SCIE1000 final S1 2021 PDF

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Summary

Semester 1 Final exam SCIE1000. Good for practice....

Description

Information SCIE1000 Course code and title

Theory & Practice in Science

Semester

Semester 1, 2021

Type

Online, non-invigilated assignment, under ‘take home exam’ conditions.

Technology

File upload to Blackboard Assignment

Date and time

Your assignment will begin at the time specified in the course announcements on Blackboard. You have a fixed 12-hour window from this time in which it must be completed. You can access and submit your paper at any time within the 12 hours. Even though you have the entire 12 hours to complete and submit this assessment, the expectation is that it will take students around 2 hours to complete. Note that you must leave sufficient time to submit and upload your answers.

Permitted materials

This assignment is closed book – only specified materials are permitted, listed below under Recommended materials. Ensure the following materials are available during the available time:

Recommended materials

Instructions

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The SCIE1000 lecture book, workshop activities & solutions, and your personal notes from the course are permitted (paper or electronic).

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UQ approved calculator; bilingual dictionary; phone/camera/scanner.

You will need to download the question paper included within the Blackboard Test. Once you have completed the assignment, upload a single pdf file with your answers to the Blackboard assignment submission link. You may submit multiple times, but only the last uploaded file will be graded. Ensure that all your answers are contained in your last uploaded file. You can print the question paper and write on that paper or write your answers on blank paper (clearly label your solutions so that it is clear which problem it is a solution to) or annotate an electronic file on a suitable device. Given the nature of this assessment, responding to student queries and/or relaying corrections during the allowed time may not be feasible. If you have any concerns or queries about a particular question or need to make any assumptions to answer the question, state these at the start of your solution to that question. You may also include queries you may have made with respect to a particular question, should you have been able to ‘raise your hand’ in an examination-type setting.

Who to contact

If you experience any interruptions during the allowed time, please collect evidence of the interruption (e.g. photographs, screenshots or emails). If you experience any issues during the allowed time, contact ONLY [email protected] You should also ask for an email documenting the advice provided so you can provide this as evidence for a late submission.

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Late or incomplete submissions

In the event of a late submission, you will be required to submit evidence that you completed the assessment in the time allowed. This will also apply if there is an error in your submission (e.g. corrupt file, missing pages, poor quality scan). We strongly recommend you use a phone camera to take time-stamped photos (or a video) of every page of your paper during the time allowed (even if you submit on time). If you submit your paper after the due time, then you should send details to SMP Exams ([email protected]) as soon as possible after the end of the time allowed. Include an explanation of why you submitted late (with any evidence of technical issues) AND time-stamped images of every page of your paper (eg screen shot from your phone showing both the image and the time at which it was taken). Academic integrity is a core value of the UQ community and as such the highest standards of academic integrity apply to assessment, whether undertaken in-person or online. This means:

Further important information

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You are permitted to refer to the allowed resources for this assignment, but you cannot cut-and-paste material other than your own work as answers.

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You are not permitted to consult any other person – whether directly, online, or through any other means – about any aspect of this assignment during the period that it is available.

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If it is found that you have given or sought outside assistance with this assignment, then that will be deemed to be cheating.

If you submit your answers after the end of allowed time, the following penalties will be applied to your final score due to the late submission: •

Less than 5 minutes – 5% penalty

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From 5 minutes to less than 15 minutes – 20% penalty

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More than 15 minutes – 100% penalty

These penalties will be applied unless there is sufficient evidence of problems with the system and/or process that were beyond your control. Undertaking this online assignment deems your commitment to UQ’s academic integrity pledge as summarised in the following declaration: “I certify that I have completed this assignment in an honest, fair and trustworthy manner, that my submitted answers are entirely my own work, and that I have neither given nor received any unauthorised assistance on this assignment”.

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Semester One Final, 2021

SCIE1000 Theory & Practice in Science

To answer each question you will need to use the information on Page 18 onwards. Your solutions will be marked on the correctness and clarity of your explanation and communication. Include units in your answer wherever relevant. Each question is graded on a 1–7 scale with the last part of the question being at an advanced level which must be attempted for students aiming for a grade of 6 or 7. 1. (a) As a UQ science student, you are volunteering at the local science museum to answer questions submitted via the museum web page. You have been asked to answer the following question from a primary school student: Our teacher told us that the universe started with a big bang, and then it just kept getting bigger. How did scientists figure that out??? ---BlueyTheDog24 Using only details provided on the information sheet, write a short paragraph (only three or four sentences) answering this question. Your communication style should be appropriate for the level of knowledge of a typical primary school student aged 11 to 12 years old. (3 marks)

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SCIE1000 Theory & Practice in Science

(b) Using what you have learned in the philosophy of science module of the course concerning how old theories are replaced by new ones, what can we say Hubble’s observation means for the “steady state’’ theory of the universe? Explain your answer. (2 marks)

(c) (Advanced) What is the average number of stars per cubic light-year in the observable universe? Be sure to state your assumptions. (2 marks)

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SCIE1000 Theory & Practice in Science

2. As the universe has expanded, its temperature has been decreasing with time. The figure below is a plot of the temperature T (in kelvin) as a function of time t (in gigayears, abbreviated as “Gyr”) since the Big Bang. It has been derived from the measurements of galaxy redshifts as reported in Ref. [1].

