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Nucleus density

  1. Nov 8, 2006 #1
    this seems like a fairly simple problem, however i'm not sure if my calculation seems right....

    the question:
    The nucleus of a uranium atom has a diameter of 1.5 * 10 to the -14 and a mass of 4.0 * 10 to the -25.

    It then asks what the density of the nucleus is.

    I know that nucleus density is Mass/Volume, and I calculated the volume to be the radius (.5(1.5 * 10 to the -14)) squared times pi. this gave me 1.76 * 10 to the -28. So am i correct with an answer of 4.0 * 10 to the -25 / 1.76 * 10 to the -28? or am i going about this problem wrong? please help.
     
  2. jcsd
  3. Nov 8, 2006 #2
    The volume of a sphere is [tex]V= \frac{4}{3}\pi r^3 [/tex] volume must have the units of length cubed. What you have calculated is the area of a circle (cross section of the sphere).
     
  4. Nov 8, 2006 #3
    ahh, that makes sense... but that still doesn't seem right for some reason. that yielded me 1.4137 * 10 to the -41 for the volume.....
     
  5. Nov 8, 2006 #4

    quasar987

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    When you cube someting small it becomes even smaller.
     
  6. Nov 8, 2006 #5
    You should 1.8E-42 (i presume m^3). You've forgotten that r = 0.5D.
     
  7. Nov 8, 2006 #6

    quasar987

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    For instance (1/2)³ is of half of one half of one half. That's 1/8, which is smaller than 1/2.
     
  8. Nov 8, 2006 #7

    Astronuc

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    i.e. [tex]V_{sphere}= \frac{\pi}{6} d^3 [/tex]
     
  9. Nov 8, 2006 #8
    thank you... i actually came up with 1.767 * 10^-42 as the volume... a really small number but it is correct.
     
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