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Fall 07 Phys 143l HW 9 Solutions

Fall 07 phys 143l hw 9 solutions

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Unformatted text preview: Physics 143 Fall Term 2007 HOMEWORK 9 Due: November 12 Problem 1: (BFG Ch.9 Problem 9) Use Eq.(9-37) to evaluate the frequency of the light emitted in a transition between two states: Assume Z=1(Hydrogen) Eq. 937 E Transition from n=2, l=1 to n=1, l=0 state: E 1 1 m c n 2 1 m c 2 13.6eV 1 2 1 1 10.2eV E 2.5 10 Hz We have one electron and one proton, so the reduce mass is: m m 1836 m 0.9995m 1836 1 m m Notice that E m. Therefore the correction is only E E m ~ 0.5 E m which means using m in Eq. 937 is sometimes precise enough. Problem 2: (BFG Ch.9 Problem 11) Find the <r2> for the ground state of hydrogen. Compare your result with <r>2 for the same state. The ground state of hydrogen: x Therefore the average values are: r 4a | x | r r e x e (The integral R 2a / e / r dr dr 3a dx can be found in some integral tables or you can just integrate by parts) r 4a | x | r r dr r e x e dx dr a (Notice of that both integral have the geometrical/integral/Jacobi factor ) P a g e | 13 r And the spread of r r 3a r r r 2.25a 0 Problem 3: (BFG Ch.8 Problem 22) T...
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