Chemical Forums
Chemistry Forums for Students => Physical Chemistry Forum => Topic started by: mugsy777 on October 08, 2007, 03:08:31 PM
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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?
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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.
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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 >:(
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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!
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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.
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:'(