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Topic: weird question  (Read 6634 times)

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Offline mugsy777

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weird question
« on: October 08, 2007, 03:08:31 PM »
you should be able to proof that the reduced mass of deutereum is approximately:
            me[1 - 0.5(me/mp) + 0.25(me/mp)^2 -...]

does anyone have any insight?

Offline Yggdrasil

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Re: weird question
« Reply #1 on: October 08, 2007, 08:13:50 PM »
This is a pretty tricky question.  Here's one hint: you'll need to make a Taylor expansion of the function 1/(1+x) where x is small.

Other than that hint, I'd say to start with a formula for the reduced mass of a two body system.

Offline mugsy777

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Re: weird question
« Reply #2 on: October 08, 2007, 08:17:08 PM »
those are exactly the two hints that I managed to figure out. I cannot get much farther due to my lack of mathematical insight when it comes to proofs  >:(

Offline mugsy777

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Re: weird question
« Reply #3 on: October 08, 2007, 08:20:37 PM »
I know that I need to apply the formula (1/1+x) * sum from n=0 to n=infinity (-1)^n*X^n
to the fraction (2mpme)/(2mp+me) but I am still not seeing the proof. I am sorry if I sound demented, or if I am wrong, I have been studying the entire weekend for an exam!

Offline Yggdrasil

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Re: weird question
« Reply #4 on: October 08, 2007, 10:06:00 PM »
You are very close to getting the right derivation.  Now, can you get 2mpme/(2mp+me) to look like 1/(1+x)?  (hint: factor out me first).  If so, what is x?  If you plug that into your formula for the Taylor expansion, you should get the right result.

Offline mugsy777

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Re: weird question
« Reply #5 on: October 08, 2007, 11:10:45 PM »
 :'(

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