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/