Problem Set 7

# Problem Set 7 - Physics 341 Problem Set#7 due October 28...

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Physics 341: Problem Set #7 due October 28 You are encouraged to work in groups on these problems, but each student must write up the solutions individually. You must also list your collaborators on your solutions, and cite any external sources you used (other than the course notes or textbook). I will give partial credit for partial answers, but only if you show your work and explain your reasoning. Be careful with units. 1. Recall that the surface brightness of an exponential disk has the form I ( R )= I 0 e - R/h R where I 0 is the central surface brightness and h R is the disk scale length. The total brightness is given by integrating this proFle from R = 0 to R = 1 : I total = Z 1 0 I ( R )2 RdR (a) Show that the total brightness of the exponential disk is I total =2 I 0 h 2 R Show your work! Hint: Let x = R/h R and rewrite the integral in terms of x and dx . Note that from integration by parts, R xe - x dx = - ( x +1) e - x plus a constant. (b) What fraction of the total light is within one disk scale length (

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Problem Set 7 - Physics 341 Problem Set#7 due October 28...

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