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Chapter 21: Problem 13

The radius of a uranium- 235 nucleus is about \(7.0 \times\) \(10^{-3} \mathrm{pm} .\) Calculate the density of the nucleus in \(\mathrm{g} / \mathrm{cm}^{3}\). (Assume the atomic mass is 235 amu.)

Short Answer

Expert verified
The density of the uranium-235 nucleus is around \(2.3 \times 10^{17} \, g/cm^3\)

Step by step solution

01

Calculate The Volume of The Nucleus

Recall that the volume \(V\) of a sphere is given by the formula \(V = \frac{4}{3} \pi r^3\), where \(r\) is the radius. To calculate the volume of the nucleus, we substitute the given radius \(r = 7.0 \times 10^{-3} \, pm\) into this formula. Note that since density will be calculated in grams per cubic centimeter (g/cm³), we need to convert picometer (pm) to cm: \(1 pm = 10^{-12} \, cm\). So, \(r = 7.0 \times 10^{-15} \, cm\). Now, calculate for \(V\)
02

Convert Atomic Mass to Grams

We know that 1 amu (atomic mass unit) is approximately equal to \(1.66 \times 10^{-24} \, grams\). So, the mass of uranium-235 in grams will be: \(235 amu \times 1.66 \times 10^{-24} \, g/amu\)
03

Calculate The Density of The Nucleus

Now we can calculate the density (\(\rho\)) of the nucleus using the formula: \(\rho = \frac{Mass}{Volume}\). Substitute the calculated values for volume and mass to find the density of nucleus.

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