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Homework #11: Due Friday November 7 by 5:30pm.
That's all for homework #11.
- Evaluate the following integral by hand (i.e., you can not just look it up in a table of integrals, or have Maple or Mathematica to do it) using the Gamma Function Γ(z) technique that I showed you in class. Refer to Appendix B.2 in your book for a refresher on the Gamma function.
Show all of your steps here. 'a' is a constant that makes the argument of the exponential unitless. Note that, while I'm assigning only one of these problems, you should be able to use this technique for many such problems.
- Calculate the quantity <v7> by hand showing all of your steps ('v' is the speed of a particle). Lack of steps=lack of credit for this problem. As with the problem above you should be able to do this for any value of the exponent. This will not be a number, but rather an expression with arbitrary values for the mass of the particle 'm,' and the temperature 'T.'
- Calculate (a) <v>, (b) <v2> and (c) comment upon whether the quantities <v>2 and <v2> are equal or not. Again, these expressions will not have numbers for the mass 'm' and temperature 'T.'
- Using Mathematica (or Maple...so yesterday) graph the Boltzmann distribution D(v) on one graph for the following temperatures: 300K, 1,000K, 3,000K, 6,000K, 10,000K, and (your age in days times your height in meters--list both of these on the graph). Turn in a hardcopy of your code and your graph. Note: While I do encourage people to assist each other on their homework, do not simply copy the code from the person assisting you (and the assist-or should not allow this either). Everyone will do things slightly differently, and no two codes will look the same.