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Desnity and Distibution

  1. Apr 19, 2008 #1

    TFM

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    [SOLVED] Desnity and Distibution

    1. The problem statement, all variables and given/known data

    I need to calculate the distance between particles. I know the density, and I know how many particles there are, but I am not sure how to calculate the distance between them.

    2. Relevant equations

    Not Sure

    3. The attempt at a solution

    Any advice would be greatly appreciated,

    TFM
     
  2. jcsd
  3. Apr 19, 2008 #2

    Hootenanny

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    Hi TFM,

    Could you please post the full question verbatim, as it is in your textbook/homework sheet.
     
  4. Apr 19, 2008 #3

    TFM

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    Assume that the sun is made of pure Hydrogen, and take the Hydrogen mass ass being 1.67x10^-27 kg. If the mean mass density of the sun is 1400 kg/m^3, what is the mean number density.

    I have calculated this to be 8.4 x 10^29 atoms per cubic meter

    hence estimate the typical inter-particle distance

    TFM
     
  5. Apr 19, 2008 #4

    Hootenanny

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    So you know that in one meter there is 8.4 x 10^29 hydrogen atoms. So what volume does each atom occupy? Next, assume that each hydrogen atom is a particle at the centre of a sphere.
     
    Last edited: Apr 19, 2008
  6. Apr 19, 2008 #5

    TFM

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    Each Hydrogen Atom will occupy a volume of [tex]\frac{1}{8.4X10^{29}}[/tex] which is [tex]1.19 x 10^{-30}[/tex] metres cubed

    TFM
     
  7. Apr 19, 2008 #6

    Hootenanny

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    Correct, so what is the radius of the sphere with such a volume?
     
  8. Apr 19, 2008 #7

    TFM

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    Volume of a sphere: [tex]Vol = \frac{4}{3}\pi r^{3}[/tex]

    So [tex] 1.19x10^{-30} = \frac{4}{3} \pi r^{3} [/tex]

    so the radius is [tex]r = \sqrt[3]{\frac{3*Vol}{4* \pi }}[/tex]

    Giving the radius: [tex]\sqrt[3]{2.84*10^{-31}}[/tex] = 6.57*10^-11 metres Cubed

    TFM
     
  9. Apr 19, 2008 #8

    Hootenanny

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    Spot on, but watch your units :wink:
     
  10. Apr 19, 2008 #9

    TFM

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    Do I now just have to take away the radius of a Hydrogen Atom?

    TFM
     
  11. Apr 19, 2008 #10

    Hootenanny

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    Personally, I would have left the answer as it is since once you get down to such small distances the concept of classical radii doesn't really apply. However, you could put both answers to be safe, it depends very much on what your tutor wants.
     
    Last edited: Apr 19, 2008
  12. Apr 19, 2008 #11

    TFM

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    Well, the question then asks you to compareit to the radius of a Hydrogen Atom and a Hydrogen Nuclei.

    TFM
     
  13. Apr 19, 2008 #12

    Hootenanny

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    Then I definitely would subtract the hydrogen radius from your answer.
     
  14. Apr 19, 2008 #13

    TFM

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    Thanks foy all your assistance, Hootenanny :smile:

    TFM
     
  15. Apr 19, 2008 #14

    Hootenanny

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    It was a pleasure TFM :smile:
     
  16. Apr 19, 2008 #15
    Is the typical distance between 2 atoms not twice the radius of this sphere? First from one atom to where the spheres meet, then to the other atom.
     
  17. Apr 19, 2008 #16

    Hootenanny

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    Indeed it is, I assumed that TFM would have realised that.
     
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