Nats 1870 Assignment 17

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NATS 1870B: Understanding Colour Assignment 1: Light Part 1 NATS 1870 B: UNDERSTANDING COLOUR Assignment 1: Light Part 1 Solutions and Marking Scheme This assignment consists of four parts: PART A: Light and the EM Spectrum (p.2) PART B: Atoms and the Nature of Matter (p.3) PART C: Blackbody Radiation (p.4-5) PART D: Spectral Analysis (p.6-7) INSTRUCTIONS: • Print the assignment, with one full page per sheet; answer all questions in pen; scan your completed assignment; upload in Moodle in electronic format AS ONE SINGLE FILE (with pages put in proper sequential order), preferably in the .pdf file format. (Do NOT submit zipped files!) • You can work together with other students on the exercises, however each student must write up and submit his/her own and unique assignment. Any plagiarism will be penalized according to the University policies. • Each assignment is worth 3% of your final grade. This assignment is due in Moodle by 11:55pm on Oct. 25 Student Name: ___________________________________________________________________ Student Number: _____________________________ Mark: Part A: /4 Part B: /4 Part C: / 11 Part D: /4 Total: 23 F-W 2013-14 Page 1 of 7 NATS 1870B: Understanding Colour Assignment 1: Light Part 1 PART A: LIGHT AND THE EM SPECTRUM / 0.5 1. In the above ‘blank’ spectrum graph, label the seven major sections of the EM spectrum according to their appropriate wavelength range. [0.5 marks] for all sections of EM spectrum labelled correctly 2. Using your answer to the previous question, fill in the table below with the correct portion of the EM spectrum (traveling in vacuum). Longest Wavelengths Highest Frequencies Highest Energies Fastest Speeds / 0.5 Radio waves Gamma rays Gamma Rays All travel at same speed [0.5 marks] for all boxes answered correctly / 0.5 3. All objects, including people, radiate some light. Why can we see each other in daytime, but we cannot see each other in total darkness? The type of light people radiate is in the infrared part of the EM spectrum, also known as ‘heat’. Our eyes are not sensitive to the infrared light, and so we cannot see this type of light (neither in the day nor in the dark). We ‘see’ objects due to visible light – the only part of the EM spectrum we are sensitive to entering our eyes, after reflecting off other objects. In the dark, there is not enough visible light reflecting off objects for us to see them. [0.5 marks] 4. Consider three types of waves: light, water and sound. What is the one fundamental difference between light and the other types of waves? Light does not need a physical medium to travel through, whereas all other types of waves do: waterwaves need water for vibrations, and sound-waves need air-molecules for vibrations. (Light is the vibrations of electric and magnetic fields.) [0.5 marks] ` wave #2 wave #3 wave #1 / 2 5. This entire wave-figure passes by you in 3 seconds. Answer the following questions based on the information contained in this wave, and explain how you obtained each answer. (A ruler will help.) [0.5 marks per each 4.5 cm correct box] / 0.5 a) How many individual wavelegths are shown? Answer: Explanation: F-W 2013-14 b) What is the wavelength of each wave? c) What is the frequency of this wave? 3 4.5 cm ± 0.5 cm 1 (wave) per second There are 3 repeating cycles shown – or, there are 3 waves. With a ruler, one can measure the length between one trough and another to be about 4.5cm There are 3 waves shown in the diagram, which passed us in 3 seconds, then the frequency is 3 waves/3 seconds, or 1 (wave)/second d) What is the speed of this wave? 4.5cm/second Speed=wavelength x frequency Speed=4.5cm x 1/second Speed= 4.5cm/second Page 2 of 7 NATS 1870B: Understanding Colour Assignment 1: Light Part 1 PART B: ATOMS AND THE NATURE OF MATTER / 0.5 6 a) Which of the two figures shown on the right correctly represents the general atomic structure of Hydrogen? Explain why. Figure B, since it shows the energy orbitals decreasing in separation as we move outward from the nucleus.[0.5 marks] / 0.5 6 b) Using the diagram from your answer in the previous question, draw the exact transition (in the correct figure) which is responsible for the red colour of the emission nebulae surrounding hot stars. [0.5 marks for sketch similar to the diagram above] 7. Absorption wavelengths (λ1 and λ2) of two different transitions in an atom are shown on the left of the image. Two energy level diagrams of this atom are shown on the right. Which energy level diagram corresponds to absorption line 1 / 1 (with wavelength λ1), and why? i n t e n s i t y 1 λ1 Energy Level Diagrams 2 λ2 λ n=5 n=4 n=3 n=5 n=4 n=3 n=2 n=2 n=1 n=1 transition A transition B Transition A (electron jumping from 1st to 2nd orbital) corresponds to the absorption line 1 (with λ1), since it shows a bigger