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# Lect12 - Le cture12 Examples and Problems 1.0 p(h/p(0 0.8...

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Lecture 12, p1 Lecture12 Examples and Problems 0 1 2 3 4 5 0.0 0.2 0.4 0.6 0.8 1.0 <h>=kT/mg mgh/kT p(h)/p(0)

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Lecture 12, p2 Midterm Exam Formula sheets: It has been pointed out that the formula sheet in the discussion problem book (dated Fall 2009) is not the same as the one in the Lecture Notes book (dated Fall 2010). The content is the same, but the layout is different. For exams, we will use the Fall 2010 (Lecture Notes) version. Exam rooms: Your exam room is determined by your discussion section. Go to the room indicated on the “Midterm Exam Rooms” web page: http://online.physics.uiuc.edu/courses/phys213/fall10/hexamrooms.html
Lecture 12, p3 Example: Boltzmann Factor A particular molecule has three states, with energy spacing ε = 10 -20 J , as shown; the molecule is in contact with the environment (reservoir), which has a temperature of 1000 K . 1 ) What is P 1 , the probability that the molecule is in the middle energy state? 2 ) What is P 2 , the probability that it is in the highest energy state? E ε ε E 2 E 1 E o

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Lecture 12, p4 Solution A particular molecule has three states, with energy spacing ε = 10 -20 J , as shown; the molecule is in contact with the environment (reservoir), which has a temperature of 1000 K . 1 ) What is P 1 , the probability that the molecule is in the middle energy state? 2 ) What is P 2 , the probability that it is in the highest energy state? E ε ε E 2 E 1 E o 1 / / 1 / 0 / / 2 / 0.725 0.725 1.45 0.485 0.282 1 1 0.485 0.235 n E kT kT E kT kT kT kT e e P e e e e e e e ε ε ε - - - - - - - - - = = + + = = = + + + + -20 23 3 10 J = 0.725 1.38 10 10 J kT ε - = × 2 0.235 0.137 1 0.485 0.235 P = = + + You can always pick E=0 at your convenience.
Lecture 12, p5 The magnetic moment of the electron is μ B = 9.28 × 10 -24 J/T . 1 ) At room temperature ( 300 K ), what magnetic field is required to make 2/3 of the electrons have their magnetic moments point along B (that’s the low energy state)? Note: This is called the “up” state. 2 ) What B is needed for 2/3 of the protons ( μ p = 1.41 × 10 -26 J/T ) to be that way? Exercise: Spin alignment

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Lecture 12, p6 The magnetic moment of the electron is μ B = 9.28 × 10 -24 J/T . 1 ) At room temperature ( 300 K ), what magnetic field is required to make 2/3 of the electrons have their magnetic moments point along B (that’s the low energy state)? Note: This is called the “up” state. 2 ) What B is needed for 2/3 of the protons ( μ p = 1.41 × 10 -26 J/T ) to be that way? Solution If you take ratios of probabilities, the normalization factor cancels.
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Lect12 - Le cture12 Examples and Problems 1.0 p(h/p(0 0.8...

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