More 0's in a Googolplex than Atoms on Earth?Date: 06/06/2001 at 16:19:56 From: Mark Kula Subject: Zeros in googolplex and atoms in the earth Is it true that there are more zeros in a googolplex than there are atoms in the earth? Date: 06/06/2001 at 17:07:44 From: Doctor Peterson Subject: Re: Zeros in googolplex and atoms in the earth Hi, Mark. What I've heard is that the googol (the number of zeros in a googolplex) is more than the number of PARTICLES in the UNIVERSE! But let's check out your more testable claim. I looked up the mass of the earth and found it to be about 6 * 10^27 grams. Let's pretend the earth is made up entirely of hydrogen atoms (since they are the lightest, so there would be more of those than the actual number of heavier atoms). One of them weighs about one atomic mass unit, or 1.66 * 10^-24 grams. So the number of atoms in the earth can be no more than 6 * 10^27 g/earth -------------------- = 3.6 * 10^51 atoms/earth 1.66 * 10^-24 g/atom That is far less than a googol - in fact, it's not much more than the square root of a googol. So if there were as many earths in the universe as there are atoms in the earth, the total number of atoms in the universe would be about a googol. Impressed? - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ Date: 06/06/2001 at 17:08:12 From: Doctor Rick Subject: Re: Zeros in googolplex and atoms in the earth Hi, Mark. Well, let's work it out... There are a googol zeros in a googolplex. That's 10^100 zeros. The mass of the earth is 5.972*10^24 kg, according to Nine Planets. http://seds.lpl.arizona.edu/nineplanets/nineplanets/earth.html Suppose the earth were made only of hydrogen atoms (the smallest possible, thus an overestimate of the number of atoms). The atomic mass of hydrogen is about 1, meaning that 6.02*10^23 (Avogadro's number) of atoms have a mass of about 1 gram. Thus it takes about 6* 10^26 atoms of hydrogen to make 1 kg. How do you find how many atoms of hydrogen it takes to make the mass of the earth? How does this figure compare with a googol? - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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