67. Physicists, mathematicians, and others often deal with large numbers. The number $10^{100}$ has been given the whimsical name googol by mathematicians. Let us compare some large numbers in by mathematicians. Let us compare some large numbers in physics with the googol

 67. Physicists, mathematicians, and others often deal with large numbers. The number $10^{100}$ has been given the whimsical name googol by mathematicians. Let us compare some large numbers in by mathematicians. Let us compare some large numbers in physics with the googol. (Note: This problem requires numerical values that you can find in the appendices of the book, with which you should become familiar.) Approximately how many atoms make up our planet? For simplicity, assume the average atomic mass of the atoms is $14 \mathrm{~g} / \mathrm{mol}$ Avogadro's number gives the number of atoms in a mole. (b) Approximately bow many neutrons are in a neutron star? Neutron stars are composed almost entirely of neutrons and have approximately twice the mass of the sun. (c) In the leading theory of the origin of the universe, the entire universe that we can now observe occupied, at a very early time, a sphere whose radius was approximately equal to the present distance of the earth to the sun. At that time the universe had a density (mass divided by volume) of $10^{15} \mathrm{~g} / \mathrm{cm}^{3}$. Assuming that one-third of the particles were protons, one-third of the particles were neutrons, and the remaining one-third were electrons, how many particles then made up the universe?