2) Here, u is in zepto-Joules [zJ], whilst r is in nano-meters [nm]. In the vicinity of r = 1.0, formulate a Taylor Series for each of these functions: Specifically, present the first-order and second-approximations in terms of r (as such, invoke an intermediate variable here). Then employing Python, prepare the appropriate graph for each of these (there will be two graphs in total). Each graph should have the exact function, together with its first-order and second-order approximations. Except for lines for the functions themselves, also have symbols that emphasize r = 0.6 and r = 0.8; use the options for dashed or dotted lines, for diamond or square symbols, etc. Also, make sure that you display a legend. Ultimately in each case, discuss which approximation you recommend for r = 0.6 and r = 0.8 (just based on their appearance on the graph).
Expert Answer:
Answer rating: 100% (QA)
Answer To formulate the Taylor series approximations for each function lets consider the firstorder and secondorder expansions around r 1 Well introduce an intermediate variable x r r to simplify the ... View the full answer
Related Book For
Posted Date:
Students also viewed these programming questions
-
CANMNMM January of this year. (a) Each item will be held in a record. Describe all the data structures that must refer to these records to implement the required functionality. Describe all the...
-
re Regular Languages and Finite Automata (a) Let L be the set of all strings over the alphabet {a, b} that end in a and do not contain the substring bb. Describe a deterministic finite automaton...
-
Outline suggestions to make observation a useful, reliable requirements elicitation technique.
-
Jackson Corporation prepared the following book income statement for its year ended December 31, 2013: For tax: Seven-year MACRS property for which the corporation made no Sec. 179 election in the...
-
What will be the effect of placing a perforated drainage pipe in the capillary fringe zone just above the water table in a wet soil? Explain in terms of water potentials.
-
Jack DeCoster owned Quality Egg, LLC, an Iowa egg production company. Jacks son, Peter DeCoster, served as the companys chief operating officer. Jack also owned and operated several egg production...
-
Palisade Creek Co. is a merchandising business that uses the perpetual inventory system. The account balances for Palisade Creek Co. as of May 1, 2019 (unless otherwise indicated), are as follows:...
-
a. Write a story problem for the expression 6 x b. Find the value of the expression. Show or explain your work. da f
-
a. The unadjusted balance of the supplies account was $12,000. At the end of the month, unused supplies of $2,500 remained. What will be the value of the adjusting entry journal related to supplies?...
-
Explain why a monopolistically competitive firm should be operating below the minimum efficient scale.
-
Facts: Elon Musk and Shelon Musk (not related, just a weird coincidence) are the two individual shareholders of Talker, Inc. ("TALKER"), a Delaware corporation that operates a social media platform...
-
Do you think that NGOs provide a net benefit to international society or not? Provide examples to support your argument.
-
Suppose that firms production function is Q=min {2K, 4L}, and r=8$ and w=16$. Find the firms long-run total cost and average cost in terms of output.
-
1.Explain how permanent increase in national real money demand functions affects real and nominal exchange rates in the long run. 2.A new government is elected and announces that once it is...
-
A square room has 3 mirrored walls of length L with one side missing. A laser is fired from the center of the open side of the room with an angle of incidence, I, toward the wall on the right. If the...
-
$10,000 was borrowed at 3.5% on July 17. The borrower repaid $5000 on August 12, and $2000 on September 18. What final payment is required on November 12 to fully repay the loan?
-
Why does helium, released into the atmosphere, eventually disappear into space?
-
Suppose that the three balls shown in Exercise 19 start simultaneously from the tops of the hills. Which one reaches the bottom first? Explain.
-
Is it possible to wholly convert a given amount of mechanical energy into thermal energy? Is it possible to wholly convert a given amount of thermal energy into mechanical energy? Cite examples to...
-
Which ONE of the following statements about the Type II error is INCORRECT? A. The Type II error is the probability of rejecting the null hypothesis when it is true. B. The Type II error is the...
-
When calculating the required sample size for a twogroup superiority RCT with a binary outcome which of ONE of the following pieces of information is NOT required? A. The probability of a Type I...
-
Which ONE of the following statements about the Type I error is INCORRECT? A. The Type I error is the probability of rejecting the null hypothesis when it is true. B. The Type I error is the...
Study smarter with the SolutionInn App