Chapter 2

Calculate the average density of a single Al-27 atom by assuming that it is a sphere with a radius of \(0.143 \mathrm{~nm}\). The masses of a proton, electron, and neutron are \(1.6726 \times 10^{-24} \mathrm{~g}, 9.1094 \times 10^{-28} \mathrm{~g}\), and \(1.6749 \times 10^{-24} \mathrm{~g}\), respectively. The volume of a sphere is \(4 \pi r^{3} / 3\), where \(r\) is its radius. Express the answer in grams per cubic centimeter. The density of aluminum is found experimentally to be \(2.70 \mathrm{~g} / \mathrm{cm}^{3} .\) What does that suggest about the packing of aluminum atoms in the metal?

Each time you inhale, you take in about \(500 \mathrm{~mL}\) (two significant figures) of air, each milliliter of which contains \(2.5 \times 10^{19}\) molecules. In delivering the Gettysburg Address, Abraham Lincoln is estimated to have inhaled about 200 times. (a) How many molecules did Lincoln take in? (b) In the entire atmosphere, there are about \(1.1 \times 10^{44}\) molecules. What fraction of the molecules in the earth's atmosphere was inhaled by Lincoln at Gettysburg? (c) In the next breath that you take, how many molecules were inhaled by Lincoln at Gettysburg?