energy jump than transition B. (We know that that shorter wavelengths correspond to higher energies, so absorption line λ1 corresponds to a more energetic transition than λ2). [1 mark] 8. The figure on the right shows 6 possible transitions / 2 in an atom. Answer the following questions, and explain your reasoning for each answer. a) Which diagram shows absorption of violet light? Answer: D Reason: out of the two absorption options (D or B), D shows a bigger orbital jump, corresponding to a more energic photon of shorter wavelength; violet is shorter-wavelength than green. b) Which diagram shows absorption of green light? Answer: B Reason: the opposite of the reason in ‘a’, since green is less energetic than violet, and ‘B’ is showing a lessenergetic orbital jump than ‘D’. c) Which diagram shows emission of blue light? d) Which diagram shows emission of orange light? Answer: C Answer: E Reason: out of the two emission options (C or E), Reason: the opposite of the reason in ‘c’, since C shows a bigger orbital jump, corresponding to a orange is less energetic than blue, and ‘E’ is more energic photon of shorter wavelength; blue is showing a less-energetic orbital jump than ‘C’. shorter-wavelength than orange [0.5 marks per each correct answer AND explanation] F-W 2013-14 Page 3 of 7 NATS 1870B: Understanding Colour Assignment 1: Light Part 1 PART C: BLACKBODY RADIATION 9 a) Compare the temperatures of a blue star and a blue jacket/coat, by using ‘order of magnitude’ estimates for temperatures of these two objects. Temperatures of blue stars are on the order of 10,000K; while temperatures of blue jackets are on the order of 300K (body temperature of about +36°C, converted to K by adding 273 round to 300K); in other words, blue stars are at least 100 times hotter than blue jackets. [0.5 marks for reasonable estimates within 1 order of magnitude of these values] b) Explain the cause of any differences in temperatures of the two blue objects above. / 0.5 The difference in these temperatures is caused by the nature of the two objects themselves. Stars are extremely hot self-luminous objects (blackbody), which generate their own light at very high temperatures (especially the blue stars). Jackets are not self-luminous objects like stars; instead we see them due to reflection of visible light that falls on them. The reason a jacket appears blue is because it reflects only the blue wavelengths in the visible light that hits it, while absorbing all other wavelengths. [0.5 marks] /1 / 0.5 10 a) Which of the three stars has the highest energy output, and why? Star B has a higher energy output, because its peak has largest height (0.5 marks for correct answer and explanation) / 0.5 10 b) Which of the three stars has the highest temperature, and why? Star A is at highest surface temperature, because it has the shortest wavelength of peak intensity (0.5 marks for correct answer and explanation) The diagram on the right shows blackbody curves of two stars. Use it to answer Questions 11-14. / 0.5 11 a) Which star (A or B) gives off more red light? _A_ b) Explain why: because it has a higher energy output at the red wavelength than star B (0.5 marks for correct answer and explanation) / 0.5 12 a) Which star (A or B) gives off more blue light? _ A _ b) Explain why: because it has a higher energy output at the blue wavelength than star B (0.5 marks for correct answer and explanation) / 0.5 13 a) What is the overall colour of star A? _ bluish _ b) What is the overall colour of star B? _ reddish _ (0.5 marks for both correct answers) 14 a) Which star (A or B) looks redder, and why? Star B looks redder because its intensity curve peaks over the reddish wavelengths, whereas star A peaks over violet-bluish wavelengths appearing bluer (0.5 marks for complete explanation) b) Which star (A or B) is at a higher surface temperature, and why? Star A has a higher surface / 0.5 temperature, because its curve peaks at a shorter wavelength than star B. (0.5 marks) / 0.5 F-W 2013-14 Page 4 of 7 NATS 1870B: Understanding Colour Assignment 1: Light Part 1 The diagram on the right shows blackbody curves of two stars. Use it to answer Questions 15-16. / 2.5 15. Using the blackbody curves for star A and C, circle the correct answer for each characteristic of the curves below. Longer wavelength of peak Lower surface temperature Looks red Looks blue Star A Star A Star A Star A Star C Star C Star C Star C Greater energy output per second Star A Star C Same Same Both Neither Both Neither 0.5 marks per each correct answer, total of 2.5 marks for question 15 16 a) Which of these stars is bigger? _A_ b) Explain why: /1 Since these stars both have the same temperature, but star A has a higher energy output than star C, then it must be because it is bigger. (Bigger  larger surface area  more photons emitted in total) Recall that the height of the curve is affected by two parameters: temperature and size of the star. (1 mark for correct answer and explanation) The diagram on the right shows blackbody curves of two stars. Use it to answer Questions 17-20. 