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# Calculating Reduced Mass - Quick Question Watch

1. A question has asked I calculate the reduced mass of Helium.

I know the equation is

= me x mn / me + mn

mn being the mass of the atom. In this case mn = 4

In my notes it then jumps straight into

= 1800me / 1800 + mn

and I don't understand why! Can anyone explain this to me? Cheers!
2. mass of electron= 1/1836 or in most a-level books 1/2000 of the mass of proton
3. That doesn't explain where 1800me / 1800 + mn comes from
4. Figured it out:

1/1800 is the approximate mass of an electron; 1/1800th of the mass of a proton

Ratio...
mass of proton : mass of electron
1800 : 1

1) Helium has two protons in its nucleus.
2) Therefore if the mass of a Hyrogen atom is 1800me = mn, the mass of a Helium atom is...

1800me = 2mn
1800 x 2 me = mn
3600me = mn

3) Substitute mn = 3600me into the overall equation

= (me x 3600me) / (me + 3600me)
= (3600me)2 / (me + 3600me)

Since me + 3600me = 3601me in the same way that y + 3600y = 3601y

= (3600me)2 / 3601me

me on top and bottom cancel

= 3600me / 3601
=0.9997222994 me

4) Calculate reduced mass in kg

Substitute in the given value of me = 9.109x10-31 kg

=0.9997222994 x 9.109x10-31 kg
= 9.106 x 10-31 kg

=)

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Updated: December 15, 2010
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