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# HW3_key - HW3_chapter 18 18-3 Q Show that 2 mkBT qtrans(a T...

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HW3_chapter 18: 18-3: Q. Show that 1/2 2 2 ( , ) B trans mk T q a T a h    in one dimension and that 2 2 2 ( , ) B trans mk T q a T a h in two dimensions. Use these results to show that trans has a contribution of /2 B kT to its total value for each dimension. A. Remember that 2 1/2 0 4 n e dn . Then, for one dimension, 2 2 2 1/2 /8 2 0 2 ( , ) h n ma B trans mk T q a T e dn a h  And for two dimensions, 2 2 2 2 /8 2 2 0 2 ( , ) h n ma B trans mk T q a T e dn a h Now 2 ln trans trans B V q T The partition function is proportional to n T , where n is the dimension, so ln 2 trans V q n TT and 2 22 B trans B nk T n T . 18-5: Q. Using the data in Table 18.1, evaluate the fraction of lithium atoms in the first excited state at 300K, 1000K, and 2000K.

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A. We can use the second line of Equation 18.10 to calculate the fraction of lithium atoms in the first excited state, with g e1 = 2, g e2 = 2, g e3 = 4, and g e4 = 2: 2 234 2 2 2 2 4 2 ... e e e e e f e e e  Using the data in Table 8.6, we find that the numerator of this fraction is
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HW3_key - HW3_chapter 18 18-3 Q Show that 2 mkBT qtrans(a T...

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