General Chemistry

Question

An atom has a diameter of 4.50 Å and the nucleus of that atom has a diameter of 9.00 x 10^-5 A. Determine the fraction of the

volume of the atom that is taken up by the nucleus. Assume the atom and the nucleus are a sphere.

fraction of atomic volume:

Calculate the density of a proton, given that the mass of a proton is 1.0073 amu and the diameter of a proton is

1.70 x 10-15 m.

density:

Answer 1

Hello, Zoe,

This is a pesky, but interesting calculation. I summarized everything in a table. I'll describe the basic steps.

Volume of a sphere is (4/3)(pi)r³. Find the radius, r, of both the atom and it's nucleus, in cubic Angstoms, A³. Use this r in the volume formula. I got volumes of 47.7 and 3,8x10^-13 A³, for the atom and nucleus, respectively. Dividing the nuceus volume by the total volume gives a crazy, but true, number: 8x10^-15. Wow, I hope my calculation is correct. The point is that an atom is largely empty space. When you sit on a chair, it is mostly emptiness. The elecrostatic forces within the atoms keep them together, and you upright. They are also the basis of chemical bonding and nuclear reactions.

diameter radius Volume

Atom 4.5A 2.25A 47.71A³

Nucleus 9x10^-5A 4.5x10^-5A 3.8x10^-13A³

Fraction (Nucleus Vol/Atom Vol) = 8x10^-15

Proton 1.7x10^-15m 8.5x10^-16m 2.65x10^-45m³

^

Proton Density 1.0073amu/2.65x10^-45m³ = 3.9x10⁴⁴amu/m³

Similar steps are taken to calculate density. The problem does not specify what units are desired, so I took the lazy route, amu/m³. Wow - a cubic meter of packed protons would have a mass of 3.9x10⁴⁴ grams. One can start to understand the enormity of stellar events in which matter is compressed into tight spaces (e.g., neutron stars, black holes). The density creates very high gravitational fields.

Please check my numbers, but the process should be valid,

Bob