Starting with the number two, multiply it by itself, then take that number and multiply itself, etc, etc.
It's been said that if a computer counted a million atoms a second that it would take billions of years to count the amount of atoms in a gram of any element. Could you count the amount of atoms this way in a year maybe?

This is to show you how large Avogadro's number really is.
Sixty seconds in a minute, sixty minutes in an hour, 24 hours in a day, 365.25 days in a year equals, call it 3.16 x 10^7 seconds. So it will take only 2 x 10^16 years. I don't think I'll wait!

I'm not sure what you're looking for, but I'm taking your "take a number, multiply it by itself, take that result and multiply it by itself again and again".


The number of atoms counted after t seconds will be:

2^{2^t}

Check it. After 2 seconds, we have (2x2) = 4
Then multiply that by itself, giving 16.

2^{2^2} = 16

3 seconds, 16x16 = 256

2^{2^3}= 256

4 seconds 256 x 256 = 65536

2^{2^4} = 65536

Ok, the equation is good.

In 1 gram of H atoms, there are 6.02x10^23 atoms.

6.02\times10^{23} = 2^{2^t}

2^t = 78.99

t = 6.30

Hmm, it takes only 6.3 seconds :rolleyes:

And the larger you get, the less number of atoms you have...


Now, taking a million atoms a second, you will have \frac{6.02\times10^{23}}{1\times10^6} = 6.02 \times 10^{17} s \approx 2\times10^{16} years