Third exam review - And now for something really really...

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And now for something really really different!
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What about intensities of spectral lines? Part is intrinsic strength, part is how many molecules . The distribution of molecules over states depends on energy and temperature. The study of this is statistical mechanics (or the statistical thermodynamics subset). We will only study a bit of the matter necessary to get molecular or atomic state distributions at this time. This is called Boltzmann statistics. It excludes such things as the electrons in metals and liquid helium, but covers ordinary vibrations, rotations, and excited electronic states of atoms and molecules, even in solids and liquids. Consider a H.O. It has equal energy level spacings. Say we have 12 molecules and have 12 quanta of energy to distribute among them. At this point we must introduce a new concept: molecules are indistinguishable . You can’t tell them apart, so you can only tell how many, not which ones. Say I have three marbles, one red, one green, one blue, and put them into two piles, two in the left and one in the right . I can distinguish color and order in the piles, so I could have 6 ways of placing them. I first picked which color for the right pile (three choices) and for each of those remaining I choose the order in the left pile (2 ways): 2*3 = 6 1 2 3 4 5 6
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But if I can’t tell order inside a pile, there are only three ways of doing this: If all marbles are blue, it’s still the same, since I have three ways of choosing which marble to put in the right pile, but no choice for the other two: they go in the left pile, either order. Say I have n piles and m i indistinguishable objects in the ith pile. The number of ways of doing this is There are 77 ways of distributing 12 molecules into piles, each pile representing molecules with a fixed number of quanta in each molecule, and having a total energy of 12. For each of the 77 ways there are a number of ways of getting that distribution, according to the above formula. Here are the 77 ways: objects of number total the is where )! ( ! 1 1 M m m M n i i i n i = = = 1 or 2 or 3 or
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██ ██ █████ ________ 110880 ███ ███ ████ _________ 110880 ██ ██ ███ ████ _________ 83160 ████ ████ _________ 83160 ██ ██ ███ ███ _ ________ 83160 ██ ██ ██ █ ████ _________ 83160 ██ ███ ███ __ _______ 55440 ██ ███ ███ _ ________ 55440 ██ ████ _ _______ 47520 █████ ________ 47520 ███ ███ ███ ███ __________ 34650 ██ ██ ██ ██ ██ _ ██ ________ 33264 ██ ██ ██ ██ ███ __ _______ 33264 ██ ██ ██ ███ ___ ______ 27720 ██ ██ ██ ███ _ ________ 27720 ██ ██ ██ ██ _ _ _______ 27720 ████ _________ 27720 ██ █ ██ _ ██ ________ 23760 ██ ███ _ ________ 23760 ███ ███ ___ ______ 23760 ███ ███ ███ __________ 18480 ██ █ ██ █ ██ _ _________ 18480 ███
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This note was uploaded on 09/22/2011 for the course CHEM 222 taught by Professor Linda during the Spring '11 term at Edmonds Community College.

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Third exam review - And now for something really really...

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