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Center of mass of molecules

  1. Oct 23, 2012 #1
    1. The problem statement, all variables and given/known data

    NH3 (ammonia) that is shown in the picture. These three hydrogen-atoms is formed as triangle.
    Center of the triangle has a distance d = 0.940 from each hydrogen atom.
    The nitrogen atom located in the vertex of a pyramid in which the three hydrogens defines "the base". Vertex is vertically above the center of the triangle. The ratio of the atomic masses of nitrogen and hydrogen is MN/MH = 13.9 and nitrogen-hydrogen length is L = 1.014.

    Data:

    d = 0.940
    MN/MH = 13.9
    L = 1.014

    picture of the situation: https://www.dropbox.com/s/ruakers7j0zgg1w/Photo%2023.10.12%2020%2054%2019.jpg




    2. Relevant equations

    Determine the x-and y-coordinate of the molecule center of mass ?
     
    Last edited: Oct 23, 2012
  2. jcsd
  3. Oct 23, 2012 #2

    tiny-tim

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    welcome to pf!

    hi evenmu! welcome to pf! :smile:
    the centre of mass is obviously on that "vertical" line marked y

    what proportion of the way along the line is it?

    and how long is that line? :wink:
     
  4. Oct 24, 2012 #3
    So, you mean that I can treat this as a right-angled triangle and find the center of mass from that ?


    righttri.gif
     
  5. Oct 24, 2012 #4

    tiny-tim

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    no, i mean that you can treat this as a straight line,

    and find the center of mass as if the three hydrogen atoms were all together at one end :wink:
     
  6. Oct 24, 2012 #5
    Okay i se it now, but i still need to find the length of the y-axis,
    and to find it, i need to treat it like a triangle. Pluss the mass of these hydrogen will alsow be
    multiplied by 3 if they goes together.

    Am I on the right path here?
     
  7. Oct 24, 2012 #6

    tiny-tim

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    yup! :smile:

    (and you can get the length from pythagoras :wink:)
     
  8. Oct 24, 2012 #7
    One more thing :)

    The ratio of mass, is it the same mass for the Nitrogen and Hydrogen atoms ?
    Bothe uses the same mass (MN/MH = 13.9) ?
     
  9. Oct 24, 2012 #8

    tiny-tim

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    sorry, not following you :redface:
     
  10. Oct 24, 2012 #9
    The Equation for Center of mass is:


    XCM = 1/M Ʃ mi*xi

    YCM = 1/M Ʃ mi*yi

    What is the mass for hydrogen and nitrogen ?

    In the problem it says: The ratio of the atomic masses of nitrogen and hydrogen is MN/MH = 13.9 ?

    How do I interpret this ?
     
  11. Oct 24, 2012 #10

    tiny-tim

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    to find the centre of mass, you only need the ratios of the masses,

    so put MN = 13.9 MH,

    you'll get a fraction with MH on top and bottom, so it'll cancel, leaving you just a number! :wink:
     
  12. Oct 24, 2012 #11


    Here is what I have done until now:


    L = 1.014m
    d= 0.940m

    (pytagoras)
    a =√(L2)-(d2) = 0.38m

    Then i set up the Ceter of mass for X- and Y-axis. Like this:

    XCM = 1/M (3*(MN/13.9)*(0.940m) + (13.9MH)*(0m)

    And the same for Y-axis.

    Is this right, or am I doing something wrong here?
     
  13. Oct 24, 2012 #12

    tiny-tim

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    fine so far :smile:

    (are you sure about the figures? that makes a very short fat molecule that looks nothing like the diagram)

    you needn't bother with the x and z coordinates …

    from symmetry, aren't they obviously 0 ?

    as to the y coordinate …

    yCM = 1/(MN + 3MH) [(MN)*(a) + (3MH)*(0m)]
     
  14. Oct 24, 2012 #13

    Yes i know, but its the exact same number that is on my homework task.

    I calculate YCM and got YCM = 0.31. Do you think that this answer is realistic, in relation to the drawing ?
     
  15. Oct 24, 2012 #14

    tiny-tim

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    let's see …

    a = .38, so it's roughly 14/(14+3) times .38, = .31 …

    yup, looks ok :smile:

    (but that's not metres, is it? :biggrin:)
     
  16. Oct 24, 2012 #15
  17. Oct 24, 2012 #16
    Can you explain way the X- and Z-axis is zero(0) ?
     
  18. Oct 24, 2012 #17

    tiny-tim

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    isn't it obvious from the diagram?

    the y axis is an axis of symmetry, so the centre of mass must lie on it :smile:

    (and the y axis is the line x = z = 0)
     
  19. Oct 26, 2012 #18


    I forgot to say, thank you very much for your help! :smile:
     
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