17. For each star, describe its colour as either reddish or bluish: / 0.5 Star A: __ bluish __ Star D: __ reddish __ / 0.5 18. Which star (A or D) has a higher surface temperature, and why? Star A is hotter, because its intensity curve peaks at shorter wavelength than B (0.5 marks for correct answer and explanation) / 0.5 19. Which star (A or D) has a higher energy output per second, and why? They have the same energy output, because their peaks reach the same height (0.5 marks for correct answer and explanation) 20 a) Which of these stars is bigger? _ D _ /1 b) Explain why: Both stars have equal energy output; however star D is colder than star A. For a colder star to output as much total energy as a hotter star, the colder star (D) must be bigger than the hotter star, to ‘compensate’ for its colder temperature. Recall that the height of the curve is affected by two parameters: temperature and size of the star. (1 mark for correct answer and explanation) F-W 2013-14 Page 5 of 7 NATS 1870B: Understanding Colour Assignment 1: Light Part 1 PART D: Spectral Analysis 21. The spectral curve on the right (below) illustrates the energy output versus wavelength for an unknown star. Which of the absorption line spectra on the left (below) belongs to this unknown star? / 0.5 a) Correct absorption line spectrum that corresponds to the spectral curve on the right: C (0.5 marks) / 0.5 b) Explain why: The black absorption lines in the ‘visual spectrum’ C on left best correspond to the location and number of the absorption dips in the graphical spectrum on the right. (0.5 marks) 22. Visual and graphical spectra of 4 different objects [our sun (without its atmosphere), toaster oven filament, neon lamp, a green leaf] are shown below. Match each object with the right set of spectra to represent it. /1 a) Sun: A Toaster oven filament: C (0.25 mark per each correct identification) F-W 2013-14 Neon lamp: D Green Leaf: B Page 6 of 7 NATS 1870B: Understanding Colour Assignment 1: Light Part 1 The collection of spectra on the right show spectra from two unknown (mystery) gases at the top, and a catalogue of spectra from known elements below. For each of the two mystery gases, identify which element(s) is/are present in this mystery gas, and briefly explain how you determined your answer. Note: it may be helpful to print this page in colour, and cut out each catalogue spectrum separately. / 0.5 23 a) Element(s) present in Mystery Gas 1: Sodium (Na) (0.5 marks) b) Explain how you determined this: / 0.5 By carefully comparing the spectrum of the Mystery Gas 1 to each spectrum in the catalogue of gases, we find the best match – to the number of the bright emission lines and their locations/wavelengths – is found in the Sodium spectrum. (0.5 marks) Therefore, the mystery gas of the street lamp is sodium. / 0.5 24 a) Element(s) present in Mystery Gas 2: Helium AND Hydrogen (0.5 marks if both listed) / 0.5 b) Explain how you determined this: By following a similar procedure of trying to match up the emission lines in the spectrum of the Mystery Gas 2 to those of the known gases, we see that no one single spectrum will match this mystery gas perfectly… Helium is close but it is missing some lines – these lines come from the Hydrogen spectrum… so, Mystery Gas 2 is actually a combination of helium and hydrogen gases together. (0.5 marks) F-W 2013-14 Page 7 of 7

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Reading Quiz #1 What was Kepler’s main contribution to the study of optics and vision? Select one: a. A first complete description of the anatomy and function of the human eye. b. His famous laws of planetary motion. c. The idea that colours of the spectrum are tied to different periodic motions of some kind. d. First mathematical description of the law of refraction of light. Feedback The correct answer is: A first complete description of the anatomy and function of the human eye. Which of these was NOT part of an intromission theory of vision? Select one: a. Democritus’ thin films of atoms, released by objects. b. All of these were not intromission theories. c. Plato’s rays of vision remotely sensing external objects. d. Aristotle’s colours emitted by objects, passing through a transparent medium. Feedback The correct answer is: Plato’s rays of vision remotely sensing external objects. What was the role of the ‘transparent medium’ in Aristotle’s theory of vision? Select one: a. Colours of objects traveled through the transparent medium to enter our eyes. b. Rays of vision reached out from our eyes to external objects through the transparent medium. Online Course [2015] Page 1

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