(a) Write down two of the six simple functions from the formula sheet that might provide a good fit to the data in this plot, and explain why each would be suitable. For each function, explain whether the unknown constants should be positive or negative. (2 marks)

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SCIE1000 Theory & Practice in Science

(b) The figure below shows a log-log plot of the same data as in the figure in part (a). Develop a linear equation to fit the data shown in this graph. To simplify writing your equation, let y represent the (unitless) natural logarithm of the temperature, and let x represent the (unitless) natural logarithm of the time. Make sure to explicitly write down your final result for the linear equation. (3 marks)

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SCIE1000 Theory & Practice in Science

(c) (Advanced) Using your answer from part (b), determine the best fit function for the temperature of the universe (in kelvin) as a function of time (in Gyr) since the Big Bang. For this question you can ignore the units of the constants in the model. (2 marks)

3. The figure below shows the intensity of the Cosmic Microwave Background (CMB) as a function of the frequency (colour) of the radiation. The recorded satellite data is shown as red plusses, and the best fit theoretical prediction for a temperature of T = 2.725 K as the solid blue curve. The error bars for the data are smaller than the points on the plot. The satellite data is also given in the table beside the figure (taken from Ref. [2]). Frequency (cm−1 ) 2.27 3.63 4.99 6.35 7.71 9.08 10.4 11.8 13.2 14.5 15.9 17.2 18.6 20.0 21.3

Intensity (MJy sr−1 ) 201 328 381 369 316 248 183 129 87.0 57.0 36.4 22.6 13.8 8.36 4.52

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Semester One Final, 2021

SCIE1000 Theory & Practice in Science

(a) The area under the curve of the CMB intensity spectrum is proportional to the total power of the CMB. Using an appropriate method, develop a simple estimate of the area under the solid curve, and comment on the accuracy of your technique. (3 marks)

(b) Use the trapezoidal method to calculate the area under the curve for the frequency range 2.27 cm−1 to 6.35 cm−1 . (2 marks)

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(c) (Advanced) The frequency of the peak of the CMB spectrum is directly proportional to the temperature of the universe. Based on this knowledge, speculate as to how the CMB spectrum plotted in this question would have differed several billion years ago. You will be graded only on the quality of your scientific reasoning. (2 marks)

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4. For a given temperature T , the intensity of light in the Cosmic Microwave Background (CMB) varies with the frequency (colour) of light ν according to I(ν) =

αν 3 , eβν/T − 1

where α, β are constants with numerical values α = 39.76 and β = 1.44. At present the temperature of the universe determined from the CMB is T = 2.725 K. This curve is plotted in the figure below.

(a) What are the units of α and β? Explain your answer.

(2 marks)

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SCIE1000 Theory & Practice in Science

(b) You are asked to find the frequency ν for which the intensity I(ν) = 320 MJy sr−1 . Formulate the equation that you need to solve numerically, and use Newton’s method to take one step towards the solution using ν0 = 6 cm−1 as your initial guess. You may use the fact that I ′ (ν0 ) = −19.36 MJy cm sr−1 . (3 marks)

(c) (Advanced) On the graph of I(ν) in part (a) above, graphically illustrate the first step of Newton’s method that you took in part (b), and indicate the location of the eventual solution. What would happen if you instead used a first guess of ν0 = 14 cm−1 ? Explain, and also illustrate this on the graph in part (a). (2 marks)

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SCIE1000 Theory & Practice in Science

5. In a new Galaxy Zoo [3] project, volunteers have been tasked with finding examples of collisions between two elliptical galaxies from a library of candidate images. (a) Citizen scientist Alpha identified 108 images as showing collisions, of which 74 were later confirmed by experts as true galaxy collisions. The same citizen discarded another 12842 images from the library as not showing galaxy collisions. However, from these 12842 images, experts later identified 56 that contained collisions. From this information, determine the binary classification test table for citizen scientist Alpha, and hence find their accuracy, sensitivity and specificity for finding images of galaxy collisions. (4 marks)

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SCIE1000 Theory & Practice in Science

(b) What is the actual prevalence of galaxy collisions in the library of candidate images? (1 mark)

(c) (Advanced) The goal of the project is to find as many of the valuable images of galaxy collisions as possible while minimising the time invested in classification by the experts — they really don’t want to go through all of the “test negative” images to find a significant number of missed collisions. In order to better understand the capabilities of several citizen scientists for future projects, an expert classified all of the images in the library. From this information, the sensitivity and specificity of citizen scientists Beta, Gamma, and Delta in identifying images of galaxy collisions are shown in the table. Who do you think has the best performance given the goals of the project? Justify your answer.

