# Confused (supposedly easy chem question: volume, density)

1. Aug 11, 2008

### uchihajeff

This doesn't seem like it should be too hard, but i'm stuck... Am i making a stupid mistake somewhere?

1. The density of potassium metal is 0.89 g/cm3. Potassium's atomic radius is 231 pm. Assuming that r nuc = 10^-4 x r atom, estimate the density of an essentially spherical 39K nucleus.

2. Relevant equations
Volume of a sphere

3. The attempt at a solution
Convert pm to cm: 231 pm = 2.31E-8 cm

Find number of grams in the whole atom by finding the volume of the atom and mulitplying it by the density: (4/3)(pi)(2.31E-8)^3 * .89 = 4.5953E-23 g

Radius of nucleus = 1E-4 * 2.31E-8 cm = 2.31E-12 cm

Volume of nucleus = (4/3)(pi)((2.31E-12)^3) = 5.1632666E-35

Find density by: 4.5953E-23/5.1632666E-35 = 8.899E11 g/cm^3

Unfortunately, that doesn't match with the answer given: The answer given is 1.26E12 g/cm^3
Thanks for any help.

Last edited: Aug 11, 2008
2. Aug 12, 2008

### lewdtenant

there is something wrong.

the "answer" * the volume of nucleus is larger than the total mass of the atom. this can't be.

3. Aug 12, 2008

### HallsofIvy

Staff Emeritus
That makes no sense! "Volume" and "mass" are not comparable. It makes no sense to say one is larger than the other!

4. Aug 12, 2008

### lewdtenant

I'm sorry, let me clarify. the supposed answer (which is a density) multiplied by the volume of nucleus is larger than the total mass of the atom.

density times volume gives mass.

5. Aug 12, 2008

### Ygggdrasil

Spheres cannot be packed together w/o leaving empty space, so it's wrong to assume the density of potassium metal is equal to the density of a potassium atom. To get the mass of a 39K atom, just convert 39 amu to grams.