Nucleus density

  • Thread starter mawalker
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  • #1
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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.
 

Answers and Replies

  • #2
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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).
 
  • #3
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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.....
 
  • #4
quasar987
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When you cube someting small it becomes even smaller.
 
  • #5
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You should 1.8E-42 (i presume m^3). You've forgotten that r = 0.5D.
 
  • #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.
 
  • #7
Astronuc
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i.e. [tex]V_{sphere}= \frac{\pi}{6} d^3 [/tex]
 
  • #8
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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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