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    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!
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    mass of electron= 1/1836 or in most a-level books 1/2000 of the mass of proton
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    That doesn't explain where 1800me / 1800 + mn comes from
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    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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