Calculating the Density of a Uranium Nucleus

In summary, the conversation is discussing the calculation of the density of a uranium atom's nucleus, with a diameter of 1.5 * 10 to the -14 and a mass of 4.0 * 10 to the -25. The formula for density is Mass/Volume, and the individual has calculated the volume using the formula for a sphere (V= \frac{4}{3}\pi r^3) but forgot to use the correct radius (r = 0.5D). After correcting this mistake, the correct volume is calculated to be 1.767 * 10^-42, resulting in a correct density of 2.264 * 10^17.
  • #1
mawalker
53
0
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.
 
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  • #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).
 
  • #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...
 
  • #4
When you cube something small it becomes even smaller.
 
  • #5
You should 1.8E-42 (i presume m^3). You've forgotten that r = 0.5D.
 
  • #6
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
i.e. [tex]V_{sphere}= \frac{\pi}{6} d^3 [/tex]
 
  • #8
thank you... i actually came up with 1.767 * 10^-42 as the volume... a really small number but it is correct.
 

Related to Calculating the Density of a Uranium Nucleus

1. What is the formula for calculating the density of a uranium nucleus?

The formula for calculating the density of a uranium nucleus is mass divided by volume. This can be written as D = m/V, where D is density, m is mass, and V is volume.

2. How do you measure the mass of a uranium nucleus?

The mass of a uranium nucleus can be measured using a mass spectrometer or by analyzing the radioactive decay of uranium atoms.

3. How do you determine the volume of a uranium nucleus?

The volume of a uranium nucleus can be estimated using the known average radius of a nucleus, which is approximately 1.2 x 10^-15 meters.

4. What is the typical density of a uranium nucleus?

The density of a uranium nucleus can vary, but on average it is about 2.2 x 10^17 kilograms per cubic meter.

5. How does the density of a uranium nucleus compare to other elements?

The density of a uranium nucleus is significantly higher than most other elements. For comparison, the density of lead, the densest naturally occurring element, is only about 1.1 x 10^13 kilograms per cubic meter.

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