Beta Gamma Delta

Sensitivity 92.1% 100% 67%

Specificity 99.3% 85.4% 99.9% (2 marks)

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6. A scientist studying the universe has written the Python code below: from pylab import * def rate(z): A = 0.6 B = 0.5 C = 9.4 zdash = A*exp(-z/C) - B*z return (zdash) t0 = 0 z0 = float(input("Please enter initial value: ")) time_end = float(input("Please enter final time: ")) number_of_steps = 20 time_step = time_end/number_of_steps z = zeros(int(number_of_steps+1)) t = zeros(int(number_of_steps+1)) z[0] = z0 t[0] = t0 i = 0 print(i,z[i]) while i < number_of_steps: i = i + 1 t[i] = t[i-1] + time_step z[i] = z[i-1] + time_step*rate(z[i-1]) print(i,z[i]) The scientist knows that you have just finished SCIE1000, and so emails it to you to get some advice. You run it, and enter two numbers. It gives the following output: Please enter initial value: 0.1 Please enter final time: 10 0 0.1 1 0.3718254266066964 2 0.567233937130043 Page 14 of 20

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SCIE1000 Theory & Practice in Science

3 0.7078576294083201 4 0.8091316697378195 5 0.8821055956118914 6 0.9347074436372816 7 0.9726346885043051 8 0.9999864581494113 9 1.0197143082402373 10 1.033944716658461 11 1.0442103586631264 12 1.0516162493108738 13 1.0569592427060288 14 1.0608140584976962 15 1.063595250817454 16 1.065601867742315 17 1.067049646798249 18 1.0680942305349759 19 1.0688479096897523 20 1.069391699903605 (a) Explain what the code is doing, and what the results show. You should write a paragraph of three to five sentences. (3 marks)

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SCIE1000 Theory & Practice in Science

(b) The code and its output could be improved in many respects. Describe what you think are the two most significant improvements that could be made. Each improvement should address a broadly separate issue. (2 marks)

(c) (Advanced) A sceptic also examines the code from part (a). They claim that, since the model parameters A, B, and C are strictly speaking inaccurate, we cannot rely on the results of the model. Explain what the sceptic means by this statement, and how you might respond to defend the use of the model. (2 marks)

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Extra space for answers

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SCIE1000 Theory & Practice in Science

Information about the universe Earth in the universe: The Earth is the third planet from the Sun in our solar system. It is towards the end of one of the arms of the spiral galaxy known as the Milky Way. The Milky Way is an average-sized galaxy made up of about 100 billion stars, the majority of which are thought to have their own planetary systems. There are about 125 billion galaxies in the observable universe. Light-years: Because the scale of the universe is so large, using SI base units to quantify it can be quite inconvenient. It is therefore common to make use of alternative units. The “light-year” is a unit of length used in astronomy that is abbreviated as “lyr.” One light-year is the distance that a beam of light propagating through space would travel in one Earth year. Doppler effect: The Doppler effect is a wave phenomenon that is responsible for the change in pitch of the sound of a train as it passes by you — the pitch is higher when it is coming towards you, and lower when it is moving away. A lower pitch means that the frequency is smaller, and the wavelength is larger. When light-emitting objects are moving away from an observer, they will see the light “redshifted” to longer wavelengths, as any visible light emitted would be shifted towards the red part of the spectrum. History of the universe: Before the 1920s the generally accepted model of the universe was that it was in a “steady state” — that is, it always had been and always would be much the same in any direction that astronomers looked from the Earth. However, astronomer Edwin Hubble examined the light coming from galaxies near the Milky Way, and found that galaxies further away emitted light that had a lower frequency and were hence “redder” than those nearby. Using the formula for the Doppler effect with light, he calculated the speed that the galaxies were moving away from the Milky Way by measuring their colour. Hubble found a remarkable result — he determined that all the galaxies he observed were moving away from the Milky Way, and their speed of recession was directly proportional to their distance from us! The proportionality constant is now known as the Hubble constant. Working backwards in time, this means that all of the galaxies initially exploded from a single point in space a long, long time ago! The current best theory for the evolution of the universe is known as the “Big Bang.” In this model the universe began approximately 13.7 billion years ago, exploding outwards from a point, and it has been expanding ever since. The distance from the Milky Way to the edge of the observable universe is currently 46.5 billion light-years in every direction. Cosmic Microwave Background: The Cosmic Microwave Background (CMB) is the remnant light left over from the Big Bang. It was discovered by accident in 1965 when Arno Penzias and Robert Wilson found that their radio telescope received unexpected microwave radiation from every direction in the sky. At one stage they thought it might be due to pigeon droppings on their telescope — eventually they received the Nobel Prize in Physics for their work! The early universe was very hot. At 10−43 s after the Big Bang the temperature was T = 1032 K, but it has been steadily falling with the ongoing expansion. The CMB was born around 375,000 years after the Big Bang, and initially reflected the temperature of the universe at that time: T = 5400 K. However, the continuing expansion caused the light to “stretch out” and become red-shifted so that the measured temperature is today a chilly T = 2.725 K. The intensity of light in the Cosmic Microwave Background (CMB) is predicted to vary with the

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