Worksheet Boltzmann Distribution Applications

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University of Illinois, Chicago *

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260

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Physics

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Dec 6, 2023

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pdf

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7

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5/7/2021 Review Test Submission: Worksheet: Boltzmann Distribution ... https://uic.blackboard.com/webapps/assessment/review/review.jsp?attempt_id=_49252015_1&course_id=_193694_1&content_id=_8526424_1&outco… 1/7 Review Test Submission: Worksheet: Boltzmann Distribution Applications PHYS 260 Intro Thermal Physics (41588) 2021 Spring Weekly Content Week 9 begins Monday, March 8 Review Test Submission: Worksheet: Boltzmann Distribution Applications User Yacoub Awimrin Course PHYS 260 Intro Thermal Physics (41588) 2021 Spring Test Worksheet: Boltzmann Distribution Applications Started 3/8/21 8:42 PM Submitted 3/14/21 6:11 PM Status Completed Attempt Score 43 out of 55 points Time Elapsed 140 hours, 28 minutes Instructions Results Displayed All Answers, Submitted Answers, Correct Answers, Feedback, Incorrectly Answered Questions Units : Include units in your answer when instructed. Use SI units only in your answers. For example, use Pascals not atmospheres. Numbers : Use either the normal form, such as 132 or 132.5, or the exponential form, which represents 132 as 1.32E+2, represents 5 x 10 4 as 5E+4 or 5E4, or represents 52 x 10 -3 as 5.2E-2, unless instructed otherwise. Do not use the form 5 x 10 4 . If your answer is positive, do not place a "+" sign before your answer. Repeat Once : You can do worksheets twice before the due date. After submitting the ±rst time, click the OK on the bottom right of the page and you will be informed of your total score and which questions were answered incorrectly (during a one- time view, so you might want to take a screen-shot for future reference). Accept the score or redo the entire worksheet. Your highest score will be recorded. Answers and feedback to all problems will be available after the due date and can be accessed within My Grades. Question 1 Selected Answers: d. e. A harmonic oscillator with energy levels ε is in equilibrium with a reservoir at temperature T . Choose the correct statements below. The ground state has the highest probability of being occupied, independent of the temperature. If kT << ε , only the ground state is occupied. 5 out of 5 points
5/7/2021 Review Test Submission: Worksheet: Boltzmann Distribution ... https://uic.blackboard.com/webapps/assessment/review/review.jsp?attempt_id=_49252015_1&course_id=_193694_1&content_id=_8526424_1&outco… 2/7 Answers: a. b. c. d. e. Response Feedback: If kT >> ε , higher energy states are preferentially occupied over lower energy states. If kT >> ε , all states will be equally occupied. If kT = 2 ε , only the second excited state is occupied. The ground state has the highest probability of being occupied, independent of the temperature. If kT << ε , only the ground state is occupied. The ground state has the highest probability of being occupied. As the temperature is increased above kT = ε , the probability of occupying higher energy states increases. Question 2 Selected Answer: 0.932 Correct Answer: 0.932 ± 1% A molecule has states with the following energies: 0, 1 ε , 2 ε , 3 ε , and 4 ε , where ε = 0.9 x 10 -20 J. Calculate the probability of molecules in the ground state (with zero energy) for a collection of molecules in thermal equilibrium at T = 242 K. Provide your answer as a number in normal form to 3 decimal places (in the form X.XXX). Hint: note that this molecule has a ±nite number of states so you must take a ±nite sum, not the expressions discussed in the video for in±nite sums. Question 3 Selected Answer: 0.149 Correct Answer: 149 ± 5% Response Feedback: A molecule has states with the following energies: 0, 1 ε , 2 ε , 3 ε , and 4 ε , where ε = 0.5 x 10 -20 J. Calculate the average number of molecules in the ±rst excited state (1 ε ) for a collection of 1000 molecules in thermal equilibrium at T = 213 K. Note that the average number of molecules in a state is just the probability of the state times the number of molecules. Provide your answer as a number in normal form. An example calculation for T = 300 K and ε = 1 x 10 -20 J: 6 out of 6 points 0 out of 6 points
5/7/2021 Review Test Submission: Worksheet: Boltzmann Distribution ... https://uic.blackboard.com/webapps/assessment/review/review.jsp?attempt_id=_49252015_1&course_id=_193694_1&content_id=_8526424_1&outco… 3/7 If there are a 1000 molecules, then the average number in the ±rst excited state is 0.081 * 1000 = 81. Question 4 Selected Answer: 0.424 Correct Answer: 0.297 ± 2% Response Feedback: A molecule has states with the following energies: 0, 1 ε , 2 ε , where ε = 0.4 x 10 -20 J. Calculate the average energy of this molecule in thermal equilibrium at T = 215 K. Provide your answer in units of ε . In other words, your solution should have the form of (number) ε , such as 2.137 ε , but the answer that you enter is just 2.137, a number in normal form with 3 decimal places (X.XXX). An example calculation for T = 300 K and ε = 1 x 10 -20 J: 0 out of 6 points
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